Improvement of accuracy of cycle jump method for analysis under cyclic load (Extension to finite deformation problem)

Abstract

In this paper, a formulation and some computational results of cycle jump method for finite strain elastic-plastic problems subject to cyclic loads are presented. The cycle jump method is to shorten the total computational time. An analysis using the cycle jump method is carried out such that a combination of a few cycles of cycle-by-cycle analysis and the cycle jump by extrapolating physical quantities such as the plastic strains for many cycles based on the results of preceding cycle-by-cycle analysis. The cycle-by-cycle analysis and the cycle jump are repeated until the desired load cycle is achieved. When the method is applied to the finite strain elastic-plastic problem, it involves the finite rotation and the finite stretch. Then, both of them are decomposed into the elastic and the plastic components. This paper presents appropriate treatments on the rotation and the stretch under the multiplicative decomposition of the deformation into the plastic and the elastic parts. Then, some numerical examples are shown. It is concluded that the proposed cycle jump approach performs well under a certain conditions. Such conditions are also described in the paper.