Effective elastic properties of solids with defects of irregular shapes

Pores and defects in real materials often have very irregular shapes. Thus, micromechanical modeling based on the analytical solutions of elasticity becomes inapplicable. The objective of this paper is to present a computational procedure to calculate the contribution of the irregularly shaped defects into the effective moduli of two-dimensional elastic solids. In this procedure, the cavity compliance tensor is constructed numerically for an individual defect, and then used in the elastic potential-based approach to predict the effective moduli of porous solids. Two computational methods are used in this paper to calculate the components of a cavity compliance tensor: finite element analysis and numerical conformal mapping. Application of this procedure to the regular hole shapes produces results that are in good correspondence with analytical predictions