ALBERT

Beschreibung: A multiscale strategy is developed for the thermo-elastic plastic stress analysis of heterogeneous multiphase materials. The strategy is based on the extended multiscale finite element method (EMsFEM) and the enriched partition of unity approach. In the formulation, the enriched numerical base functions are adapted into the EMsFEM, which show good applicability to the local deformation pattern. Thus, the microscopic variable fields can be reproduced precisely, which are crucial for the nonlinear analysis. Numerical examples of two-phase heterogeneous media with regular and irregular microstructures demonstrate the validity and efficiency of the proposed method.

Beschreibung: The smooth orthogonal decomposition (SOD) method is one of the output only modal analysis methods, which is originally suggested for the undamped/lightly damped systems. In this paper, the error sources of the SOD method for damped vibrating systems have been investigated. Then, in order to improve the accuracy of SOD for modal analysis of damped systems, some modifications have been made on the traditional SOD algorithm, and instead of the forward two-point differential operator D , the central eight-point differential operator D m is used. In order to compare the accuracy of improved SOD and traditional SOD, the two methods are applied for vibration analysis of a discrete system subjected to the random white noise with the same excitation arrangement. The estimated results are compared with the exact solution obtained by the structural eigenvalue problem. The comparison reveals that the improved SOD is more accurate than the traditional SOD method. In addition, the effects of the excitation arrangement and the measurement noise on the estimated modal parameters are investigated.

Beschreibung: Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box ( p -box) model. Although tremendous efforts have been devoted to propagating random or p -box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.

Beschreibung: This paper deals with the combined effect of pressure and geometric imperfection on buckling of stressed thin films on a semi-infinite rigid substrate. Analytical approximate solutions are proposed by using the total potential energy of the system and the Rayleigh–Ritz’s method, and their stabilities are also determined. The present analytical approximate solutions agree very well with the numerical solutions obtained via the improved shooting method. The effect of pressure mismatch together with imperfection on the critical stress (above which the film buckles) and on the film-center deflection is characterized. It is found that, compared with the classical case of the Euler column buckling, the equilibrium solutions and critical stress of the film are strongly dependent on the linear combination of the pressure mismatch and imperfection amplitude.

Beschreibung: Because of the production process and constraint conditions, a circular graphene sheet may be opposed to structural defect and pin hole, respectively. Some of the defects and pin hole on a circular graphene sheet can be considered as an eccentric hole. So, analyzing the behavior of a circular graphene sheet with an eccentric hole is important. Free vibration of an eccentric annular graphene sheet, as the basis of any dynamical analysis, is analytically studied in this paper. Nonlocal thin plate theory is used to model the problem. The translational addition theorem for cylindrical vector wave functions is employed to solve the equation of motion for various boundary conditions. Results are compared with the literature, and their accuracy is approved. Effects of boundary conditions, geometrical properties and nonlocal parameter changes on symmetric and antisymmetric vibrational modes are investigated. It is approved that the eccentricity has a significant effect on the natural frequencies. Also, symmetric and antisymmetric modes of an annular graphene sheet have different behavior when geometrical and nonlocal parameters change.

Beschreibung: Solutions are offered for a cylindrically orthotropic circular tube of finite length with radial inhomogeneity and subjected to torsional shear loads, and the end effects are emphasized in this study. By explicit expressions of the shear stresses, the actual stress distributions all over the body can be thoroughly examined. The concept of end effect coordinates is introduced to estimate the extent of an end effect when the trends and features are explored. According to the examples, when considering end surfaces subjected to a power-distributed shear load or a tangential ring shear load, the extent of an end effect is strongly dependent on material anisotropy. In general, for a given material anisotropy, variations of the longitudinal shear stress and transverse shear stress reveal different trends along the radial coordinate. The end effect extent of the longitudinal shear stress is larger on the cylindrical surfaces than inside the body, and it is larger on the inner surface than on the outer surface. Furthermore, while no end effects in the transverse shear stress are detected on both the inner and outer cylindrical surfaces, we cannot ignore them inside the tube body.

Beschreibung: A numerically efficient laminated composite beam element subjected to a variable axial force is presented for a coupled stability analysis. The analytical technique is used to present the thin-walled laminated composite beam theory considering the transverse shear and the restrained warping-induced shear deformation based on an orthogonal Cartesian coordinate system. The elastic strain energy and the potential energy due to the variable axial force are introduced. The equilibrium equations are derived from the energy principle, and explicit expressions for the displacement parameters are presented using the power series expansions of displacement components. Finally, the member stiffness matrix is determined using the force–displacement relations. In order to verify accuracy and efficiency of the beam element developed in this study, numerical results are presented and compared with results from other researchers and the finite beam element results, and the detailed finite shell element analysis results using ABAQUS; especially, the influence of variable axial forces, the fiber orientation, and boundary conditions on the buckling behavior of the laminated composite beams is parametrically investigated.

Beschreibung: It is well known that the specimen preparation method and the resulting sand fabric significantly affect sand behavior and sand liquefaction resistance. In many cases, the fabric and behavior of reconstituted sand samples do not represent those of in-situ deposits. Therefore, understanding the influence of specimen preparation and sand fabric on its behavior, particularly at the critical state, is important for relating the behavior of laboratory reconstituted specimens to in-situ soil response. In this study, the effect of sand fabric and specimen preparation method on the shearing behavior of sand is studied using triaxial shear tests. Dry funnel pluviation (DFP) and wet tamping (WT) are used to prepare the specimens. The results from instability lines and stress–strain curves indicate that the liquefaction resistance of specimens prepared with the DFP method is more than specimens reconstituted by the WT method.

Beschreibung: New exact solutions for isotropic Kirchhoff plates, with no kinematic boundary constraints, are inferred by an analogy with the cross-section warping of orthotropic, homogeneous Saint-Venant beams bent and twisted by a shear force. The procedure is based on a formal equivalence between the elastic equilibrium conditions, respectively, for the tangential stresses in terms of a warping function in a Saint-Venant beam and for the bending–twisting moment in a Kirchhoff plate. The analysis refers to simply or multiply connected plates with an isotropic elastic stiffness proportional to the beams warping function. The result extends the one provided by the author for the special case of simple torsion ( Barretta , Acta Mech 224(12):2955–2964, 2013 ). An example for a circular plate is developed, thus providing a new benchmark for computational mechanics.

Beschreibung: The interface energy theory developed by Huang et al. is further extended to incorporate the effect of the residual interface stresses on the effective specific heats of multiphase thermoelastic nanocomposites. First, a micromechanics-based method is employed to derive the expressions of the effective specific heats at constant-strain and constant-stress of the composites. Second, in order to take into account the influence of the interface stresses on the overall properties of the nanocomposites, a thermoelastic interface constitutive relation expressed in terms of the first Piola–Kirchhoff interface stresses and the Lagrangian description of the generalized Young–Laplace equations are presented. Finally, by means of the Helmholtz free energy of the “equivalent inclusion” (the inclusion together with its interface), analytical expressions of the size-dependent effective specific heats of the nanocomposites are obtained. The model is illustrated by an example of a “three-phase thermoelastic composite” showing that the overall properties of the nanocomposites are influenced by the “residual interface stresses,” which was sometimes ignored in the literature.

Beschreibung: A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.

Beschreibung: This paper presents the study on natural frequency characteristics of a thin-walled functionally graded material (FGM) cylindrical shell with rings support under symmetric uniform interior pressure distribution. The FGM properties are graded along the thickness direction of the shell. The FGM shell equations with rings support and interior pressure are established based on first-order shear deformation theory. The governing equations of motion were employed, using energy functional and by applying the Ritz method. Ten boundary conditions represented by end conditions of the FGM shell are the following: simply supported-simply supported, clamped-clamped, free-free, clamped-free, clamped-simply supported, free-simply supported, sliding-sliding, sliding-simply supported, sliding-free and sliding-clamped. This problem was solved with computer programming using MAPLE package for numerical investigation. Comparison of the results is carried out to verify the validity of the proposed procedure with published works. The influence of interior pressure, ring support position and number of rings support, and effect of the ten boundary conditions on natural frequency characteristics are studied. The results presented can be used as an important benchmark for researchers to validate their numerical methods when studying natural frequencies of shells with ring and pressure.

Beschreibung: Mechanical behavior of filled rubber is very different from the corresponding unfilled gum rubber. To understand such difference, a multiscale material model of a filled rubber, which combines molecular mechanics, statistical mechanics and micromechanics, has been developed. The model has been used to explore how filler particles and filler–elastomer bond strength influence the overall elastic properties of a filled rubber. The model confirmed the well-established phenomena such as non-uniform strain amplification, but now, the model added much more detailed molecular information such as cross-linking density, bond strength at filler–elastomer interface, etc. to the whole phenomena. This capability enables us to investigate the influences of the factors on the overall mechanical properties of filled rubber. The results revealed that the degree of stretching is significantly amplified in elastomer chains that locate in between the filler particles along the loading direction. The degree of non-uniform stretching increases with filler volume fraction. The fully stretched elastomer chains contribute significantly greater force and stiffness than those that are stretched less. Both the Mullins effect and the Payne effect come from the non-uniform filler size and/or spatial distribution. Reducing non-uniformity of filler size and spatial distribution can decrease the degree of the Mullins effect and the Payne effect. Improving bond strength at filler–elastomer interface can delay the Mullins effect and the Payne effect but cannot eliminate them.

