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  • Articles  (26)
  • plasticity  (26)
  • Wiley-Blackwell  (26)
  • American Institute of Physics (AIP)
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  • Mathematics  (26)
  • 1
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    Implicit constitutive modelling for viscoplasticity using neural networksThis paper was partially presented at XIXth International Congress of Theoretical and Applied Mechanics, Kyoto, in August 1996 (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 195-219 
    Details
    ISSN: 0029-5981
    Keywords: implicit constitutive modelling ; viscoplasticity ; plasticity ; neural networks ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Up to now, a number of models have been proposed and discussed to describe a wide range of inelastic behaviours of materials. The fatal problem of using such models is however the existence of model errors, and the problem remains inevitably as far as a material model is written explicitly. In this paper, the authors define the implicit constitutive model and propose an implicit viscoplastic constitutive model using neural networks. In their modelling, inelastic material behaviours are generalized in a state-space representation and the state-space form is constructed by a neural network using input-output data sets. A technique to extract the input-output data from experimental data is also described. The proposed model was first generated from pseudo-experimental data created by one of the widely used constitutive models and was found to replace the model well. Then, having been tested with the actual experimental data, the proposed model resulted in a negligible amount of model errors indicating its superiority to all the existing explicit models in accuracy. © 1998 John Wiley & Sons, Ltd.
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  • 2
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    An anisotropic elastoplastic-damage model for plain concreteThis paper is dedicated to Prof. F. Ziegler on the occasion of his 60th birthday (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 703-727 
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    ISSN: 0029-5981
    Keywords: damage ; plasticity ; concrete ; cracking ; Rankine criterion ; finite element analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A material model for plain concrete formulated within the framework of multisurface elastoplasticity-damage theory is proposed in this paper. Anisotropic stiffness degradation as well as inelastic deformations are taken into account. The applicability of the model encompasses cracking as well as the non-linear response of concrete in compression. The effect of different softening laws on the stress-strain relationship and on the dissipation is investigated in the context of a 1D model problem. The integration of the evolution laws is based on the standard return map scheme. Further computational issues include the stability of the local iteration procedure and the treatment of the apex region of the damage surface. The model is employed for re-analyses of a cylinder splitting test and of a notched concrete beam. Results from the composite elastoplastic-damage model are compared with test results and results from other material models for concrete, respectively. © 1998 John Wiley & Sons, Ltd.
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  • 3
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    Application of a parallel algebraic multigrid method for the solution of elastoplastic shell problems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 4 (1997), S. 223-238 
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    ISSN: 1070-5325
    Keywords: parallel computing ; algebraic multigrid ; CG method ; plasticity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The algebraic multigrid method (AMG) can be applied as a preconditioner for the conjugate gradient method. Since no special hierarchical mesh structure has to be specified, this method is very well suited for the implementation into a standard finite element program. A general concept for the parallelization of a finite element code to a parallel machine with distributed memory of the MIMD class is presented. Here, a non-overlapping domain decomposition is employed. A non-linear shell theory involving elastoplastic material behaviour of von Mises type with linear isotropic hardening is briefly introduced and a parallel algebraic multigrid method is derivated. As a numerical example we discuss the pinching of a cylinder undergoing large elastoplastic deformations. The performance of the solver is shown by using speed-up and scale-up investigation, as well as the influence of the problem size and the plasticity. © 1997 John Wiley & Sons, Ltd.
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  • 4
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    A cycle-oriented incremental analysis of shakedown problems (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3163-3179 
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    ISSN: 0029-5981
    Keywords: shakedown ; cyclic loads ; plasticity ; FEM ; incremental analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An effective method for determination of a quasi-static shakedown loading and of a steady-state response is proposed. The classical optimization problem based on Melan's theorem is suitably reformulated to meet the requirements of incremental analysis. The main attention is focused on the reduction of a computational time required for a completion of a transient elastic-plastic phase of deformation. The method differs significantly from classical incremental analyses. Here, a load cycle is approximated by the finite number of loading systems covering the cycle. Each system is then combined with a separate domain of the structure in which the load system can be treated as a dominant one. In this manner, the structure consists of parts, each of them undergoing suitably chosen one-parameter loading only. Such a modification allows us to build a set of non-linear equations for all loading systems covering the whole load cycle. As a consequence the structure can be treated as the one in which the transient plastic phase of deformation is analysed load cycle by load cycle without making load increments inside the considered cycle. Due to this innovation a significant reduction of the computational time required for the solution of the steady-state response of the structure is obtained what is illustrated on 3-D frames. © 1997 John Wiley & Sons, Ltd.
