A globally convergent smoothing Newton method for the second order cone complementarity approach of elastoplasticity problems

Abstract

A new algorithm for solving small-deformation elastoplasticity problems as second order cone complementarity problems (SOCCPs) is presented. The SOCCP is derived from the Hellinger–Reissner variational principle, and then solved with a smoothing Newton method that is modified from the globally convergent Qi-Sun-Zhou method. The method is compared with two well-established methods: the return-mapping method and the conic programming (CP) approach with primal–dual interior-point method. Numerical results indicate that the proposed method shares common characteristics of CP class methods and offers better convergence efficiency in some cases. Moreover, it is shown that the proposed method can be imbedded in the framework of conventional finite element codes with only a few modifications, which makes it easy-to-implement and adaptive to large-scale parallel computing.