Generalized Mori-Tanaka approach in peridynamic micromechanics of multilayered composites of random structure

The basic feature of peridynamics is a continuum description of material behavior as the integrated nonlocal force interactions between material points. Besides the conventional local theory, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175-–209)has no spatial derivatives of displacement. A linearized bond-based peridynamic model is used to analyze random structure CMs subjected to the remote volumetric homogeneous boundary conditions. Effective properties are expressed through the local stress polarization tensor averaged over the external interaction interface of inclusions rather than in an entire space. Any spatial derivatives of displacement fields are not required. Inclusions are considered as identical aligned layers with a statistically homogeneous distribution in the space. For one infinite layer in the infinite homogeneous matrix,3D peridynamic equilibrium equation is reduced to the 1D integral equation with 1D micromodulus obtained by integrations of the original 3D micromodulus over the cross-sections (parallel to layers) of a horizon region. One estimates the average strain and stress fields in the extended layer by the use of averaging displacement and traction over the external interaction interface. Effective moduli for peridynamic multilayered CM are estimated in the matrixform representations usually used in locally elastic multilayered CM and basedon the consideration of the normal and tangential parts of the effective moduli matrix.