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  • 5
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    AN EFFICIENT STRESS ALGORITHM WITH APPLICATIONS IN VISCOPLASTICITY AND PLASTICITY (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 991-1013 
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    ISSN: 0029-5981
    Keywords: finite elements ; stress algorithm ; viscoplasticity ; plasticity ; kinematic hardening ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with two main topics. The first one concerns the equivalence of stress algorithms, based on a Backward-Euler-step applied on viscoplastic models of Chaboche-type, and their elastoplastic counterpart. Generally, the stress algorithm yields a system of non-linear algebraic equations and the corresponding consistent tangent operator, occurring in the principle of virtual displacements, leads to a system of linear equations. This procedure can be obtained utilizing only numerical methods. The second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of Armstrong/Frederick terms, which is equivalent to a multi-surface plasticity model. Applying this model a so-called problem-adapted stress algorithm is derived, where only one non-linear equation must be solved. This result is independent of the number of terms in the hardening model. Furthermore, only the viscoplastic algorithm must be implemented, since it includes the elastoplastic constitutive model as a special case. © 1997 by John Wiley & Sons, Ltd.
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  • 6
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    A FINITE ELEMENT FORMULATION OF THE RIGID-PLASTIC LIMIT ANALYSIS PROBLEM (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2063-2086 
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    ISSN: 0029-5981
    Keywords: limit analysis ; plasticity ; upper bound theorem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure for the finite element computation of the limit load of rigid-perfectly plastic solids is presented. The approach is based on the kinematic theorem of limit analysis, which is formulated so as to reduce the problem to the search of the essentially free minimum of a convex, but not everywhere differentiable, function. A conceptually simple solution strategy is presented and its effectiveness is demonstrated with reference to a few significant examples. Plane strain solids composed of materials governed by von Mises plasticity condition are considered, but extensions to a more general context can be envisaged. © 1997 by John Wiley & Sons, Ltd.
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  • 7
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    An approach to limit analysis with cone-shaped yield surfaces (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4011-4032 
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    ISSN: 0029-5981
    Keywords: limit analysis ; soil mechanics ; non-smooth optimization ; plasticity ; Drucker-Prager ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an algorithm for limit analysis with mixed approach by finite elements with application to geotechnical problems. The emphasis is on a special technique to deal with the singularity at the apex of a cone-shaped yield surface. The approach is based on the direct application of the sub-differential concept to the flow law and is essentially different from the Lagrange multipliers technique. The proposed algorithm does not require the regularization usually adopted for the singularities at the boundary of the plastic admissible stress region that occur in soil models. The case of a Drucker-Prager model is particularly considered, as well as the Mohr-Coulomb model in plane strain conditions. The algorithm is applied to a footing and a shallow tunnel. © 1997 John Wiley & Sons, Ltd.
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  • 8
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    A plane stress softening plasticity model for orthotropic materials (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4033-4057 
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    ISSN: 0029-5981
    Keywords: plasticity ; orthotropy ; fracture energy ; plane stress ; masonry ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A plane stress model has been developed for quasi-brittle orthotropic materials. The theory of plasticity, which is adopted to describe the inelastic behaviour, utilizes modern algorithmic concepts, including an implicit Euler backward return mapping scheme, a local Newton-Raphson method and a consistent tangential stiffness matrix. The model is capable of predicting independent responses along the material axes. It features a tensile fracture energy and a compressive fracture energy, which are different for each material axis. A comparison between calculated and experimental results in masonry shear walls shows that a successful implementation has been achieved. © 1997 John Wiley & Sons, Ltd.
