A domain decomposition method for bodies with heterogeneous microstructure basedon material regularization

A domain decomposition method is developed to reduce the computational complexity of boundary value problems associated with the structural analysis of bodies with arbitrary external geometry\ loading and linearly elastic microstructure[ The purpose of the method is to augment existing numerical discretization methods of analysis\ such as the _nite element method[ The approach is to partition and decouple the heterogeneous body into more computationally tractable\ nonoverlapping\ subdomains whose union forms the entire domain under analysis[ This is achieved by approximating the subdomain boundary conditions[ The approximate boundary conditions\ of displacement or traction type\ are supplied from the solution to a relatively computationally inexpensive auxiliary boundary value problem characterized by a simple regularized microstructure[ Since the decoupled subdomains may then be analyzed separately\ the memory requirements are reduced and computing procedures are trivially parallelizable[ A!posteriori error bounds are developed for solutions generated by this process[ It is shown that\ in the special case of uniform exterior loading\ the error bounds collapse into forms which imply results pertaining to e}ective property ordering coinciding with those published by Huet "0889