The overall elastoplastic behavior of multiphase materials with isotropic components

A multiphase material is considered, which consists of a homogeneous elastoplastic matrix containing a homogeneous statistically uniform random set of ellipsoidal elastic inclusions. An approach based on the multiparticle effective field method is introduced for determining the overall elastoplastic behavior of the material under monotonic loading. A secant modulus concept is employed, and linearized problems are solved at each step of an iterative procedure. Physically consistent assumptions are used for linearizing nonlinear functions which depend on the phase averages of the second invariant of stress and on the stress deviator. Exact expressions for the second moments of the microstresses are employed.