Cavities vis-a-vis rigid inclusions: Elastic moduli of materials with polygonal inclusions

Abstract

In this paper we explore the correspondence between rigid inclusions and cavities [Dundurs(1989, J. Appl. Mech. 56, 786–790)] as applied to the effective elastic moduli of materials with polygonal rigid inclusions and cavities. In the analysis we use a complex variable method of elasticity and a conformal transformation to solve for the stress field due to a single rigid inclusion. Then we use a far field approach to obtain the effective elastic constants of composites with a dilute concentration of rigid polygonal inclusions. By employing the Dundurs correspondence we can automatically obtain the result for the effective elastic moduli of materials with cavities. Finally, we use effective medium theories to predict the elastic moduli of materials containing a finite concentration of inclusions.