Generalised self consistent homogenisation as an inverse problem

This paper presents a numerical development of the usual generalized self-consistent method (GSCM) for homogenisation of composite materials. The classical self-consistent scheme is appropriate for phases that are “disordered”, i.e. what is called “random texture”. The main idea of self consistent methods is to replace the problem of the interaction among many particles by the problem of interaction of one particle and an infinite matrix: the effective medium. In the case of particle inclusions, the upper and the lower bounds for the effective properties can be well estimated . We formulate a coupled thermo-mechanical problem for non linear composites having properties depending on temperature. Usually, GSC method results with closed formulae for bounds of effective mechanical characteristics, obtained via some symbolic manipulations. In the case of the thermo-elastic-plastic behaviour of components, such an approach becomes tedious. In this paper, the problem defined over a domain composed of concentric cylinders of matrix and inclusion and surrounded by an infinite “effective” material is solved using FEM. The FE solution can be repeated several times, for different trial values of unknown material characteristic of the external domain. The set of “correct” effective parameters minimises the error between the solution of a homogenised model and the one, obtained by FEM, for the “heterogeneous” domain. In the present paper we use an artificial neural network (ANN) to identify the value of the effective parameters in the frame of this numerical scheme.