Generalised self-consistent like homogenisation for the thermo-mechanical analysis of composites

This paper presents a development of the usual generalized self-consistent method for homogenisation of composite materials. We take into consideration a special class of heterogeneous materials, formed by a matrix and “fibrous inclusions”. The microstructure of these composites consists of a continuum phase and a set of isolated inclusions randomly distributed inside the matrix, but having the longitudinal direction parallel one another. The matrix can be non linear, and inclusions can be non-homogeneous, i.e. they can have their own microstructure, composed of concentric rings of different materials. The problem is formulated for the coupled thermo-mechanical field. Starting from the generalized self-consistent homogenization, a generalized self-consistent like (GSCL) method is formulated, suitably enriched to take into consideration the non-linear behaviour of the initial materials, the heterogeneity of the inclusions and the dependence of the properties on the 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 the superconducting strands used for the coils of the future ITER experimental reactor.