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  • 9
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    CONSISTENT LINEARIZATION FOR THE EXACT STRESS UPDATE OF PRANDTL-REUSS NON-HARDENING ELASTOPLASTIC MODELS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1219-1235 
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    ISSN: 0029-5981
    Keywords: plasticity ; numerical integration algorithms ; consistent linearization ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a consistent algorithm, which combines the advantages of the exact time integration of Prandtl-Reuss elastoplastic models and the quadratic asymptotic convergence of Newton-Raphson iteration strategies. The consistent modulus is evaluated by a full linearization of the exact stress update procedure. Numerical tests for a thin wall tube subjected to combined loads of tension and torsion are performed to illustrate the accuracy and efficiency of the consistently linearized exact stress update algorithm described in the paper. For comparison purpose numerical results of the radial return method are also given.
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  • 10
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    SOME NOVEL DEVELOPMENTS IN FINITE ELEMENT PROCEDURES FOR GRADIENT-DEPENDENT PLASTICITY (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2477-2505 
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    ISSN: 0029-5981
    Keywords: higher-order continua ; plasticity ; localization ; mixed elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Improved algorithms are proposed for a gradient plasticity theory in which the Laplacian of an invariant plastic strain measure enters the yield function. Particular attention is given to the type of finite elements that can be used within the format of gradient-dependent plasticity. Assuming a weak satisfaction of the yield function, mixed finite elements are developed, in which the invariant plastic strain measure and the displacements are discretized. Two families of finite elements are developed: one in which the invariant plastic strain measure is interpolated using C1-continuous polynomials, and one in which penalty-enhanced C0-continuous interpolants are used. The performance of both families of finite elements is assessed numerically in one-dimensional and two-dimensional boundary value problems. The regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated, both for mesh refinement and for the directional bias of the grid lines.
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  • 11
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    MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 2: NUMERICAL SIMULATION (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3601-3623 
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    ISSN: 0029-5981
    Keywords: strong discontinuity analysis ; localization ; damage ; plasticity ; strain softening ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the basis of the strong discontinuity analysis of standard local stress-strain constitutive equations, a finite element framework for the simulation of strong discontinuities, which belongs to the family of assumed enhanced strain methods, is presented. Taking the standard linear triangle as the underlying element, an additional incompatible mode leads to the formulation of an enriched strain field which is shown to be able to appropriately capture strong discontinuities. The presented numerical simulations show that mesh size and mesh alignment dependencies can be completely removed.
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  • 12
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    ERROR ESTIMATION AND ADAPTIVITY IN ELASTOPLASTICITY (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 189-217 
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    ISSN: 0029-5981
    Keywords: a posteriori error ; finite element ; plasticity ; adaptativity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method is developed to control the parameters of a finite element computation for time-dependent material models. This method allows the user to obtain a prescribed accuracy with a computational cost as low as possible. To evaluate discretization errors, we use a global error measure in constitutive relation based on Drucker's inequality. This error includes, over the studied time interval, the error of the finite element model and the error of the algorithm being used. In order to master the size of the elements of the mesh and the length of the time increments, an error estimator, which permits estimating the errors due to the time discretization, is proposed. These tools are used to elaborate two procedures of adaptivity. Various examples for monotonous or non-monotonous loadings, for 2-D or axisymmetric problems, show the reliability of these procedures.
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  • 13
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    AN IMPLICIT PROJECTION ALGORITHM FOR SIMULTANEOUS FLOW OF PLASTICITY AND DAMAGE IN STANDARD GENERALIZED MATERIALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3065-3082 
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    ISSN: 0029-5981
    Keywords: biomechanics ; damage ; finite element method ; plasticity ; standard generalized material ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Motivated by mechanical analysis of cancellous bone, a 3D constitutive law describing the simultaneous flow of rate-independent plasticity and damage is developed in the framework of thermodynamics of irreversible processes with internal variables. Following the hypothesis of standard generalized materials, a free energy and a dissipation potential are postulated and the associated flow rules derived with the tools of convex analysis. On the computational side, the classical implicit projection (or catching up) algorithm used in plasticity is extended to account for the additional flow of damage. Due to the existence of a dissipation potential, linearization of the incremental algorithm provides a symmetric tangent operator. Numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the quadratic convergence of the algorithm.
