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 homogeneous matrix containing aligned ellipsoidal uncoated or coated inclusions arranged in a doubly 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 a modified version of the Neumann series; the fast convergence of this method is demonstrated for concrete examples. The nonlocal macroscopic constitutive equation relating the cell averages of stress and strain is derived in explicit iterative form of an integral equation. A doubly periodic inclusion field in a finite ply subjected to a stress gradient along the functionally graded direction is considered. The stresses averaged over the cell are explicitly represented as functions of the boundary conditions. Finally, the employed of proposed explicit relations for numerical simulations of tensors describing the local and nonlocal effective elastic properties of finite inclusion plies containing a simple cubic lattice of rigid inclusions and voids are considered. The local and nonlocal parts of average strains are estimated for inclusion plies of different thickness. The boundary layers and scale effects for effective local and nonlocal effective properties as well as for average stresses will be revealed. (C) 1999 Elsevier Science Ltd. All rights reserved.