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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 315-336 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Algorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso-error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator. The model has been applied to three shell/plate structures.
    Additional Material: 17 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2477-2505 
    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.
    Additional Material: 21 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4033-4057 
    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.
    Additional Material: 13 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 521-539 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity. To properly solve the set of non-linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements. For appropriate boundary conditions this formulation can also be derived from a variational principle. Accordingly, the theory is complete.The addition of gradient terms becomes significant when modelling strain-softening solids. Classical models then result in loss of ellipticity of the governing set of partial differential equations. The addition of the gradient terms preserves ellipticity after the strain-softening regime has been entered. As a result, pathological mesh dependence as obtained in finite element computations with conventional continuum models is no longer encountered. This is demonstrated by some numerical simulations.
    Additional Material: 7 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2509-2529 
    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.
    Additional Material: 13 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2887-2906 
    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.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3391-3403 
    ISSN: 0029-5981
    Keywords: continuum damage mechanics ; localization ; gradient dependence ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
    Additional Material: 8 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Mechanics of Cohesive-frictional Materials 3 (1998), S. 323-342 
    ISSN: 1082-5010
    Keywords: concrete fracture ; computational modelling ; continuum damage mechanics ; localization ; regularization ; gradient enhancement ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Classical continuum damage theory for quasi-brittle fracture exhibits an extreme sensitivity to the fineness and orientation of the spatial discretization in finite element simulations. This sensitivity is caused by the fact that the mathematical description becomes ill-posed at a certain level of accumulated damage. The ill-posedness can be removed by the use of a gradient-enhanced damage model. In this model, higher-order deformation gradients give rise to a non-local effect, which regularizes the localization of deformation and thus renders numerical analyses mesh-objective.The mesh objectivity of the gradient-enhanced damage approach is demonstrated by the application to two concrete fracture experiments: a double-edge notched bar subjected to a uniaxial, tensile load and a single-edge notched beam under anti-symmetric four-point loading. Both the initiation and the propagation of damage can be simulated. Particularly the latter aspect calls for an appropriate definition of the strain measure which governs the evolution of damage. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 18 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Mechanics of Cohesive-frictional Materials 1 (1996), S. iii 
    ISSN: 1082-5010
    Keywords: Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 837-844 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A scheme is presented that automatically determines the magnitude of the time step in quasistatic boundary value problems discretized via some customary method (finite elements, finite differences). The basic idea stems from the path-following techniques widely employed in purely static analyses in the sense that the incremental displacements, measured in some suitable norm, are constrained to a prefixed value. Examples of trusses composed of a viscoelastic material are included to demonstrate the effectiveness of the method.
    Additional Material: 6 Ill.
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