Adaptive Load Incremental Step in Large Increment Method for Elastoplastic Problems

Abstract

As a force-based finite element method (FEM), large increment method (LIM) shows unique advantages in material nonlinearity problems. In LIM for material nonlinearity analysis, adaptive load incremental step is a fundamental step for its successful application. In this work, a strategy to automatically refine the load incremental step is proposed in the framework of LIM. The adaptive load incremental step is an iterative process based on the whole loading process, and the location and number of post-refined incremental steps are determined by the posteriori error of energy on the pre-refined incremental steps. Furthermore, the iterative results from the pre-refined incremental steps can be utilized as the initial value to calculate the result for the post-refined incremental steps, which would significantly improve the computational accuracy and efficiency. The strategy is demonstrated using a two-dimensional example with a bilinear hardening material model under cyclic loading, which verifies the accuracy and efficiency of the strategy in LIM. Compared with the displacement-based FEM, which relies upon a step-by-step incremental approach stemming from flow theory, the adaptive load incremental step based on the whole loading process of LIM can avoid the cumulative errors caused by step-by-step in global stage and can quantify the accuracy of results. This work provides a guidance for the practical application of LIM in nonlinear problems.