Exact integration of the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening

Kossa, Attila; Szabó, Loránd

doi:10.1016/j.ijplas.2008.08.003

Cited by 36 publications

(10 citation statements)

References 32 publications

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“…where {σ NURBS } is the stress return location associated with the NURBS model and {σ e } is the exact stress return [14]. Although errors of over 20% are present in the model, exactly the same level of errors are observed in the von Mises yield surface integrated with a conventional bE stress integration procedure.…”

Section: Materials Point Investigationsmentioning

confidence: 90%

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

Coombs

Motlagh

2017

Computer Methods in Applied Mechanics and Engineering

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Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThis paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al. [8] to include isotropic hardening of the yield surfaces. The approach allows any smooth isotropic yield envelope to be represented by a NURBS surface. The key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material. The model is integrated using a fully implicit backward Euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations. This provides a powerful framework for elasto-plastic constitutive models where, unlike the majority of models presented in the literature, the underlying numerical algorithm (and implemented code) remains unchanged for different yield surfaces. The performance of the algorithm is demonstrated, and validated, using both material point and boundary values simulations including plane stress, plane strain and three-dimensional examples for different yield criteria.

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Section: Materials Point Investigationsmentioning

confidence: 90%

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

Coombs

Motlagh

2017

Computer Methods in Applied Mechanics and Engineering

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“…, Doghri , Hartmann and Haupt , Simo and Meschke , Matzenmiller and Taylor , Miehe , Wei et al . , Alfano and Rosati , Auricchio and Taylor , Lof and van den Boogaard , Bruhns and Bongmba , Keavey , Assensio and Moreno , Auricchio and Veiga , Kossa and Szabo , Szabo , and many others. Recently, other developments have been made by, for example, Kollmann and Cordts for an implicit time integration scheme for viscoplasticity, Snyder and Bathe and Kojić and Bathe for thermoelastoplastic and creep problems, Boisse et al .…”

Section: Introductionmentioning

confidence: 99%

Automatic consistency integrations for the stress update of J₂ elastoplastic rate constitutive equations with combined hardening

Yin

Xiao

2014

Numerical Meth Engineering

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SUMMARYA novel method is introduced to study numerical integrations of J2 elastoplastic rate constitutive equations with general combined hardening. The basic idea is to transform the usual time rate constitutive equations into those with reference to the equivalent plastic strain. By virtue of tensorial matrix operations, we show that these transformed equations may be converted to a linear differential system governing the shifted stress and the plastic multiplier. From this system, we derive explicit integrations for the shifted stress and then for the back stress and the Cauchy stress. We demonstrate that these results are accurate up to within a third order term of the equivalent plastic strain increment. In particular, for pure kinematic hardening, we show that the integrations obtained can achieve automatic enforcement of both the plastic consistency condition and the loading condition, thus bypassing the numerical treatment of the latter two. Furthermore, we explain that, with the new algorithm for the stress update, the continuum tangent moduli may be used to ensure a quadratic rate of convergency in Newton's iteration scheme for the balance equation. Numerical examples suggest that the new algorithm may be more accurate and efficient than the widely used return algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

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“…Menzel and Steinmann, 2001;Sloan, 1987;Sloan and Booker, 1992, Wallin and Ristinmaa, 2001Kossa and Szabo, 2009). The major advantages of this class of methods are its algebraic simplicity and accuracy for sensitive constitutive models.…”

Section: Introductionmentioning

confidence: 99%

Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge–Kutta integration scheme

Borgqvist

Wallin

2012

International Journal of Damage Mechanics

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This article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge-Kutta scheme originally proposed by Ellsiepen (1999) is investigated. The diagonal implicit Runge-Kutta scheme is applied to the balance of momentum as well as the constitutive evolution equations. When applied to finite strain multiplicative plasticity, the diagonal implicit Runge-Kutta scheme destroys the plastic incompressibility of the underlying continuum evolution laws. Here, the evolution laws are modified such that the incompressibility of the plastic deformation is preserved approximately. The presented numerical examples reveal that a significant increase in accuracy can be obtained at virtually no cost using the diagonal implicit Runge-Kutta scheme. It is also shown that for the model including a discontinuous evolution law, the superiority of the diagonal implicit Runge-Kutta scheme over the implicit Euler scheme is reduced.

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Exact integration of the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening

Cited by 36 publications

References 32 publications

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

Automatic consistency integrations for the stress update of J₂ elastoplastic rate constitutive equations with combined hardening

Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge–Kutta integration scheme

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Exact integration of the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening

Cited by 36 publications

References 32 publications

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

Automatic consistency integrations for the stress update of J2 elastoplastic rate constitutive equations with combined hardening

Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge–Kutta integration scheme

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Automatic consistency integrations for the stress update of J₂ elastoplastic rate constitutive equations with combined hardening