Computational homogenization in linear elasticity of peristatic periodic structure composites

A composite material (CM) of periodic structure with the peristatic properties of constituents, as proposed by Silling, is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. New volumetric periodic boundary conditions (PBCs) are introduced at the interaction boundary of a representative unit cell (UC). A generalization of the Hill’s equality to peristatic composites is proved. The general results establishing the links between the effective moduli and the corresponding mechanical influence functions are obtained. The discretization of the equilibrium equation acts as a macro-to-micro transition of the deformation-driven type, where the overall deformation is controlled. Determination of the microstructural displacements allows one to estimate the peristatic traction at the geometrical UC’s boundary, which is exploited for estimation of the macroscopic stresses and the effective moduli. The proposed approach is demonstrated computationally through one-dimensional examples.