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  • 14
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    MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 1: FUNDAMENTALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3575-3600 
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    ISSN: 0029-5981
    Keywords: strong discontinuity analysis ; localization ; damage ; plasticity ; strain softening document ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses some fundamental aspects about the use of standard constitutive equations to model strong discontinuities (cracks, shear bands, slip lines, etc.) in solid mechanics analyzes. The strong discontinuity analysis is introduced as a basic tool to derive a general framework, in which different families of constitutive equations can be considered, that allows to extract some outstanding aspects of the intended analysis. In particular, a link between continuum and discrete approaches to the strain localization phenomena is obtained. Applications to standard continuum damage and elastoplastic constitutive equations are presented. Relevant aspects to be considered in the numerical simulation of the problem (tackled in Part 2 of the work) are also presented.
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  • 15
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    LARGE DISPLACEMENT ELASTOPLASTIC ANALYSIS OF SEMIRIGID STEEL FRAMES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 741-762 
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    ISSN: 0029-5981
    Keywords: elastoplastic analysis ; mathematical programming ; plasticity ; semirigid connections ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical programming approach for the large displacement analysis of elastoplastic plane frames with flexible, partial-strength beam-to-column connections is proposed. The incremental formulation is developed within the framework of a discrete model, piecewise linear yield surfaces and large displacement theory. It is based on the fundamental relations of equilibrium, compatibility and constitutive laws, all expressed in incremental form. The irreversible plasticity laws are used in a stepwise holonomic format. A feature of the final mathematical programming problem, known as a non-linear complementarity problem, is that the governing relations exhibit symmetry as a result of the use of fictitious quantities and non-linear residuals. The iterative predictor-corrector computational scheme adopted has the ability of tracing historically a sequence of plastic hinge activations and/or unloadings well beyond any critical point. Numerical examples are presented to illustrate and validate the accuracy of the approach.
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  • 16
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    Bounding-surface plasticity for non-linear analysis of space structures (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 797-808 
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    ISSN: 0029-5981
    Keywords: bounding-surface ; plasticity ; non-linear ; space structures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a method for the non-linear analysis of space structures subjected to static and cyclic loading. A bounding-surface kinematic hardening plasticity model is used to simulate the hardening and hysteritic material behaviour. The model is used in conjunction with the lumped plasticity assumption coupled with the concept of a yield surface in force space. A hardening coefficient matrix which is a function of the plastic strain and the elastic stiffness matrix is introduced while the vectorial nature of the material memory parameters is maintained. This provides a smooth transition from the elastic to the plastic regime which simulates the hysteresis loops quite accurately. An updated Lagrangian formulation is used together with a predictor/corrector solution method. Several examples are presented to demonstrate the accuracy and efficiency of the method.
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    URL: http://dx.doi.org/10.1002/nme.1620380506
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  • 17
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    Pressure-dependent plasticity models: Loading-unloading criteria and the consistent linearization of an integration algorithm (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 339-345 
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    ISSN: 1069-8299
    Keywords: numerical integration ; plasticity ; pressure-dependent plasticity ; porous metals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general methodology for the numerical integration of pressure-dependent plasticity models is developed, and the corresponding ‘linearization moduli’ are derived.
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    URL: http://dx.doi.org/10.1002/cnm.1640110407
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    Easy adaptation of a commercial FEM code for self-similarity (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 117-125 
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    ISSN: 1069-8299
    Keywords: self similarity ; FEM ; plasticity ; crack growth ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Self-similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self-similar. In heat conductivity, the progressive phase transformation near a point-shaped heat source results in a self-similar situation. The problem may be non-linear and history-dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self-similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited.This short communication demonstrates how an available FEM code (including many commercial codes) may be conveniently used for investigations of self-similar situations in solid mechanics. Quasistatic elastic-plastic problems are considered. The theory covers a general material behaviour including large strains and large deformations. The FEM code must allow for a user-defined material. The technique is demonstrated on a problem for an edge crack growing while the scale of yielding is large. The result is compared with calculations using a node relaxation technique.
