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 the finite element method. The theory implemented is compared with other micro-structural formulations: micro models and the serial-parallel mixing theory, in terms of result accuracy and computational cost. The comparison shows that for linear analysis, the homogenization proposed is an excellent alternative to the other formulations considered. Its computational cost is substantially lower than the one required by the micro-model and it is able to capture some micro-structural phenomena that it is not automatically recorded by the serial-parallel mixing theory. 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 prohibitive computational cost because it requires solve the sub scale at each gauss point and each 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 method is an excellent alternative for the simulation of materials with complex micro structures. The method is also very promising for non linear simulations, * Corresponding author

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