Tlastoplastic properties of multicomponent composites

Abstract

Predicting the inelastic properties of materials with random discontinuities is one of the most important current developments in the mechanics of deformable solids. Modeling the macroscopic governing relations and calculating the effective characteristics of such media in many cases permits satisfactory estimation of the strain properties, limiting state, and load-carrying capacity of structural elements made of composites, powders, and other types of structural materials. The macroscopic behavior of multicomponent rigid-plastic and elastoplastic composites was examined in [I, 2] within the framework of flow theory. Here, we examine the use of the method of generalized singular approximation of the theory of random fields to describe small elastoplastic strains of composite materials with an arbitrary number of constituents. A similar problem was solved in a correlation approximation in [3, 4]. Let a micro-inhomogeneous medium occupying a volume V bounded by the surface S be composed of n different elastoplastic constituents connected to each other with ideal adhesion~ The governing relations for the material of each constituent are given by the equations