Beschreibung: This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Kármán-type equation for the geometric nonlinearity, the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions.

Beschreibung: Homogenization methods utilizing classical elasticity-based Eshelby tensors cannot capture the particle size effect experimentally observed in particle–matrix composites at the micron and nanometer scales. In this paper, a new homogenization method for predicting effective elastic properties of multiphase composites is developed using Eshelby tensors based on a simplified strain gradient elasticity theory (SSGET), which contains a material length scale parameter and can account for the size effect. Based on the strain energy equivalence, a homogeneous comparison material obeying the SSGET is constructed, and two sets of equations for determining an effective elastic stiffness tensor and an effective material length scale parameter for the composite are derived. By using Eshelby’s eigenstrain method and the Mori–Tanaka averaging scheme, the effective stiffness tensor based on the SSGET is analytically obtained, which depends not only on the volume fractions and shapes of the inhomogeneities (i.e., phases other than the matrix) but also on the inhomogeneity sizes, unlike what is predicted by the existing homogenization methods based on classical elasticity. To illustrate the newly developed homogenization method, sample cases are quantitatively studied for a two-phase composite filled with spherical, cylindrical, or ellipsoidal inhomogeneities (particles) using the averaged Eshelby tensors based on the SSGET that were derived earlier by the authors. Numerical results reveal that the particle size has a large influence on the effective Young’s moduli when the particles are sufficiently small. In addition, the results show that the composite becomes stiffer when the particles get smaller, thereby capturing the particle size effect.

Beschreibung: Attaining accurate representative geometry for a finite element analysis at various scales can be a challenging research task. Added complications arise when the geometry is representing a manufactured or biological composite. In this study, a representative geometry of linear fibrous composites was created at the microscale and is employed to reproduce crystalline microfibril stacking of Kevlar to form a single fibril joined by a non-ordered crystal structure. The structure can have ellipsoidal or rectangular microfibrils stacked in ellipsoidal or rectangular fibrils and may have any desired packing ratio within the 1–100% range. In order to build a fibrous structure along a path, a Random Walk methodology was used. Since the directionality of the fibers is random, but always stepping from one side of the path toward the other, the fibers can wind around each other and tangle or terminate if needed. Another key concept of this method is the addition of a rotation matrix operation for the path of the fibers. This allows the path around the three local coordinates to be in a linear or sinusoidal direction. The resultant geometry produced can represent the tortuous path nanofibrils undergo. Moreover, rotation about the path axis allows for the twisted geometry of ring spun yarn, and metal cable to be reproduced. Inclusion of spherical objects to the path of the fibers has been accommodated to reproduce fiber projection around, or end at, an obstruction in their path. This approach allows representing impurities at the fibril, fiber, or yarn level of composite fabric manufacturing.

Beschreibung: In this paper, we present a novel theory of the higher-order quantum stress and its formulations in the framework of density functional theory. Specifically, we have systematically derived the third-order quantum stress expression based on the higher-order Cauchy–Born rule in combination with the higher-order strain gradient theory. The higher-order quantum stress formulation provides a theoretical foundation for first-principle calculation of stress couples at atomistic scale, which may help us understand possible quantum strain gradient effects, and related ferroelectric and flexoelectric effects at small scales.

Beschreibung: The development of constitutive equations of linear viscothermoelasticity, free of the paradox of infinitely fast propagation of heat, is in the focus of this work. Two models from hyperbolic thermoelasticity— theory with one relaxation time and theory with two relaxation times —provide the stepping-stone. The setting for these models is offered, respectively, by the primitive thermodynamics of Edelen and the thermodynamic orthogonality of Ziegler, in both cases involving internal parameters. The telegraph-like heat conduction is governed in the first case by the Maxwell–Cattaneo model and in the second by the Fourier law. In the first case, temperature and its first derivative appear in the thermomechanical constitutive relation, whereas in the second case also the second derivative is present.

Beschreibung: In micromechanics, the stress–force–fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.

Beschreibung: We report results of 3D discrete element method simulations aiming at investigating the role of the boundary vibration in inducing frictional weakening in sheared granular layers. We study the role of different vibration amplitudes applied at various shear stress levels, for a granular layer in the stick-slip regime and in the steady-sliding regime. Results are reported in terms of friction drops and kinetic energy release associated with frictional weakening events. We find that a larger vibration amplitude induces larger frictional weakening events. The results show evidence of a threshold below which no induced frictional weakening takes place. Friction drop size is found to be dependent on the shear stress at the time of vibration. A significant increase in the ratio between the number of slipping contacts to the number of sticking contacts in the granular layer is observed for large vibration amplitudes. These vibration-induced contact rearrangements enhance particle mobilization and induce a friction drop and kinetic energy release. This observation provides some insight into the grain-scale mechanisms of frictional weakening by boundary vibration in a dense sheared granular layer. In addition to characterizing the basic physics of vibration-induced shear weakening, we are attempting to understand how a fault fails in the earth under seismic wave forcing. This is the well-known phenomenon of dynamic earthquake triggering. We believe that the granular physics are key to this understanding.

Beschreibung: The natural wool felt is becoming increasingly popular and important as a resource material in various applications. In this study, a constitutive equation that describes the deformation wave propagation in the felt material is derived using a hysteretic piano hammer model. A nonlinear partial differential equation with third-order terms that takes into account the elastic and hereditary properties of a microstructured felt is used to study a pulse propagation in the one-dimensional case. The boundary value problem is considered, and the numerical solution describing the strain wave propagation is provided. It is shown that the speed of a deformation wave increases with the growth of its amplitude. Also, the nonlinearity makes the front slope of a pulse steeper, which causes the eventual breaking of a pulse. The solution of the linear problem is analyzed, and the rate of the wave attenuation in the felt material is estimated.

Beschreibung: The governing equations of motion of generalized gradient Kirchhoff and Mindlin plates are derived on the basis of the generalized gradient elasticity with both stress and strain gradient parameters. The present plate models incorporate two material length scale parameters that can capture the size effect. The proposed models are capable of dealing with size-dependent plates at nanoscale dimension with complex geometries and boundary conditions with the help of Hamilton’s principle. The static bending and free vibration of a rectangular simply supported all around generalized gradient Kirchhoff and Mindlin plates are solved analytically using Navier’s solution. A circular gradient elastic plate, clamped all around, is also analyzed under linear static loading. Finally, the present solutions are discussed in relation to their corresponding conventional ones.

Beschreibung: Surface tension plays an important role in nanosized materials. In this paper, the stress field induced by surface tension around an arbitrarily shaped nanosized hole is investigated through complex variable method using truncated series, with an emphasis on the relationship between the hoop stress and the curvature of the hole’s boundary curve. Our numerical results for various shapes of holes show that maximum hoop stress always appears nearby, but not exactly at the point of maximum curvature on the hole’s boundary. Surprisingly, for elliptical holes with certain aspect ratios and typical non-elliptical holes (such as triangular, square and rectangular holes), our results show that hoop stress can even attain a local minimum (not a local maximum) or even the overall minimum at the point of maximum curvature. In particular, surface tension-induced hoop stress can be very large around nanosized holes. On the other hand, the surface tension-induced stress field is always localized for nanosized holes of arbitrary shapes and fades away with increasing distance from the hole.

Beschreibung: This paper investigates the heat conduction phenomena at nanoscale by reformulating the Nosé–Hoover thermostat for nonequilibrium molecular dynamics simulation. Inspired by the Nosé–Hoover mechanics, the feedback temperature force caused by the temperature control is reformulated to a more general level, aiming at (1) controlling the temperature locally at several distinct spots and (2) eliminating the rigid-body translation and rotation which are unexpectedly introduced into the system due to the feedback temperature force, so that accurate trajectories of atoms can be generated and the heat conduction simulation at nanoscale can be performed successfully. Correspondingly, the definition of temperature is modified; the expression of the Hamiltonian is generalized. To demonstrate the capability and feasibility of this newly formulated algorithm, we studied heat conduction phenomenon in a beam-like finite size specimen via our in-house developed computer code. The results, temperature distributions across the specimen, are shown to reach steady state after a period of time which cannot be achieved by the original Nosé–Hoover thermostat. Also, it is concluded that the heat conduction at nanoscale exhibits the same feature of Fourier’s law at macroscopic scale, namely that the heat flux is linearly proportional to the temperature gradient, if the temperature is averaged over a sufficiently large time interval and large spatial region. The thermal conductivity can thereafter be calculated based on the linear relation between the heat flux and the temperature gradient. It is found that the obtained numerical value of thermal conductivity matches the experimental result very well.

Beschreibung: Elasticity solutions of two-dimensional functionally graded rotating annular and solid disks with variable thickness are presented. Material properties vary through both the radial and axial directions continuously. Axisymmetric conditions are assumed for the two-dimensional functionally graded disk. The graded finite element method (GFEM) has been applied to solve the equations. The distributions of displacements and stresses in radial and axial directions for four different thickness profiles (constant, linear, concave and convex) and various power law exponents have been investigated. The achieved results show that by the use of functionally graded materials and variable thicknesses, the stresses are reduced, so a higher capability of angular velocity can be obtained. Also, using two-dimensional functionally graded materials leads to a more flexible design in comparison with conventional one-dimensional functionally graded materials. The GFEM solution of a functionally graded thin rotating annular disk has been compared with the published literature and it shows good agreement.

