One Inclusion in the Infinite Peristatic Matrix

Abstract

A basic problem of of micromechanics is analysis of one inclusion in the infinite matrix subjected to a homogeneous remote loading. A heterogeneous medium with the bond-based peri-dynamic properties (see Silling, J. Mech. Phys. Solids 2000; 48:175–209) of constituents is considered. At first a volumetric boundary conditions are set up at the external boundary of a final domain obtained from the original infinite domain by truncation. An alternative sort of truncation method is periodisation method when a unite cell (UC) size is increased while the inclusion size is fixed. In the second approach, the displacement field is decomposed as linear displacement corresponding to the homogeneous loading of the infinite homogeneous medium and a perturbation field introduced by one inclusion. This perturbation field is found by the Green function technique as well as by the iteration method for entirely infinite sample with an initial approximation given by a driving term which has a compact support. The methods are demonstrated by numerical examples for 1D case. A convergence of numerical results for the peristatic composite bar to the corresponding exact evaluation for the local elastic theory are shown.