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Accurate integration scheme for von‐Mises plasticity with mixed‐hardening based on exponential maps

Accurate integration scheme for von‐Mises plasticity with mixed‐hardening based on exponential maps Purpose – This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works. Design/methodology/approach – An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner. Findings – The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate. Research limitations/implications – Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening. Practical implications – Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes. Originality/value – The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

Accurate integration scheme for von‐Mises plasticity with mixed‐hardening based on exponential maps

Engineering Computations , Volume 24 (6): 28 – Aug 28, 2007

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Publisher
Emerald Publishing
Copyright
Copyright © 2007 Emerald Group Publishing Limited. All rights reserved.
ISSN
0264-4401
DOI
10.1108/02644400710774806
Publisher site
See Article on Publisher Site

Abstract

Purpose – This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works. Design/methodology/approach – An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner. Findings – The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate. Research limitations/implications – Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening. Practical implications – Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes. Originality/value – The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance.

Journal

Engineering ComputationsEmerald Publishing

Published: Aug 28, 2007

Keywords: Integration; Algorithmic languages

References