Beschreibung: The work is devoted to establish a model for the interface problem of a nonhomogeneous coating/substrate system. In the model, according to the distribution of material properties, three types of interface problems are considered: (i) The material properties and their derivatives are continuous on the interface; (ii) the material properties are continuous, but their derivatives are discontinuous on the interface; and (iii) the material properties as well as their derivatives are discontinuous on the interface. In order to solve the complex interface problems, a transient interaction energy integral method (IEIM) is developed in this paper. The transient thermal stress intensity factors are evaluated using the IEIM combined with the finite element method and the finite difference method. The influences of the interface discontinuity and the geometric parameters on the transient TSIFs are investigated. Particularly, the crack growth behavior with different interface discontinuities is discussed.

Beschreibung: We present a comparative study of the ability of some micromechanics estimates to predict the overall properties of heterogeneous materials. We focus mainly on cracked materials, for which this task is difficult and many estimates fail. We study particularly the interaction direct derivative estimate, proposed by Zheng and Du, which is an approximation of the generalized self-consistent scheme, but has the very convenient property to be always explicit. A modified version of this estimate, called full-range IDD by Zheng and Du, yields good results when comparing all poromechanical coefficients predicted by the estimate to finite element simulations of a 2D cracked material in plane strain, up to crack density factors of 1 for aligned cracks and 0.60 for randomly oriented cracks. The accuracy of finite element computations of the overall moduli is also commented by plotting the convergence of the average of the properties as well as the confidence intervals on these averages.

Beschreibung: Nanostructured metals with bimodal grain size distribution, composed of coarse grain (CG) and nanograin (NG) regions, have proved to have high strength and good ductility. Here, numerical investigation, based on the mechanism-based strain gradient plasticity theory and the Johnson–Cook failure model, focuses on effects of (1) distribution characteristics of the CG regions and (2) the constitutive relation of the NG with different grain sizes on fracture behavior in a center-cracked tension specimen of bimodal nanostructured Cu. High strain rate simulations show that both of them directly influence load response and energy history, and importantly, they are closely related to the fracture pattern. This study shows that both CG region bridging and crack deflection toughen the bimodal nanostructured Cu significantly, while debonding enhances the overall ductility moderately. Simulations also show that with volume fraction of the CG regions increasing, both structural strength and ductility of the bimodal nanostructured Cu specimen can be improved.

Beschreibung: In this work, the electromechanical behaviors of nano-grained ferroelectric ceramics are numerically studied with different grain sizes. The material under investigation is nano-grained barium titanate ceramic, which shows noticeable grain size dependence of the electromechanical characteristics. A 2D polycrystal phase-field model is developed to investigate the hysteresis loops and the process of the microstructural evolution upon applied bipolar electric field. A core–shell model has been selected to treat the grain interior and the grain boundary with separate ferroelectric properties. Such treatment is analogous to the consideration of a grain-boundary-affected zone as in the study of nano-crystalline plasticity. The grain size dependence of the ferroelectric properties, e.g., coercive electric field and remnant polarization, is examined based on this model, and the mechanism of the grain size dependence is analyzed.

Beschreibung: This paper investigates edge delamination in an orthotropic layered structure composed of a thin film and a substrate under a temperature change. An edge interface crack is analyzed for two configurations in which it emerges from an interior or corner edge of the film. Special attention is paid to the effects of orthotropic material constants on delamination cracking. The necessary material parameters involved in the energy release rate and mode mixity for the interface crack are found based on a modified Stroh formalism. The explicit dependence of the energy release rate and mode mixity on one orthotropic parameter for the film is discovered using an orthotropy rescaling technique. The effects of other material parameters on the energy release rate and mode mixity are examined numerically, and the growth and arrest of edge interface cracks are discussed based on an energy criterion.

Beschreibung: In this paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half-space is assumed to be welded. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate secular equation of fourth order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From the secular equation obtained, an approximate formula of third order for the velocity of Rayleigh waves is established.

Beschreibung: Commonly used orthotropic Hill’s criterion of plastic flow initiation (Hill in Proc R Soc Lond A 193:281–297, 1948 ) suffers from some constraints and inconsistencies, which are of two different origins. Firstly, in case of high orthotropy degree, the quadratic form corresponding to Hill’s criterion may change type from convex and closed elliptic to concave and open hyperbolic in the deviatoric stress space (Ottosen and Ristinmaa in the mechanics of constitutive modeling, Elsevier, Amsterdam, 2005 ). Secondly, application of classical Hill’s criterion to transversely isotropic materials shows a discrepancy between Hill’s limit curves in the transverse isotropy plane and the Huber-von Mises prediction for isotropic materials (Huber 1904 ; von Mises 1913 ). The basic result of the present paper is to propose the new transversely isotropic von Mises–Hu–Marin’s-type criterion of hexagonal symmetry that is free from both constraints. The new enhanced Hu–Marin’s-type limit surface represents an elliptic cylinder, the axis of which is proportional to stress/strength, in contrast to Hill’s-type limit surface possessing the hydrostatic axis. Hence, this condition does not exhibit the deviatoricity property, which is a price for coincidence with the Huber–von Mises condition in the transverse isotropy plane, but with cylindricity ensured for an arbitrarily high orthotropy degree. The hybrid-type transversely isotropic Hu–Marin’s criterion of mixed symmetry based on additional biaxial bulge test, capable of fitting experimental findings for some complex composites, is also proposed. Application of this criterion has been verified for a unidirectional SiC/Ti composite examined by Herakovich (Thermal stresses V, Lastran Corp. Publ. Division, pp 1–142, 1999 ).

Beschreibung: This is a modest contribution dedicated to the work and virtue of George Weng, a prominent figure in material mechanics and a dear intellectual friend. The paper starts with the basics of gradient theory as applied to elasticity, plasticity and dislocation dynamics by introducing weak non-locality in the constitutive equations through Laplacian terms and corresponding deterministic internal lengths (ILs) characterizing the dominant deformation mechanisms. It then considers the interaction of such deterministic ILs with surface effects associated with internal or external surfaces, as well as stochastic effects associated with pre-existing or deformation-induced random microstructures. Experimentally observed stress drops and strain bursts are interpreted through combined gradient-stochastic models. Statistical features of corresponding deformation processes that cannot be fitted with Boltzmann–Gibbs–Shannon entropy statistics are interpreted by Tsallis q-entropy statistics. Some benchmark novel experiments for the direct determination of ILs for plasticity (by testing bulk specimens with gradient grain size) and dislocation dynamics (by testing thin films in TEM with gradient dislocation density) are proposed.

Beschreibung: A multiscale approach is pursued to develop a shear-lag model in combination with core–surface and core–shell models for capturing size-scale effect on mechanical properties of ZnO nanowire (NW)-reinforced nanocomposites. Surface effects are represented by a zero-thickness (finite-thickness) surface with different elastic modulus from the central part of NW. The molecular dynamics technique is utilized for calculating thickness of the shell in the core–shell model. Linear elasticity for an axisymmetric problem and the cylindrical coordinate system is used to find the closed form of governing equations. The effect of different parameters, including diameter and aspect ratio of NWs, is studied to demonstrate the application of the developed model. Numerical results disclose that NWs with a larger aspect ratio and a smaller diameter can carry a larger portion of applied stress and are preferable in designing high-performance nanocomposites. This result is in agreement with the reported computational and experimental data.

Beschreibung: We consider an axisymmetric Stokes flow in an infinite right circular cone, which has a source of momentum (a Stokeslet) on its axis. It produces an infinite sequence of eddies in the conical flow region. A boundary problem for a stream function is solved. The picture of the streamlines is obtained. We investigate an eddy structure of the flow. The results can be used for constructing nanoreactors while carrying out chemical reactions in strictly localized nanosized spatial regions.

Beschreibung: The evaluation of crack initiation, short-crack growth as well as crack path at microscopic scale is a crucial issue for the safety assessment of macroscopically fracture-free structural components. In the present paper, the crack propagation at the material microscale is modeled by taking into account the spatial variability of mechanical characteristics of the material as well as the local multiaxial stress field disturbance induced by inhomogeneities (inclusions or voids). By adopting some crack extension criteria under mixed mode, the short-crack path is determined. A microstructure dependence of the crack path arises in the short-crack regime, while the microstructure of the material does not influence the crack propagation for sufficiently long cracks. A mean weighted equivalent stress-intensity factor (SIF) is computed for kinked short cracks, where the range of such a SIF can be used as a key parameter dictating their fatigue crack growth rate.

