9317365 Zargaryan The purpose of this exploratory research is to develop a new approach, based on the use of asymptotic expansions to generate successive approximations, for the prediction of the macro- mechanical properties of heterogeneous materials (e.g., composites) and for the simultaneous determination of the global response of structural and mechanical components fabricated from these materials. In addition, this method permits the calculation of local states of stress and deformation at or near the various interfaces in the material, which is essential for the prediction of failure. ***