Application of closest point projection method to unified hardening model

Abstract

This paper presents a framework of the closest point projection method (CPPM) based on the unified hardening (UH) model. The UH model based on the Cam-clay model and the concept of the subloading yield surface was rewrote as a concise form of classical elasto-plastic model. Then the CPPM algorithm combining the exact elastic property and the spatially mobilized plane (SMP) strength criterion by the transformed stress method could be conveniently derived for the numerical implementation of the UH model. According to this algorithm, the consistent tangent operator corresponding to the final stress state of the integration increment was deduced formally. And the mean stress probed by the elastic predictor was avoided to be negative or zero for the usage of exact elastic property. Eventually, the accuracy, robustness and efficiency of the proposed integration scheme were demonstrated by the numerical examples including the boundary value problems of the single integral point and multi-elements of geotechnical engineerings, which was respectively compiled as the single integral point program and the user defined subroutine (UMAT) of the commercial finite element program ABAQUS.