A variant of the theory of plasticity of two-phase composite media

Abstract

A mathematical model is developed describing the mechanical behavior of an elastic-plastic composite on the basis of phase properties and the micro-structural geometry. The overall yield condition and hardening rule are obtained in general form for two-phase composites with different phase properties. The constituents may be elastic-perfectly plastic or strain hardening ones. The case of a plastic state of both components is investigated in detail. The loading surface in the space of macro stresses has singular points. Plastic micro strains cannot be eliminated from the system of equations, and must be considered as additional hardening parameters. The hardening of composites with ideally plastic constituents is limited. The limiting surface exists in the space of macro stresses which defines the condition of perfect plasticity. However, it is not associated with the plastic flow law.