Elastic solids with high concentration of arbitrarily oriented multiphase particles

Abstract

The effective properties of elastic solids are strongly linked to their interacting micro-constituent phases. For materials containing dilute distributions of single-phase inhomogeneities, the overall behavior can be estimated in a straightforward manner. But in the non-dilute case, due to the complex inter-particle and particle-matrix interactions the treatment is rather involved. When the particles are heterogeneous, not only become the mentioned interactions more complex, but must properly account for the intra-particle interactions as well. The present work addresses an analytical approach to determine the overall moduli of elastic solids containing random distributions of arbitrarily oriented ellipsoidal heterogeneities at high concentrations. The approach is based on the extension of the equivalent inclusion method (EIM) to interacting multi-inhomogeneities. The long and short range interaction effects are intrinsically incorporated by the eigenstrain field. In the process, the average of the associated disturbance strain is computed within a representative volume element (RVE) using a superposition scheme. For verification of the proposed theory several theoretical estimates, experimental results, and bounds for the problems which have been obtained in the literature are reexamined. Consideration of more complex scenarios further demonstrates the efficacy of the proposed theory.