Numerical homogenization for composite materials analysis. Comparison with other micro mechanical formulations

Abstract

This work presents a two-scale homogenization procedure to analyze three dimension composite structures by FEM. The theory implemented is compared with other micro-structural formulations: micro models and serial–parallel mixing theory, in terms of result accuracy and computational cost. The comparison shows that for linear analysis, the homogenization is an excellent alternative to the other formulations. Its computational cost is substantially lower than the one required by the micro-model and it is able to capture several micro-structural phenomena that it is not automatically recorded by the serial–parallel methodology. It will also be shown that the extension of the proposed theory to the non-linear range stills represents a challenge. The major limitation is its computational cost because it requires to solve the sub scale at each gauss point and load step. However, the comparison shows that this cost is in terms of CPU time but not in terms of memory. Based on the results obtained, it can be concluded that the homogenization is an excellent alternative for simulation of materials with complex micro structures. The method is also very promising for non linear simulations, when coupled with a threshold criteria to decide whether it is necessary to analyze the RVE or not.