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    URL: http://dx.doi.org/10.1002/cnm.1640110205
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    Elasto-plastic finite element analysis with fuzzy parameters (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 531-548 
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    ISSN: 0029-5981
    Keywords: fuzzy set ; finite element ; plasticity ; geotechnical ; reliability index ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an elastoplastic analysis based on fuzzy mathematics and using finite element method will be described. The Drucker-Prager yield criterion and the elasto-plastic matrix are fuzzified for the non-linear analyses which adopt the initial stress method for the solution. A numerical example is given to illustrate the possible variations in the displacements and the extent of plastic zones at the discrete membership functions. A reliability index of a membership grade based on the concept of non-probabilistic entropy is also proposed.
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    URL: http://dx.doi.org/10.1002/nme.1620380403
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    A plasticity model and algorithm for mode-I cracking in concrete (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2509-2529 
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    ISSN: 0029-5981
    Keywords: concrete ; cracking ; fracture ; mode-I ; plasticity ; softening ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of plasticity models which utilize Rankine's (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions. The formulation encompasses isotropic and kinematic hardening/softening rules, and incremental (flow theory) as well as total (deformation theory) formats are considered. An Euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the Euler backward scheme. Particular attention is paid to the corner regime, that is when the two major principal stresses become equal. A detailed comparison has been made of the proposed plasticity-based crack formulations and the traditional fixed and rotating smeared-crack models for a homogeneously stressed sample under a non-proportional loading path. A comparison between the flow-theory-based plasticity crack models and experimental data has been made for a Single Edge Notched plain concrete specimen under mixed-mode loading conditions.
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    URL: http://dx.doi.org/10.1002/nme.1620381503
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    A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 4009-4034 
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    ISSN: 0029-5981
    Keywords: boundary elements ; damage mechanics ; fracture growth ; multipole algorithms ; plasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we introduce a method to reduce the solution cost for Boundary Element (BE) models from O(N3)operations to O(N2logN) operations (where N is the number of elements in the model). Previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh. We have developed the Spectral Multipole Method (SMM) which can be used not only for problems with arbitrary geometries but also with a variety of element types. The memory necessary to store the required influence coefficients for the spectral multipole method is O(N) whereas the memory required for the traditional Boundary Element method is O(N2). We demonstrate the savings in computational speed and fast memory requirements in some numerical examples. We have established that the break-even point for the method can be as low as 500 elements, which implies that the method is not only suitable for extremely large-scale problems, but that it also provides a useful bridge between the small-scale and large-scale problems. We also demonstrate the performance of the multipole algorithm on the solution of large-scale granular assembly models. The large-scale BE capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and brittle fracture.
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    URL: http://dx.doi.org/10.1002/nme.1620382307
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  • 22
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    Non-linear finite element formulation of kinematic limit analysis (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2775-2807 
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    ISSN: 0029-5981
    Keywords: bearing capacity ; incompressibility ; plasticity ; upper bound theorem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of the research presented in this paper was to develop a general computational method for kinematic limit analysis problems that involve the determination of an optimal kinematically admissible velocity field of the studied structure under external loads. With the failure velocity field available, we can obtain a numerical estimate of the limit load exerted to the structure. The general kinematic limit analysis is characterized by the minimization of the plastic potential power dissipation functional of the mechanical system. This minimization problem was approached previously by linear and non-linear programming schemes. In this paper, a new non-linear solution scheme is described which is based on previous research on the regularized method. The regularized functional is a convex and non-linear functional whose minimum represents a viscoplastic potential power dissipation, the velocity which minimizes this functional was proved to be kinematically admissible and can be obtained by the augmented Lagrangian method. This paper demonstrates that the non-linear programming scheme is applicable to direct limit analysis. The basic idea of using this optimization method is to tranform the functional with a non-linear term of the first-order derivatives of the velocity to a functional in which this term is uncoupled with the strain rates, and in consequence the augmented Lagrangian (transformed functional) can be solved more easily. Some special problems related to incompressibility and discontinuity are discussed. A simple and accurate scheme is proposed to deal with the incompressibility problem and the problem of the linear Mohr-Coulomb yield surface in the principal stress space. Examples of plane stress and plane strain problems are given for von Mises and Mohr-Coulomb materials. Numerical results are provided in graphical form which serves to illustrate the kinematic admissibility. The limit loads obtained agreed well with the analytical results, which demonstrates the efficiency and accuracy of the non-linear computational method presented.