Beschreibung: In this paper, an exact procedure for the reconstruction of multiple concentrated damages on a straight beam is proposed. The concentrated damages are modelled as Dirac’s delta distributions capturing the effect of concentrated stiffness reduction. The presented procedure requires the knowledge of vibration mode shape displacements together with the relevant natural frequency, for the reconstruction of each damage position and intensity. The exact solution of the inverse problem at hand has been pursued by exploiting the analytical structure of the explicit closed form expressions provided for the vibration mode shapes of beams in the presence of an arbitrary number of cracks. The proposed procedure is first presented under the hypothesis that the displacements of a vibration mode shape are known at the cracked cross-sections. In this case, explicit closed form expressions of the crack severities are formulated. A further simple reconstruction approach allows the evaluation of the exact positions and intensity of the concentrated damages, if displacements of two vibration mode shapes are known at a single cross-section between two consecutive cracks. The proposed reconstruction procedure is applied for the identification of multiple cracks on a free–free beam where measurements have been simulated by means of a finite element analysis.

Beschreibung: A theory describing the behavior of chemically non-reacting binary mixtures can be based on a detailed formulation of the governing equations for the individual components of the mixture or on treating the mixture as a single homogenized continuous medium. We argue that if we accept that both approaches can be used to describe the behavior of the given mixture, then the requirement on the equivalence of these approaches places restrictions on the possible structure of the internal energy, entropy, Helmholtz potential, and also of the diffusive, energy, and entropy fluxes. (The equivalence of the approaches is understood in the sense that the quantities used in one approach can be interpreted in terms of the quantities used in the other approach and vice versa. Further, both approaches must lead to the same predictions concerning the evolution of the physical system under consideration). In the case of a general chemically non-reacting binary mixture of components at the same temperature, we show that these restrictions can indeed be obtained by purely algebraic manipulations. An important outcome of this analysis is, for example, a general form of the evolution equation for the diffusive flux. The restrictions can be further exploited in the specification of thermodynamically consistent constitutive relations for quantities such as the interaction (drag) force or the Cauchy stress tensor. As an example of the application of the current framework, we derive, among others, a generalization of Fick’s law and we recover several non-trivial results obtained by other techniques. The qualitative features of the derived generalization of Fick’s law are demonstrated by a numerical experiment.

Beschreibung: This paper studies the stress field and crack nucleation behavior in a disclinated nanowire with a continuum model. The surface stress effects of the nanowire is accounted for with the Gurtin-Murdoch model. The Green’s functions for the stress fields of a single wedge disclination and a single edge dislocation in a cylindrical nanowire are solved respectively with the complex variable method. To make the superposition principle valid, the stress field induced by the residual surface tension is properly handled in the Green’s functions. After that, the distributed dislocation method is applied to simulate the crack nucleation behavior. The influences of the surface stress effects on the stress fields of the wedge disclination and edge dislocation as well as on the Griffith crack nucleation behavior are systematically discussed.

Beschreibung: The growth of preexisting spherical micro-void in an infinite elastoplastic body under thermal load is analyzed. Based on the geometrical nonlinearity with large deformation and the yield criterion of perfect plasticity, a mathematical model of the problem is presented. The Lagrangian and Euler coordinate systems are introduced to describe the thermal expansion deformation. By the elastoplastic analysis, the distributions of the stresses near the cavity are obtained. When the initial radius of a preexisting micro-void tends to be infinitely small, the critical temperature of cavitation can be calculated. The instability of the micro-void inside the infinite body is discussed. The results of numeric computation indicate that the radius of the cavity and the radius of the plastic zone would rapidly grow when the remote temperature increases and approaches the critical temperature.

Beschreibung: Elasticity is the prototype of constitutive models in Continuum Mechanics. In the nonlinear range, the elastic model claims for a geometrically consistent physico-mathematical formulation providing also the logical premise for linearized approximations. A theoretic framework is envisaged here with the aim of contributing a conceptually clear, physically consistent, and computationally convenient formulation. A reasoning about the physics of the model, from a geometric point of view, leads to conceive constitutive relations as instantaneous incremental responses to a finite set of tensorial state variables and to their time rates along the space-time motion. Integrability of the tangent elastic compliance, existence of an elastic stress potential, and conservativeness of the elastic response, under the conservation of mass, are given a brand new treatment. Finite elastic strains have no physical interpretation in the new rate theory, and referential local placements are appealed to, just as loci for operations of linear calculus. Frame invariance is assessed with a consistent geometric treatment, and the clear distinction between the new notion and the property of isotropy is pointed out, thus overcoming the improper statement of material frame indifference. Extension of the theory to elasto-visco-plastic constitutive models is briefly addressed. Basic computational steps are described to illustrate feasibility and convenience of calculations according to the new theory of elasticity.

Beschreibung: In this paper, the application of fractional continuum mechanics to rate independent plasticity is presented. This new formulation is non-local due to the properties of the applied fractional differential operator during the definition of kinematics. In the description, a small fractional strains assumption is used together with additive decomposition of total fractional strains into elastic and plastic parts. Classical local rate independent plasticity is recovered as a special case.

Beschreibung: A Timoshenko beam excited by a sequence of identical moving masses is studied as a time-varying problem. The effects of centripetal and Coriolis accelerations besides the vertical component of acceleration of the moving mass are considered. Using Galerkin procedure, the partial differential equations of motion which are derived by Hamilton’s principle are transformed to ordinary differential equations. The incremental harmonic balance method is implemented to determine the boundary curve of instability and other companion curves of resonance in the parameter plane. A new approach for identifying the conditions of resonance is investigated by presenting an intuitive definition of resonance for time-varying systems. The influence of employing different deformation theories on the critical parameter values of stability and resonance curves is studied. The validity of the instability and resonance curves is examined by numerical simulations and also ascertained through comparing with those reported in the literature.

Beschreibung: In this paper, controlling flow around a backward-facing step by means of a dielectric barrier discharge plasma actuator is experimentally investigated. The pressure distribution on the step surface as well as the natural oscillations of the flow in the shear layer at three different Reynolds numbers from 18,000 to 54,000 (based on the step height) are measured in the wind tunnel. Then, by installing plasma actuators at different positions, the changes in pressure distribution and the length of the separation bubble are investigated. It was found that for controlling the separation bubble and expediting the flow recovery process the best position for installation of the plasma actuator is the upstream of the separation point i.e., step tip edge. Installing the actuator inside the separation bubble has a relatively low effect on the separation zone length. In addition, the most effective way for exciting the shear layer is utilizing the unsteady actuation with an exciting frequency equal to the natural frequency of the vortex shedding.

Beschreibung: The frequency-dependent dynamic effective properties (velocity, attenuation and elastic modulus) of nanoporous materials with randomly positioned spherical cavities are studied. The surface energy theory proposed by Huang and Wang (Handbook of micromechanics and nanomechanics. Pan Stanford Publishing Pte Ltd., Singapore, pp 303–348, 2013 ) is used to derive the non-traditional boundary condition on the surface of the nanocavity and further the scattering matrix of a single nanocavity. Then, the total wave field is obtained by considering the multiple scattering processes among the dispersive spherical cavities. The configuration average of the total wave field results in the coherent waves or the averaged waves. The numerical examples of the effective speed, the effective attenuation of the coherent waves and associated effective dynamic modulus of a nanoporous material are given and shown graphically. The effects of surface elasticity and the residual surface tension are both considered. Moreover, the influences of the non-symmetric parts of in-plane surface stress and the out-of-plane parts of the surface stress are also discussed based on the numerical examples.

Beschreibung: In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped–clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon–Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases ( pq z =  k 0 and q =  q 0 ), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Beschreibung: The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order, the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou (J. Fluid Mech. 393:59–87, 1999 ). A careful study of the governing partial differential system for the first-order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window, stability is again lost to exponentially growing solutions as the Reynolds number is increased.

Beschreibung: The present note treats a special case of a previous work published in Acta Mechanica (Kumari and Nath in Acta Mech 146:139–150, 2001 ). Analytical and asymptotic solutions are presented not found in the previous paper.

Beschreibung: An interfacial imperfection coupling model is proposed to characterize the imperfect interface in a bi-layered multiferroic cylinder by extending the generalized linear spring model of the uncoupled imperfect interface. Based on the model, fracture analysis is performed on the multiferroic cylinder containing intra-layer cracks. Parametric studies on the stress intensity factor (SIF) yield three main conclusions: (a) the mechanical imperfection can enhance the SIF independently; (b) the magnetic or electric imperfection can reduce the SIF only through its coupling with the mechanical imperfection; and (c) the magneto-electric imperfection coupling does not affect the SIF in any case.

Beschreibung: An analytical model is developed to predict the elastic stress response of a thick-walled cylindrically curved panel subjected to a radial temperature gradient under the assumption of generalized plane strain. The ends of the panel in the angular direction are guided by rigid supports that allow a displacement in the circumferential direction but fix the curvature of the middle surface. As thermal load is applied to the panel, couples act on those ends, giving rise to pure bending conditions even in the case of homogeneous heating. Moreover, the free ends in the axial direction of the panel are taken into consideration. The stresses caused by different types of steady-state thermal loads in the panel are analyzed. Further, the elastic limits leading to plastic flow according to the yield criteria of both Tresca and von Mises are investigated. The results are presented in graphical form.

Beschreibung: Experimental results have shown that composite cantilever beams with ultra high molecular-weight polyethylene fibres are collapsed by a new mode of microbuckling, which involves elastic bending and shearing of the plies, and plastic shear of the interfaces. Different finite element modelling strategies were employed in this study. Simulation results reveal that an enough number of interfacial cohesive layers, accurate partition of the shear stiffness between plies and interfaces, and accurate partition of the flexural stiffness between plies are important in predicting the collapse responses. The sensitivity of the predicted microbuckling responses to the overall effective shear modulus and interlaminar shear strength of long composite beams are also investigated.

