Triply periodical particulate matrix composites in varying external stress fields

We consider a linear elastic composite medium, which consists of a homogeneous matrix containing aligned ellipsoidal uncoated or coated inclusions arranged in a periodic array and subjected to inhomogeneous boundary conditions. The hypothesis of effective field homogeneity near the inclusions is used. The general integral equation obtained reduces the analysis of infinite number of inclusion problems to the analysis of a finite number of inclusions in some representative volume element (RVE). The integral equation is solved by the Fourier transform method as well as by the iteration method of the Neumann series (first-order approximation). The nonlocal macroscopic constitutive equation relating the unit cell averages of stress and strain is derived in explicit closed forms either of a differential equation of a second-order or of an integral equation. The employed of explicit relations for numerical estimations of tensors describing the local and nonlocal effective elastic properties as well as average stresses in the composites containing simple cubic lattices of rigid inclusions and voids are considered. (C) 1999 Elsevier Science Ltd; All rights reserved.