Implementation of a generalized midpoint algorithm for integration of elastoplastic constitutive relations for von mises' hardening material

This paper presents a detailed description of the computer implementation of a generalized midpoint algorithm for integration of constitutive relations for von Mises' hardening material. A nonlinear scalar equation for determination of the plastic multiplier is derived. The solution of this equation for a hardening material, by the Newton-Raphson method, usually converges in three-four iterations. The results obtained by the generalized midpoint method for the hollow sphere under internal pressure are compared with analytical and converged subincrementation solutions. A pseudocode of the algorithm and a module in the C programming language is given in the Appendix.