Integration of constitutive equations with a new explicit scheme

Precise integration of a constitutive law is required whenever a boundary value problem is to be solved. In this paper a new explicit scheme for the integration of elasto-plastic constitutive models, that consist of algebraic yield condition and differential evolution equations, is presented. The scheme was primarily developed for the integration of constitutive models in boundary value problems which are solved with a direct solving technique (like in Abaqus/Explicit). Although the scheme is as fast and as simple for implementation as unstable explicit forward-Euler scheme, it can reach the same level of accuracy as commonly used backward-Euler scheme. Two examples are shown in the paper, the first one being simple for demonstration purposes only, whereas in the second one the scheme is also implemented in the Abaqus/Explicit user subroutine VUMAT. The obtained results confirm that the scheme is accurate and stable. It can be concluded in consequence, that the scheme is very handy for implementation of complex elasto-plastic constitutive laws into finite element software.