Representation of cyclic hardening and softening properties using continuous variables

Abstract

Abstract Our aim is the modeling of cyclic hardening, cyclic softening, cyclic mean stress relaxation, and additional nonproportional cyclic hardening. We do so by means of hardening functionals for back stress and yield stress without employing additional memory surfaces. Rather, we suppose all quantities to evolve simultaneously during elastic-plastic loading in a continuous manner. The basic idea is to formulate evolution equations for the hardening variables, which are of the “hardening/dynamic recovery” format with respect to a transformed arc length. The corresponding transformation is influenced by continuously evolving parameters, measuring strain amplitude and nonproportionality during the recent process history. Although the resulting, model has a very simple structure, it is capable of describing the basic phenomena under quite general loading conditions.