Effective elastic properties of solids with two-dimensional inclusions of irregular shapes

A computational procedure to calculate the contribution of irregularly shaped inclusions into the effective moduli of two-dimensional elastic solids is proposed. This procedure is based on the analysis of a representative volume element subjected to a prescribed macrostress. For each type of inclusion, the compliance contribution tensor is constructed using a combination of Kolosov–Muskhelishvili complex variable technique and numerical conformal mapping. Application of this procedure to regularly shaped inhomogeneities produces results that are in good correspondence with analytical predictions. The effective properties are first derived in the approximation of non-interacting inclusions. Then, several first-order micromechanical models for interacting inclusions are considered.