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

Abstract

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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