Statistical average of residual stresses in elastically homogeneous medium with random field of noncanonical inclusions

We consider a linearly elastic composite material (CM), which consists of a homogeneous matrix containing a statistically homogeneous random set of noncanonical (i.e. nonellipsoidal) inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are different. One proposes a new exact representation for the first statistical moments of stresses in the phases expressed trough the averaged boundary integrals over the inclusion boundaries. These integrals presenting the perturbations introduced by a single inclusion inside the infinite matrix are evaluated by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. Increasing of volume fraction of inclusions can lead to change of a sign of local residual stresses estimated by either the new approach or the classical one. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D infinite domains containing statistically homogeneous random field of inclusions.