Thermo-Mechanical Analysis of Non Linear Hierarchical Composites using the Generalized Self Consistent Like Method

This paper presents a development of the usual generalized self-consistent method for homogenization of composite materials [1], [2]. 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 to 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