The Determination of the Efficient Elastic Modules in Composition Material

Abstract

The numerical-analytical method of the determination of the efficient elastic modules in composition material is offered. The material is prototyped by endless elastic medium with alike disjoint inclusions, located in nodes two-dimensional or three-dimensional orthogonal of the lattice. On the first stage by method finite element (FEM), considering periodic nature of the strain condition and connected with this particularities strained, are defined strain and displacement on border of the inclusion typical element. On second stage these given are used directly for calculation of the efficient modules by means of the energy method and principle Eshelby J. D., allowing define the energy elastic deformation in typical element by calculations integral on surfaces of the inclusion. The proposed method in equal degree efficient at decisions of the worded problems, both for isotropic, and for anisotropic ambiences (transversal- isotropic and orthotropic). The decisions are received for circular and elliptical inclusions in flat event, but in three-dimensional event for spherical and ellipsoidal of the inclusions.