Multi Scale Modeling of Thermoelastic Properties of Composites with Periodic Structure of Heterogeneities


The majority of processes in composite materials involve a wide range of scales. Because of the scale disparity in multi scale problem, it's often impossible to resolve the effect of small scales directly. In this paper we perform multi scale modeling in order to analyze properties of composite materials with periodical structure under temperature and stresses influence. We consider a homogeneous matrix with periodic system of spherical particles separated from the matrix by an interphase. Each component has its own thermodynamic and mechanical (elastic) properties. We replace differential equations with rapidly varying coefficients by homogenized equations having effective parameters, which incorporate multi scale structure and properties of any component. We study, how effective properties of the system "matrix-interphase-inclusion" can depend on sizes of inclusions, thickness of interphase, mechanical and thermodynamic properties of components of a composite material.