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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This work presents a new procedure to deal with the delamination problem found in laminated composites, based in a continuum mechanics formulation. The procedure proposed obtains the composite constitutive performance with the Serial/Parallel mixing theory, developed by F. Rastellini. This theory characterizes composite materials by coupling the constitutive behaviour of the composite components, imposing an iso-strain relation among the components in the fibre (or parallel) direction and an iso-stress relation in the remaining directions (serial directions). The proposed procedure also uses a damage formulation to characterize the constitutive behaviour of matrix component in order to obtain the stress-strain performance of this material.With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial direction. This reduction provides a composite performance equivalent to what is found in a delaminated material.To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.

A damage constitutive model in conjunction with a 2-D finite element discretization is presented for predicting onset and evolution of matrix cracking and subsequent stiffness reduction of symmetric composite laminates with arbitrary stacking sequence subjected to membrane loads. The formulation uses laminae crack densities as the only state variables, with crack growth driven by both mechanical stress and residual stress due to thermal expansion. The formulation is based on fracture mechanics in terms of basic materials properties, lamina moduli, and critical strain energy release rates G IC and G IIC , only. No additional adjustable parameters are needed to predict the damage evolution. Spurious strain localization and mesh size dependence are intrinsically absent in this formulation. Thus, there is no need to define a characteristic length. Comparison of model results to experimental data is presented for various laminate stacking sequences. Prediction of crack initiation, evolution, and stiffness degradation compare very well to experimental data.