Effective elastic modulus of heterogeneous peristatic bar of random structure

AbstractThe basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated nonlocal force interactions between infinitesimal particles. In contrast to these classical theories, the peridynamic equation of motion introduced by Silling (2000) is free of any spatial derivatives of displacement. A heterogeneous bar of statistically homogeneous random structure of constituents with the peristatic mechanical properties is analyzed by the standard averaging tool of micromechanics. The applicability of local elasticity theory is demonstrated for description of effective elastic behavior of this bar. The approach proposed is based on numerical solution (for both the displacements and peristatic stresses) for one heterogeneity inside infinite homogeneous bar loaded by a pair of self-equilibrated concentrated remote forces. This solution is substituted into the general scheme of micromechanics of locally elastic media adapted for the considered case of 1D peristatic structures. A convergence of effective modulus estimations is demonstrated for both the peristatic composite bar and locally elastic bar