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Integration of nonlinear mixed hardening models

Integration of nonlinear mixed hardening models Purpose – The purpose of this paper is to present a new effective integration method for cyclic plasticity models. Design/methodology/approach – By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm. Findings – The numerical tests show the robustness and high efficiency of the proposed integration scheme. Research limitations/implications – The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening. Practical implications – Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses. Originality/value – The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Multidiscipline Modeling in Materials and Structures Emerald Publishing

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Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
1573-6105
DOI
10.1108/1536-540911178252
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to present a new effective integration method for cyclic plasticity models. Design/methodology/approach – By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm. Findings – The numerical tests show the robustness and high efficiency of the proposed integration scheme. Research limitations/implications – The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening. Practical implications – Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses. Originality/value – The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

Journal

Multidiscipline Modeling in Materials and StructuresEmerald Publishing

Published: Sep 27, 2011

Keywords: Differential equations; Vectors; Plasticity; Exponential based integration method; Discrete consistent tangent matrix; Cyclic plasticity; Nonlinear mixed hardening; Exponential isotropic hardening

References