A domain decomposition method for bodies with heterogeneous microstructure based on 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 finite element method. The approach is to partition and decouple the heterogeneous body ino 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 effective property ordering coinciding with those published by Huet (1990). (C) 1999 Elsevier Science Ltd. All rights reserved.