A General Solution to the Two-Surface Plasticity Theory

Abstract

This paper obtains a closed-form general solution to the two-surface plasticity theory for linear stress paths. The simple two-surface model is discussed first. It is shown that according to this model, the response of the material stabilizes immediately during the first loading cycle. That is, the memory surface reaches its maximum size with a radius equal to the maximum effective stress and then remains unchanged thereafter, while the yield center translates along a line parallel to the stress path, thus always leading to a constant plastic strain growth rate. As a result, the model predicts that under any cyclic linear loading conditions, the material response can always be ratchetting, with no possibility of shakedown of any kinds, which violates those aspects of material behavior that are generally deemed essential in constitutive modeling. The general two-surface theory is also discussed in this paper, and some comments are made.