Beschreibung: The size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified couple stress theory. For a three-dimensional orthotropic body, three additional material length scale parameters should be involved in the modified couple stress theory (with respect to the three shear moduli). However, in this study and without restricting the generality, we assume that the 2D couple stress state of the orthotropic micro-plate is described solely by only one material length scale parameter in accordance with the in-plane shear modulus. Furthermore, this reasonable assumption allows us to compare qualitatively the results with those obtained by the nonlocal elasticity theory, which also uses only one material length scale parameter to capture the size effect. Using Hamilton’s principle, the governing equilibrium equation of the micro-plate and the associated general boundary conditions are derived in terms of the deflection. The resulting initial boundary value problem is of fourth order, and it is solved employing the analog equation method. Example problems are presented for orthotropic skew micro-plates, and useful conclusions are drawn from the investigation of their micron-scale response. Some of the findings detected in studying the microstructure vibratory response of orthotropic skew micro-plates, based on the modified couple stress theory, are also verified by those obtained by the nonlocal elasticity theory. Nevertheless, a new important finding is that both the frequency and critical load parameters increase by increasing the material length scale parameter of the modified couple stress theory, which is in direct contradiction to that of the nonlocal elasticity theory where these parameters decrease by increasing the nonlocal parameter.

Beschreibung: A model is developed for the elastic response of a thermo-responsive hydrogel subjected to swelling under an arbitrary deformation with finite strains. The constitutive equations involve the stress–strain relation, the nonlinear diffusion equation for water molecules, the heat conduction equation, and the Allen–Cahn equation for a scalar order parameter (proportional to the concentration of hydrophilic segments in polymer chains). Material constants are found by fitting equilibrium mass uptake diagrams for macro- and microgels under unconstrained and constrained swelling in the vicinity of the volume phase transition temperature. Quantitative agreement is demonstrated between the experimental data and the results of simulation. The effect of composition of hydrogels (concentrations of monomers and cross-linker) on adjustable parameters is analyzed numerically.

Beschreibung: The paper presents the analytical results aimed at studying the deformations of cantilever beams based on Reddy higher-order shear theory. Five different displacement boundary conditions are investigated. The first two conditions are conventional simplified displacement boundary conditions, and the third one is determined by the least squares method. Besides, two new simplified boundary conditions are given by considering the definition of the fixed end of cantilever beams. Compared with the solutions by the finite element method, results by the two new boundary conditions are found to be much better than those by the conventional ones, especially for deep beams. The new boundary conditions which are first presented are not as good as the condition determined by the least squares method, but they are simple and easy to be coded by engineers.

Beschreibung: This article is mainly focused on accurate solutions for axial impact buckling of functionally graded cylindrical shells in a heated environment. A new analytical methodology is developed, and a rigorous solving procedure is conducted to guarantee the accuracy of the obtained results. Various aspects related to boundary conditions, geometric parameters, material properties and temperature variations are investigated systematically. The numerical results reveal that in-plane boundary conditions have an obvious influence on the shell. If the reflection of stress waves occurs, critical stresses should further decrease with the interaction of incident and reflected waves. The ability of FGCSs in resisting buckling failure can be improved by controlling the material exponent.

Beschreibung: This paper is concerned with the theoretical treatment of transient thermoelastic problems involving a multilayered hollow cylinder with piecewise power law nonhomogeneity due to the asymmetrical heating of its surfaces. The thermal and thermoelastic constants of each layer are expressed as power functions of the radial coordinate, and their values continue on the interfaces. The exact solution for the two-dimensional temperature change in a transient state is obtained using the Laplace transformation and separation-of-variables method. The exact solution for the thermoelastic response of a multilayered hollow cylinder under the state of generalized plane strain, where the strain is not bound, is obtained herein. Some numerical results for the temperature change and the stress distributions are presented in figures. The influence of the functional grading on the thermal stresses is investigated. Furthermore, the influence on the axial stress of the restraint condition in the axial direction is investigated.

Beschreibung: Accurate evaluation of transverse stresses in soft-core sandwich laminates using the existing 2D finite element (FE) models involves cumbersome post-processing techniques. In this paper, a simple and robust method is proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in soft-core sandwich laminates by using a displacement-based C 0 continuous 2D FE model derived from refined higher-order shear deformation theory (RHSDT) and a least square error (LSE) method. In this refined higher-order shear deformation theory (RHSDT), the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly early varying displacement field. The transverse displacement is assumed to have a quadratic variation within the core, and it remains constant in the faces beyond the core. The proposed C 0 FE model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C 1 continuity requirement of the transverse displacements associated with the RHSDT. The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. Thus, the proposed method is quite simple and elegant compared to the usual method of integrating the 3D equilibrium equations at the post-processing stage for the calculation of transverse stresses in a sandwich laminates. The accuracy of the proposed method is demonstrated in the numerical examples through the comparison of the present results with those obtained from different models based on HSDT and 3D elasticity solutions.

Beschreibung: The flow identified by Berker (Encyclopedia of Physics, Springer, Berlin, 1963 ) on the motion induced between two parallel infinite plates rotating at angular velocity Ω with offset centers of rotation was solved by Abbot and Walters (J Fluid Mech 40:205–213, 1970 ). Here, we consider the same problem in a fluid uniformly rotating at angular velocity ω . The flow is then governed by a Reynolds number R and σ = ω/Ω which represents the ratio of Coriolis to inertial forces. As in the original problem, the loci of centers of rotation projected onto the mid-plane form logarithmic spirals. Sample similarity profiles at fixed R and σ are given in graphical form. Features of the logarithmic spirals in both the inertial and rotating frames of reference are also presented in graphical form.

Beschreibung: In the proposed paper, the analytical solution of the problem on an axisymmetric stress-strength state of an infinite elastic layer (a plate) with an absolutely rigid inclusion, coupled with this plate, is solved. The upper plate plane side is under the axisymmetric compressive load. The bottom side of the plate could be in different conditions with the absolutely rigid base: it can be the conditions of a smooth contact or the conditions of a full adhesion. The integral Weber-type transformation is applied to the axisymmetric Lamé equations for the displacements and stress field construction. It leads to a one-dimensional vector inhomogeneous boundary problem. With the help of this problem solution, after satisfying a boundary condition, the initial problem is reduced by solving an integral singular equation on the finite interval. The equation is solved approximately by the orthogonal polynomial method with the previous extraction of the solution’s singularities on the interval ends.

Beschreibung: The purpose of this paper is to address the wave reflection over the rotating piezoelectric boundary surface in the framework of inhomogeneous wave theory which can introduce an additional reflected surface wave over the boundary surface to solve the problem of discrepancy between independent wave modes and boundary equations. A set of homogeneous equations in displacements and electric potential is derived within the rotatory coordinate system in the presence of the Coriolis and centrifugal acceleration presenting noticeable influence upon the wave propagation and reflection. Other than the transverse wave, the performed plane example shows that there is a critical point of when angular velocity equals the wave frequency for the quasi-longitudinal wave. The results also reveal that the angular velocity is accompanied by the modification of reflected waves especially in the case of reflected surface mode as well as the reflection angles, the amplitudes, and energy ratio coefficients.

Beschreibung: This paper presents a new dynamic crack growth prediction tool based upon the symmetric Galerkin boundary element method (SGBEM) in the Laplace domain, combined with the maximum hoop stress (MHS) criterion. The fast Laplace inverse transform developed by Durbin is employed to obtain time-domain solutions of the stress intensity factors required by the MHS criterion. In this work, the proposed Laplace SGBEM tool is used to predict crack trajectories in homogeneous and non-homogeneous isotropic brittle materials under dynamic loading conditions. The effect of the elastic constant mismatches is investigated for the influence of crack–inclusion interaction on crack growth.

Beschreibung: In this paper, the static and stability stiffness matrices of a gradient elastic flexural Bernoulli–Euler beam finite element are analytically constructed with the aid of the basic and governing equations of equilibrium for that element. The flexural element has one node at every end with three degrees of freedom per node, i.e., the displacement, the slope and the curvature. The stability stiffness matrix incorporates the effect of axial compressive force on bending. Use of these stiffness matrices for a plane system of beams enables one through a finite element analysis to determine its response to static loading and its buckling load. Because the exact solution of the governing equation of the problem is used as the displacement function, the resulting stiffness matrices and the obtained structural responses are also exact. Examples are presented to illustrate the method and demonstrate its merits.

Beschreibung: There can be no doubt as to the importance of vortical motion in fluid mechanics. Yet, very little attention is given typically to the balance law of angular momentum and to its role in defining the fundamental character of stress, which as a result is usually assumed as a symmetric tensor. Here, we allow for the possibility of couple-stresses, along with general non-symmetric force–stresses, and develop a self-consistent size-dependent theory within the context of classical continuum mechanics. This development relies upon the identification of the following key components for the dynamic response of three-dimensional fluid continua: (i) fundamental, uniquely defined kinematical measures of flow, (ii) an independent set of energy conjugate variables, (iii) the corresponding permissible natural and essential boundary conditions, and (iv) a non-redundant set of body-force and inertial contributions. Based upon this formulation, one can recognize that the previous couple-stress theory for fluids suffers from some inconsistencies, which may have restricted its applicability in the study of viscous flows. After presenting the general formulation of the new consistent theory, we specialize for incompressible viscous flow and consider the problem of generalized Poiseuille flow within this size-dependent fluid mechanics. Finally, we conclude that the theory presented here may provide a basis for a broad range of fluid mechanics applications and for fundamental studies of flows at the finest scales for which a continuum representation is valid.

