EFFECTIVE DISPLACMENTS OF PERIDYNAMIC HETEROGENEOUS BAR LOADED BY BODY FORCE WITH COMPACT SUPPORT
Valeriy A. Buryachenko
Abstract
A statistically homogeneous random bar with the bond-based peridynamic properties of constituents is considered for a static case. For both statistically homogeneous 1D composites and homogeneous remote loading, the effective properties of both the peridynamic composites and locally elastic ones are described by constant tensor of the local effective moduli. However, even for locally elastic composites subjected to inhomogeneous loading, the effective deformations are described by a nonlocal (either the differential or integral) operator. Estimation of this effective displacement is performed by exploitation of the most popular tools and concepts used in conventional elasticity of composite materials with their adaptation to peridynamics. This is extraction from the material properties of a constituent of the matrix properties. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts. The current paper is dedicated to the estimation of effective deformations of a 1D statistically homogeneous peridynamic composite bar for the prescribed self-equilibrated body forces. The method is based on estimation of a perturbator introduced by one inclusion inside an infinite homogeneous bar. The statistical averages of the total displacements are estimated by summation of these perturbators for all possible locations of inclusions in the framework of a generalized effective field method.