Study of Two‐Surface Plasticity Theory

This paper investigates how the two‐surface plasticity theory predicts material behavior under nonproportional loading conditions. Closed‐form solutions are found for a thin‐walled tube subjected to combined internal pressure and axial load, and the tube response under cyclic linear stress paths is discussed. The investigation shows that according to the two‐surface plasticity theory, the response of the material will stabilize immediately during the first 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 yielding a constant plastic strain growth rate. As a result, the two‐surface plasticity theory predicts that under any cyclic linear loading conditions, the response of the material can always be ratchetting, with no possibility of shakedown of any kind, which violates those aspects of material behavior that are generally deemed essential.