Generalized self-consistent homogenization using the Finite Element Method

TLDR: This paper forms a coupled thermo‐mechanical problem for non linear composites having properties depending on temperature and proposes a “problem‐oriented” technique of solution using the Finite Element Method to solve the elastic‐plastic problem.

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.