Effective thermoelastic properties of graded doubly periodic particulate matrix composites in varying external stress fields

We consider a linear elastic composite medium, which consists of a homogene ous matrix containing aligned ellipsoidal uncoated or coated inclusions arr anged in a doubly periodic array and subjected to inhomogeneous boundary co nditions. The hypothesis of effective field homogeneity near the inclusions is used. The general integral equation obtained reduces the analysis of in finite number of inclusion problems to the analysis of a finite number of i nclusions in some representative volume element (RVE). The integral equatio n is solved by a modified version of the Neumann series; the fast convergen ce of this method is demonstrated for concrete examples. The nonlocal macro scopic constitutive equation relating the cell averages of stress and strai n is derived in explicit iterative form of an integral equation. A doubly p eriodic inclusion field in a finite ply subjected to a stress gradient alon g the functionally graded direction is considered. The stresses averaged ov er the cell are explicitly represented as functions of the boundary conditi ons. Finally, the employed of proposed explicit relations for numerical sim ulations of tensors describing the local and nonlocal effective elastic pro perties of finite inclusion plies containing a simple cubic lattice of rigi d inclusions and voids are considered. The local and nonlocal parts of aver age strains are estimated for inclusion plies of different thickness. The b oundary layers and scale effects for effective local and nonlocal effective properties as well as for average stresses will be revealed. (C) 1999 Else vier Science Ltd. All rights reserved.