Estimation of effective elastic moduli of random structure composites by the method of fundamental solutions

One considers linearly elastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical shape. Effective elastic moduli as well as the first statistical moments of stresses in the phases are estimated through the averaged boundary integrals over the inclusion boundaries. The modified popular micromechanical models are based on the numerical solution for one inhomogeneity inside the infinite matrix loaded by remote homogeneous effective field. This solution is obtained by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. The problem here addressed, consists in computing the displacement and traction fields of an elastic object, which has piecewise constant Lamé coefficients, from a given displacement (or stress) field on the infinity. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D domains.