Numerical Procedures for Non Linear Analysis of Composites

Three procedures are presented for non linear analysis of composites, which include information from the micro level(s). The first one considers the purely numerical construction of yield surfaces at macroscopic level for composites, the components of which may represent diverse behaviour at micro level ranging from plasticity to damage and stick-slip. This procedure allows for any elastic-plastic code at macro level to incorporate important information from the micro level. Both associated and non associated plasticity is foreseen as well as isotropic hardening. The method is used also for obtaining failure surfaces. The second procedure is a generalized self consistent method which deals with the homogenization of non linear fibre reinforced composites in a coupled thermo mechanical setting. This procedure is particularly suitable for inclusions randomly dispersed in a matrix. Usually in the framework of a self consistent scheme, the homogenised material behaviour is obtained with a symbolic approach. For the non linear case this becomes rather tedious. The procedure presented is fully numerical. 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 iterating between the two single solutions. Finally, the third method is a hierarchical FE3 procedure which considers three structural levels with elastic-plastic behaviour. In this case periodic structures at the lower levels are considered which helps to speed up the otherwise heavy computation. Examples will be shown for each of these procedures.