Triply periodical particulate matrix compositesinvarying external stress fields

We consider a linear elastic composite medium, which consists of ahomogeneousmatrix containing aligned ellipsoidal uncoated or coated inclusions arranged in aperiodic arrayand subjected to inhomogeneous boundary conditions. The hypothesis of effectivefieldhomogeneity near the inclusions is used. The general integral equation obtained reducestheanalysis of infinite number of inclusion problems to the analysis of a finite number of inclusionsinsome representative volume element (RVE) . The integral equation is solved by theFouriertransform method as well as by the iteration method of the Neumann series ( first-orderapproximation) . The nonlocal macroscopic constitutive equation relating the unit cellaverages ofstress and strain is derived in explicit closed forms either of a differential equation ofasecond-order or of an integral equation. The employed of explicit relations fornumericalestimations of tensors describing the local and nonlocal effective elastic properties aswell asaverage stresses in the composites containing simple cubic lattices of rigid inclusions andvoids areconsidered.