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

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.

Citation

Rezaiee‐Pajand, M. and Nasirai, C. (2007), "Accurate integration scheme for von‐Mises plasticity with mixed‐hardening based on exponential maps", Engineering Computations, Vol. 24 No. 6, pp. 608-635. https://doi.org/10.1108/02644400710774806