Beschreibung: The propagation of a steady wavefront in a medium with three levels of plastic deformation is considered: (a) dislocation, (b) meso-scale and (c) macro-scale. To take into account collective mechanisms of microplasticity, a relaxation term describing the momentum exchange between meso- and macro scales is incorporated into a dislocation-based constitutive law. This leads to a nonlinear second-order differential equation. Analytical and numerical analyses of the equation are performed. Using as example D16 aluminum alloy, we determine the parameters that provide a satisfactory correspondence between calculated and experimental profiles of particle velocity.

Beschreibung: Theoretical issues related to the covariant structure of non-isothermal generalized plasticity in large deformations are studied in depth. For this purpose, the tensor analysis on manifolds is utilized and the manifold structure of both the ambient and the state spaces is postulated. Building on this, a covariant structure of the theory is constructed within a strain–space formulation. Thermomechanical loading criteria in both Lagrangian and Eulerian descriptions are derived in a deformation–temperature space. Based on geometrical concepts, classical non-isothermal plasticity is derived as a special case. The invariance properties of the local form of the balance of energy equation are systematically engaged for the derivation of the thermomechanical state equations. It is specifically shown that the local form of the covariant balance of energy equation does not yield the Doyle–Ericksen formula and the standard entropy–temperature constitutive relation, unless a further assumption is made. A derivation of the spatial form of the Duhamel–Neumann hypothesis on a decomposition of the rate of deformation tensor into its mechanical and thermal parts is performed as well. The covariance concept is specialized further by the construction of a material model within the context of classical metal plasticity. The proposed model is tested numerically for the solution of two problems of non-isothermal large-scale plastic flow.

Beschreibung: An efficient group-theoretic method is proposed for the buckling analysis of symmetric prestressed space structures. Tangent stiffness matrices and geometric stiffness matrices of trusses, cables, and frames are given, and thus, the proposed method is applicable not only to pin-jointed structures but also to more general structures with frame and cable elements. Important contribution of initial prestresses is considered in formulating the tangent stiffness matrices for the prestressed structures. By adopting irreducible representations of a symmetry group and projection operator theory, the associated stiffness matrices are converted to symmetry-adapted forms. Subsequently, the original buckling problem is decomposed into a series of independent subproblems with smaller dimensions, which obtain precise solutions but lead to significant reduction in computational cost. To describe the typical process for the group-theoretic method, efficient buckling analyses on four types of symmetric prestressed space structures composed of cables, trusses, and/or frames are carried out. The computational efficiency of the proposed method is dramatically improved in comparison with those of FEM and the conventional numerical method. Comparing the results with the corresponding ones from ABAQUS and published data, we verify that the proposed method is elegant and reliable.

Beschreibung: In this paper, the quasi-static stability of moderately thick skew viscoelastic composite plates subjected to in-plan forces is analyzed using the element-free Galerkin method. The study is based on the first-order shear deformation theory and the method of effective moduli. The shape functions are constructed using the moving least squares approximation and the essential boundary conditions are introduced into the formulation through the Lagrange multiplier method and the orthogonal transformation techniques. The method is programmed and several numerical examples are presented to demonstrate the scope and efficacy of the procedure. Also, local buckling of viscoelastic stepped plates is studied.

Beschreibung: In this paper, we introduce a homotopy analysis method into the structural reliability analysis and propose a different algorithm from the traditional Hasofer–Lind–Rackwitz–Fiessler type of iterations to solve the reliability index. Due to the powerful function of homotopy analysis in solving nonlinear equations, the method presented in this paper yields high efficiency and strong convergence of the reliability analysis. We first establish the Karush–Kuhn–Tucker (KKT) condition of the optimization problem for reliability index in the first-order reliability method. Next, we construct the corresponding combined homotopy equations for the KKT condition and apply the path-tracking algorithm to efficiently solve the equations. Finally, several numerical examples and an engineering application are provided to validate the effectiveness of the present method.

Beschreibung: This paper considers the plane problem for two identical semi-infinite magnetoelectroelastic (MEE) materials, which are adhered together by a thin interlayer. A limited permeable crack is assumed to form in the interlayer parallel to its faces, and the interlayer is softer than the adherent MEE materials. To avoid singularities in the vicinity of a crack, which do not exist in reality, the extended pre-fracture zones including three distinct zones, i.e., the mechanical yield zone, the electrical saturation zone and the magnetic saturation zone, of finite lengths are introduced as crack continuations. The problem is formulated mathematically as a system of three linear equations, which can be solved exactly. The unknown lengths of the extended pre-fracture zones are determined by requiring that the stress, the electrical displacement and the magnetic induction are all finite at the ends of these zones. The fracture parameters, such as the crack opening displacement, and the jumps in the electrical and/or magnetic potentials through the crack region as well as the energy release rate are obtained. All these parameters are presented in a simple explicit form which can be determined efficiently without complicated computation that makes the present results rather convenient for any theoretical analysis and engineering applications. Additionally, numerical results are presented to study the influence of various factors on fracture parameters.

Beschreibung: The nominal strength of structures made of quasibrittle materials shows a noticeable decrease or increase in brittleness with respect to the increase in structure dimension; this is the well-known size effect on strength. The present study aims to analyze and experimentally validate the size effect on laminate composite glass fibers using cohesive laws. This work not only correlates the nominal strength with the size of the failure processing zone but also relates the size of the failure processing zone at failure load to the specimen dimension and geometry. Our study provides a useful tool that enables engineers to obtain a set of design charts that relate the nominal strength of the structure to the size and shape of the specimen. Moreover, it aims to apply a new method to study the effect of structure size on the tensile strength of fiber polymer composite. The results of nominal strength are validated using a matrix of experimental work, and they agree very well with the experimental data. The other fracture properties are compared using an extended finite element method. The output of the analysis is a valuable graph that gives the nominal strength of the open-hole specimen.

Beschreibung: Three-dimensional vortex dynamics in the wake behind a flat plate at 20 ○ angle of attack are explored by means of the Hilbert–Huang transform. While a completely regular vortex shedding is observed at Reynolds number Re  = 500 with a distinct shedding frequency and only a single subharmonic frequency, a complex shedding behavior is observed at Re  = 525 and above. The low-frequency variations of the energy content and frequency in time are deduced from the Hilbert spectra. The low-frequency modulations along the span of the plate are substantially increased from Re  = 525 to Re  = 800. The mean marginal spectra reveal that the energy in the low-frequency band increases with increasing Re . A corresponding reduction of the energy content in the high-frequency band is observed at the highest Reynolds number.

Beschreibung: The problem of thermal convection in a horizontal layer of ferrofluid-saturated porous medium is investigated theoretically in the presence of a uniform vertical magnetic field and throughflow. The flow in the porous medium is described by the modified Brinkman equation with fluid viscosity different from effective viscosity. The rigid, however permeable ferromagnetic boundaries are considered to be insulated to temperature perturbations. The resulting eigenvalue problem is solved both numerically using the Galerkin technique and analytically using regular perturbation technique with wave number a as a perturbation parameter and observed that the results complement with each other. The direction of throughflow has no influence on the stability characteristics of the system, and the effect of throughflow-dependent Peclet number Q is to delay the onset of ferroconvection. The Prandtl number Pr (〉1) has insignificant while the nonlinearity of fluid magnetization parameter M 3 has no influence on the onset of ferroconvection. Besides, an increase in the value of the Darcy number Da and the magnetic number M 1 is to hasten, while an increase in the ratio of viscosity parameter λ is to delay the onset of ferroconvection.

Beschreibung: Elastic spherical contact, especially conformal contact, is a widely encountered problem in mechanical design and wear analysis, but corresponding universal methods do not exist. A new approximate universal solution for the normal contact between frictionless spherical surfaces is established by combining analytical and numerical methods. The proposed model is not limited to an elastic half-space and can be universally used to calculate the pressure distribution of conformal and non-conformal contact. The validity and universality of the model were verified by a large number of three-dimensional finite element analyses of different materials and structures. With the new model, users can investigate the complex relationships between key parameters, such as maximum contact pressure, radius of contact region, normal load radii, and radial clearance, and apply this understanding in design and wear analysis of products with spherical contact surfaces, such as bearings.

Beschreibung: Large deflection analysis of geometrically exact beams under conservative and nonconservative loads is considered. A Chebyshev collocation method is used for the discretization of the governing equations of the spatial beam with intrinsic formulation. In the case of nonconservative (follower) loads, since the formulation is expressed in a deformed frame, the formulation is fully free from any displacement or rotational variables, and a direct solution can be achieved. In the case of conservative loads, the applied loads are functions of beam rotations, and in order to retain the intrinsic nature of the formulation, a direct integration of rotations is avoided and an iterative solution of the governing equations in addition to an update on the beam rotations as a post-processing step has been employed. A number of test cases have been considered and are compared to the existing experimental as well as numerical results in the literature. A very good agreement has been observed in the comparison cases, and it is shown that the intrinsic formulation in conjunction with a Chebyshev collocation method while exhibiting advantages in ease of implementation, computational cost and convergence characteristics over other methods can effectively capture the large deflection behavior of spatial beams under various load conditions.

