Thermo-mechanical modelling of fibrous composites using the generalised self consistent like method

This paper presents a development of the usual generalized self-consistent (GSC) method for homogenisation of composite materials. Usually, GSC method results with closed formulae for bounds of effective mechanical characteristics, obtained via some symbolic manipulations. However in the case of non linear behaviour of components, such a method may become tedious. In this paper, the problem is defined for n-layered cylindrical inclusions embedded in a matrix. Yielding and hardening of the matrix, as well as fibre breaking can be taken into account in the numerical procedure. Furthermore, all material characteristics can be temperature dependent. In our approach, the effective properties are determined by minimizing a functional expressing the difference (in some chosen norm) between the solution of the heterogeneous problem and the equivalent homogenous one. The heterogeneous problem is solved with the Finite Element method, while the second one has its analytical solution. The two solutions are written as a function of the (unknown) effective parameters, so that the final global solution is found by a minimisation procedure.