    Additional Material: 25 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381607
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    Dual finite element analysis for plasticity-friction torsion of composite bar (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 1901-1916 
    Details
    ISSN: 0029-5981
    Keywords: plasticity ; friction ; torsion ; finite element method ; equilibrium model of FEM ; variational inequalities ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The quasi-static problem of torsion of an elastic-plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic-plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law - it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381107
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  • 24
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    Numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3403-3431 
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    ISSN: 0029-5981
    Keywords: damage ; plasticity ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with a class of rate-independent metal plasticity models which exhibit non-linear isotropic hardening, non-linear kinematic hardening (Chaboche-Marquis model) and ductile damage (Lemaitre-Chaboche model). The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent operator is obtained by exact linearization of the algorithm. Despite the complexity of the constitutive equations, closed-form expressions are derived, without any approximations. Analytical, numerical and experimental results are presented and discussed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620382004
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  • 25
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    Some observations on element performance in isochoric and dilatant plastic flow (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2887-2906 
    Details
    ISSN: 0029-5981
    Keywords: element performance ; plasticity ; locking ; spurious mechanisms ; dilatancy ; contractancy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of finite elements is scrutinized in isochoric and dilatant/contractant plastic flow. Standard displacement based elements, uniformly and selectively integrated elements, and elements with augmented strain rate fields are considered in plane-strain, axisymmetric and three-dimensional configurations with particular reference to the kinematic constraint imposed by dilatant/contractant plastic flow. It turns out that findings for isochoric deformations do not necessarily carry over to cases with plastic dilatancy or contraction. For the elements with augmented strain rate fields the danger of spurious mechanisms in ideal plasticity is brought out. A particular strategy which augments only the normal strain rates at the expense of a lesser improvement for the bending behaviour does not suffer from the possibility of spurious modes, while preserving the ability to accommodate dilatant/contractant plastic flow. Illustrative examples on plane-strain, axisymmetry and three-dimensional structures are included which support the above findings.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381704
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    A generalized fictitious crack model based on plastic localization and discontinuous approximation (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3167-3188 
    Details
    ISSN: 0029-5981
    Keywords: plasticity ; discontinuity ; regularization ; interface relation ; crack band ; mesh realignment ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Modelling of crack behaviour is an important topic when establishing realistic macroscopic constitutive relations for brittle materials, such as ceramics, concrete, rock, etc. Upon introducing discontinuous approximation of the continuum, a crack model is derived on the basis of the Rankine plasticity model and the fictitious crack concept of Hillerborg et al.1 The derivation results in a crack band relation, whose constitutive properties are based on failure kinematics that resemble the classical shear band concept. It appears that it is, essentially, the acoustic tensor that governs the constitutive relation for the crack band. This tensor has previously been analysed extensively to determine conditions for loss of ellipticity and possibility for discontinuous bifurcation in the rate of deformation field. In the present approach a similar analysis is carried out to determine conditions that characterize fracture initiation and crack band orientation. The model is implemented together with a mesh realignment strategy, and a solution advancement formulation, that ensures the crack propagates along critical interfacial directions. These directions depend on the actual stress state and are kept fixed after plastic localization (or cracking) has occurred. Hence, a ‘fixed crack’ model is obtained. Numerical results involving successive crack development as well as failure of concrete beams are presented.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381809
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