Beschreibung: Based on the England–Spencer plate theory, the elastic field in a transversely isotropic functionally graded plate with holes is analyzed by transforming the original three-dimensional (3D) problem into a two-dimensional (2D) one. The general solutions of the governing equations for the 2D problem are expressed by four analytic functions α(ζ) , β(ζ) , ϕ(ζ) and ψ(ζ) when there are no transverse forces acting on the plate surfaces. In a multiply-connected domain, the four analytic functions are expressed as the sum of logarithmic functions that are multi-valued and holomorphic functions, and should meet the conditions of single-valuedness of displacements. 3D elasticity solutions are then obtained for a transversely isotropic FGM plate with a circular hole subject to loads at infinity based on the power series method. Explicit expressions for concentration factors of the resultant forces are presented. For the degenerated case of homogeneous materials, the present elasticity solutions are exactly the same as those based on plane stress elasticity and classical plate theory. In addition, the elasticity solutions for an infinite FGM plate subject to in-plane point forces ( X , Y ) and moments ( M X , M Y ) are derived, among which the solutions of point moments are reported for the first time. There are obvious differences between the present solutions of point forces and the existing solutions reported in the literature. In particular, the present solutions for homogeneous materials include a 3D correction term, which depends on the thickness-to-radius ratio, to those of plane stress elasticity. Finally, the elasticity solution for the point moment M Z is discussed.

Beschreibung: We consider viscous, heat-conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity—instead of the classical partition into so-called fluxes and driving forces—the apparent antisymmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared with the speed of sound, the Maxwell–Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case, this approximation via a scale separation argument is no longer possible. We introduce the new concept of entropy invariant model reduction, leaving the entropy production unchanged under the reduction from partial momentum balances to a single mixture momentum balance. This results in an extension of the Maxwell–Stefan equations to chemically active mixtures with an additional contribution to the transport coefficients due to the chemical interactions.

Beschreibung: In the present paper, a new nonlocal treatment for micro-mechanical damage modeling is introduced based on the background cell concept. The nonlocal damage variable in the modified GTN damage model is defined as the weighted porosity in analogy to the element-free Galerkin method. The evolution of the damage variable is related to the support domain surrounds the integration point. The efficient computational algorithm is taken from the regular background cell and implemented into the commercial finite element code ABAQUS via the user interface UMAT for both two-dimensional and three-dimensional problems. To verify the nonlocal damage model, extensive computational simulations of 2D and 3D cracked as well as holed specimens are presented and confirmed that the nonlocal damage overcomes mesh sensitivity and is computationally more efficient than other nonlocal treatment methods. The computational simulation of a compact-tension shear specimen reveals that the nonlocal damage model is able to predict mixed-mode crack growth independently of the element orientation.

Beschreibung: This paper deals with the free vibration validation of a family of mechanical and piezoelectric eight-node hexahedral elements, presenting rotational degrees of freedom in addition to the classical displacement ones. Their formulations are based on the 3D virtual rotations of a nodal fiber within the finite element that enriches the mechanical displacement vector, stiffness and mass matrices approximations. The performances of these elements for free vibration problems are assessed by means of several beam, plate and shell modal tests, and their results are compared with analytical, experimental and numerical reference solutions. In particular, it is shown that these elements are well adapted for evaluating the modal response of thin and thick elastic and piezoelectric structures, and their accuracy is close to those of the classical mechanical and piezoelectric 20-node hexahedral elements.

Beschreibung: The aim of this study is to investigate the stability of regular dry stone masonry walls under in-plane seismic loading. The combination of analytical and numerical approaches was used to identify the collapse mechanism and the seismic resistance of different arrangements of stone blocks. In the performed analyses, a minimum value of the horizontal base acceleration due to which one part of the wall loses its stability was adopted as a measure of the seismic resistance. To identify the arrangement of stone blocks that is optimal in terms of seismic resistance, several numerical analyses were performed using the combined finite-discrete element method.

Beschreibung: A model of cracking in a circular disk with mixed boundary conditions on the boundary is suggested. It is assumed that the cracking process zone is a finite length layer containing a material with partially disturbed bonds between separate structural elements in the plastic flow state at constant stress. Limit equilibrium analysis of the zone of weakened interparticle bonds of the material (prefracture) is performed on the basis of the criterion of critical opening of prefracture zone faces.

Beschreibung: The generalized differential quadrature (GDQ) method is used to analyze the effect of non-homogeneity, orthotropy, and thickness variation on the vibration characteristics of rectangular plates on the basis of Kirchhoff’s plate theory. The non-homogeneity of the plate material is assumed to arise due to the exponential variations in Young’s moduli, shear modulus, and density of the plate material with the in-plane coordinates. The thickness of the plate is taken as the Cartesian product of linear variations along two concurrent edges of the plate. In the GDQ method, the derivative of a function with respect to a space variable at a given grid point is approximated as a weighted linear sum of the function values at all of the grid points in the computational domain of that variable. Numerical results have been obtained for four different combinations of boundary conditions at the edges, namely: (1) fully clamped; (2) two opposite edges are clamped and the other two are simply supported; (3) two opposite edges are clamped and the other two are free; and (4) two opposite edges are simply supported and the other two are free. The effect of various plate parameters on the natural frequencies is studied for the first three modes of vibration. Three-dimensional mode shapes for a specified plate are plotted. A comparison of results obtained by the present method with those available in the literature is presented.

Beschreibung: Miniaturization and the need for novel materials with unique properties have driven composite materials to the forefront of research in solid mechanics. The response of a composite microstructure is dependent on the properties of individual phases, their distribution, the volume fractions and the scale of observation. The microstructures under investigation are sampled randomly from an infinite two-phase linear elastic planar checkerboard using a binomial distribution. A versatile methodology for investigating the effective response of such microstructures at finite scales is based on the Hill–Mandel macrohomogeneity condition. In this methodology, rigorous bounds are obtained as solutions to stochastic Dirichlet and Neumann boundary value problems from the level of a statistical volume element to that of a representative volume element (RVE). Within the framework of planar elasticity, the concept of a scaling function is introduced which unifies the treatment of several microstructures and quantifies the approach to RVE. It is demonstrated that the scaling function depends on the phase contrast and the mesoscale. Certain exact properties of the scaling function are derived rigorously, and its functional form is established using extensive numerical simulations on 163,728 microstructural realizations at varying contrasts, mesoscale and boundary conditions.

Beschreibung: The purpose of this investigation is to obtain the critical fracture stress, σ f , in a cracked elasto-plastic plate subjected to mixed-mode loading. A new model estimating the magnitude of critical fracture stress based on the plastic zone during crack propagation is developed. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Apart from the obvious and ideal benefits of being able to quantify crack propagation rates without the necessity to determine empirical coefficients and exponents experimentally, such an approach would lead to a better understanding of the factors which affect the crack growth rate.

Beschreibung: A new criterion has been developed to predict the onset of liquid (heavier fluid) entrainment from a stratified two-phase region. The criterion was developed based on the local instability of the interface between two fluids due to the suction effect associated with the discharging of the lighter fluid. To validate the proposed criterion, comparisons were conducted between the measured critical height at the onset and those predicted using a three-dimensional analysis of the flow through two configurations: (1) a single branch mounted on an inclined wall with an inclination angle ranging between −90° and + 60° and (2) dual branches mounted on a vertical wall with the plane passing through the branch centerlines and inclined with an angle α ranging between 0° and 60°. Comparisons demonstrate a very good agreement between the predicted and the measured values for both single and dual branches. This verifies that the onset of liquid entrainment mechanism occurs due to local flow instability of the interface, analogous to Rayleigh–Taylor instability.

Beschreibung: The viscoelastic behavior of hydrated soft biological tissue is strongly influenced by the mechanical interaction of its interstitial fluid with the solid phase. The classical uniaxial steady biphasic theory for soft tissue with high moisture content under confined compression is extended by replacing the Darcy steady flow assumption with an unsteady internal fluid flow model that involves an unsteady flow coefficient based on non-equilibrium thermodynamics. The finite deformation, non-equilibrium, unsteady biphasic viscoelastic analysis derived from conservation of linear momentum, which includes the mass terms neglected in some steady models, produces a nonlinear hyperbolic partial differential equation for the solid phase displacements, with a finite propagation velocity of the disturbance from the plunger in contrast to the instantaneous propagation of the classical parabolic steady description for cartilage. For confined compression of a small cylinder of hydrated soft biological tissue, the new hyperbolic equation is solved for the solid phase local displacements during both loading and relaxation as a function of time and position by a finite difference scheme of Shampine. A parametric study shows the influence of the unsteady coefficient on the predicted behavior, for both a linear elastic and a linear viscoelastic solid phase and for a constant permeability, by a comparison of the respective solid phase displacement distributions at the end of a constant rate plunger displacement at 0.001/s, 1/s and 1,000/s. Models assuming the Darcy relation predict physically realistic responses only for slow rates. The concavity of the stress–time curve for the solid phase at the plunger during a constant displacement of the plunger even at slow rates may be adjusted from softening to hardening by increasing the unsteady coefficient to increase the drag force exerted by the fluid on the solid phase. Because of unsteady fluid flow, overshoot of the solid phase displacement may occur initially during relaxation and also again near the end of the approach to equilibrium. A Zener standard linear viscoelastic solid phase slows the relaxation to equilibrium in comparison with a linear elastic solid phase.

