A simple implicit scheme for stress response computation in plasticity models

Abstract

In this work, the authors propose an efficient numerical method for evaluating the plastic response of a material for the applied load. Focus is confined to plasticity models using a yield surface and to small strains. The main advantage of the method is that there is no iteration need be done for the yield surface drift correction and applies a single point integration. To compute the response of a material for a particular loading, the incremental constitutive equation is derived from the plasticity model used and then it is numerically integrated. Since finite increments are used in the numerical integration procedure, computational errors crop up and accumulate causing inconsistencies in the response calculation. This is usually seen in the form of a yield surface drift. To alleviate this problem, the quantities updated have to be corrected appropriately so that the yield condition is satisfied. The authors propose a method here which corrects implicitly the quantities updated to avoid the yield surface drift. No iterations are involved. The discrete consistency condition is used in the proposed model. The authors have shown in this work that the method can be applied easily to several yield conditions and hardening rules. A numerical study is performed to evaluate the performance of the model compared to the other methods to show the efficiency of this method in the response calculations for yield surface models.