Domain decomposition methods to evaluate effective elastic properties of random fibre composites in the framework of the double-scale homogenization

The paper deals with the evaluation of the effective elastic properties in the framework of domain decomposition. The field of random fibre composites, for which the network of heterogeneities is complex and leads to several numerical shortcomings, is considered. 2D representative volume elements (RVEs) of the composite are generated and some elastic properties are estimated with the help of the double-scale homogenization. Such methodology is reliable but turns out to be potentially inefficient due to the required size of RVEs. Two adaptations of domain decomposition methods in the framework of double-scale homogenization are proposed to drastically reduce the calculation costs: a Schur complement method, and a mixed Schur complement and FETI-1 method. Several numerical tests are performed which highlight reliability and efficiency of the first one in the present context.