Beschreibung: The boundary value problem of torsion of a solid cylinder is analyzed for a class of hyperelastic materials that exhibit the power law type dependence of the strain energy density on the magnitude of the deformation gradient. The Saint Venant hypotheses are generalized by including the non-homogeneous longitudinal and radial deformations. A nonlinear variational problem with respect to the function of the radial/surface deformation, the function of the longitudinal deformation, the normalized torque and the normalized axial force is formulated. The asymptotic analytical solutions are obtained for the hard device torsion and for large angles of twist. They illustrate the power law type dependencies of the axial force and the reaction torque on the angle of twist with the exponents p and p −1, respectively. For Treloar (neo-Hookean) materials with p = 2, the classical results can be obtained. The finite element analysis of the hard device torsion is performed by MATLAB. The results indicate that for a homogeneous class of materials and large angles of twist non-homogeneous radial/surface deformation can be observed.

Beschreibung: Many rubber-like materials present a phenomenon known as Mullins effect. It is characterized by a difference of behavior between the first and second loadings and by a permanent set after a first loading. Moreover, this phenomenon induces anisotropy in an initially isotropic material. A new constitutive equation is proposed in this paper. It relies on the decomposition of the macromolecular network into two parts: chains related together and chains related to fillers. The first part is modeled by a simple hyperelastic constitutive equation, whereas the second one is described by an evolution function introduced in the hyperelastic strain energy. It contributes to describe both the anisotropic stress softening and the permanent set. The model is finally extended to soft tissues’ mechanical behavior that present also stress softening but with an initially anisotropic behavior. The two models are successfully fitted and compared to experimental data.

Beschreibung: This study is concerned with the neutrality of a coated circular piezoelectric inclusion when the matrix is subjected to remote uniform electroelastic loadings. Two design schemes are proposed to make the coated inclusion neutral. In the first scheme, the thickness of the coating can be designed for given electroelastic constants of the composite so as to make the inclusion neutral to certain remote uniform loadings. In the second scheme, the electroelastic constants of the coating can be designed for given electroelastic constants of the inclusion and the matrix, and given coating thickness so as to make the inclusion neutral to any remote uniform loadings. The analysis indicates that even in the absence of the coating, the piezoelectric inclusion can be made neutral if the electroelastic constants of the two-phase composite satisfy a restriction.

Beschreibung: This paper presents a theoretical study on propagation of torsional surface waves in a homogeneous viscoelastic isotropic layer with Voigt type viscosity over an inhomogeneous isotropic infinite half space. The non-homogeneity in half space is assumed to arise due to exponential variation in shear modulus and density. A closed-form solution has been obtained for the displacement in the layer as well as for a infinite half space. The dispersion and absorption relations for an torsional wave under the assumed geometry have been found. Numerical results are presented for propagation characteristics in terms of a number of non-dimensionalized parameters and have been produced graphically. This study investigates the effect of various parameters, namely non-homogeneity parameter, internal friction, the layer width and complex wave number on dissipation function and phase velocity of the torsional wave. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close agreement.

Beschreibung: In Part I of the present study, the static analysis for the sliding of two identical spheres under displacement and force control was carried out. For linear and circular sliding trajectories, the contact traction evolution was analytically specified for both monotonic and reciprocal sliding regimes. Similarly, for the specified gravity loading, the driving force evolution and the sliding path were also determined. In the present Part II of the analysis, the dynamic response for the same sliding modes is presented. The contact traction and velocity evolutions are considered in detail. The analytical formulae are proposed for prediction of the tangential restitution coefficient, critical velocity, and time of contact for the displacement and load-controlled motions. The effects of loading and reloading in reciprocal sliding are also considered with account for the slip and sliding regimes. The generated results have practical aspects and can be implemented in modeling of the asperity and rough surface interaction, wear analysis and also in the development of the numerical discrete element method.

Beschreibung: Modified couple stress theory is a size-dependent theorem capturing the micro/nanoscale effects influencing the mechanical behaviors of the micro- and nanostructures. In this paper, it is applied to investigate the nonlinear vibration of carbon nanotubes under step DC voltage. The vibration, natural frequencies and dynamic pull-in characteristics of the carbon nanotubes are studied in detail. Moreover, the effects of various boundary conditions and geometries are scrutinized on the dynamic characteristics. The results reveal that application of this theory leads to the higher values of the natural frequencies and dynamic pull-in voltages.

Beschreibung: This paper presents an analytical approach to investigate the buckling and postbuckling behavior of functionally graded cylindrical shells subjected to thermal and axial compressive loads. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The governing equations are established within the framework of classical thin shallow shell theory taking both geometrical nonlinearity in von Kármán–Donnell sense and initial imperfection into consideration. Thermal stability analysis also incorporates the effects of tangential edge constraints. A Galerkin procedure is applied to derive expressions of load-deflection relations from which the thermal buckling loads and postbuckling curves of the shells are obtained by an iteration. Effects played by material and geometrical properties, tangential stiffness, imperfection and buckling modes are discussed.

Beschreibung: The classical linearized approximation to describe the elastic response of solids is the most widely used model in solid mechanics. This approximate model is arrived at by assuming that the norm of the displacement gradient is sufficiently small so that one can neglect the square of the norm in terms of the norm. Recent experimental results on Titanium and Gum metal alloys, among other alloys, indicate with unmistakable clarity a nonlinear relationship between the strain and the stress in the range of strain wherein one would have to use the classical linearized theory of elasticity, namely wherein the square of the norm of the strain can be ignored with regard to the value of the strain, leading to a dilemma concerning the modeling of the response, as the classical nonlinear Cauchy elastic model would collapse to the linearized elastic model in this range. A novel and important generalization of the theory of elastic materials has been suggested by Rajagopal in Appl Math 48: 279–319, 2003 and Zeit Angew Math Phys 58: 309–317, 2007 that allows for an approximation wherein the linearized strain can be a nonlinear function of the stress. In this paper, we show how this new theory can be used to describe the new experiments on Titanium and Gum metal alloys and also clarify several issues concerning the domain of application of the classical linearized theory.

Beschreibung: Beltrami–Schaefer stress functions are general solutions of the equilibrium equations of an elastic body without body force. In this paper, the representation of the non-uniqueness of these solutions is deduced by converting the equations into operator matrix form—including an operator matrix and its generalized inverse—and then deriving the representation using linear algebra. The completeness of the representation is proved in the process. In addition, the non-uniqueness of Helmholtz’s decomposition of a vector is proved.

Beschreibung: This study focuses on the development of a stochastic finite element-based methodology for failure assessment of composite beams with spatially varying non-Gaussian distributed inhomogeneities. The material properties in the individual laminae are modeled as non-Gaussian random fields, whose probability density functions and the correlations are estimated from the test data. The non-Gaussian random fields are discretized into a vector of correlated non-Gaussian random variables using the optimal linear expansion scheme that preserves the second-order non-Gaussian characteristics of the fields. Subsequently, the estimates of the failure probability are obtained from Monte Carlo simulations carried out on the vector of correlated random variables. Issues related to the computational efficiency of the proposed framework and the variabilities in the material properties are discussed. Numerical examples are presented, which highlight the salient features of the proposed method.

Beschreibung: The band gaps of a laminated piezoelectric/piezomagnetic phononic crystal with graded interlayer are studied in this paper. First, the transfer matrix method and the Bloch theorem are used to derive the dispersion equation. Next, the graded interlayer with different gradient profiles between the piezoelectric and the piezomagnetic materials is considered. The graded interlayer is modeled as a system of homogenous sublayers with both piezoelectric and piezomagnetic effects simultaneously. The effect of the graded interlayer on the band gap is introduced by inserting an additional interlayer transfer matrix in the calculation of the total transfer matrix. Finally, the dispersion equation is solved numerically, and the dispersive curves are shown in the Brillouin zone. The band gaps of the phononic crystal with graded interlayer are compared with that without graded interlayer. The influences of the graded interlayer with different gradient profiles on the band gap of a laminated piezoelectric/piezomagnetic phononic crystal are discussed based on the numerical results.

Beschreibung: Based on the strain gradient theory and the unified yield criterion, the borehole problem of an elasto-plastic plane strain body containing a traction-free hole subjected to uniform far-field stress is studied. The unified expressions for the plastic region radius and the stress concentration factor considering the size effect are derived on the basis of the unified yield criterion, respectively, which can be reduced to those based on the Tresca, von Mises and twin-shear criteria. The dependences of the plastic region radius and the stress concentration on the yield criteria, the material strain hardening level and the size effect are discussed. As a result, it is concluded that the influences of yield criteria and strain hardening level on the plastic region radius and the stress concentration are significant, and the size effect cannot be ignored when the hole size is in the order of tens of microns.