Generalized self‐consistent homogenization using the Finite Element Method

Abstract This paper presents a development of the usual generalized self‐consistent method for homogenization of composite materials. The classical self‐consistent scheme is appropriate for phases that are “disordered”, i.e. what is called “random texture”. In the case of both linear and non linear components, the self‐consistent homogenization can be used to identify expressions for bounds of effective mechanical characteristics. In this paper we formulate a coupled thermo‐mechanical problem for non linear composites having properties depending on temperature. The solution is found in a non‐classical way, as we use the Finite Element Method to solve the elastic‐plastic problem at hand. In this sense we propose a “problem‐oriented” technique of solution. The method is finally applied to the real case of superconducting strands used for the coils of the future ITER experimental reactor.