On the effective behavior of viscoelastic composites in three dimensions
Résumé
We address the calculation of the effective properties of non-aging linear viscoelastic composite materials. This is done by solving the microscale periodic local problems obtained via the Asymptotic Homogenization Method (AHM) by means of finite element three-dimensional simulations. The work comprises the investigation of the effective creep and relaxation behavior for a variety of fiber and inclusion reinforced structures (e.g. polymeric matrix composites). As starting point, we consider the elastic-viscoelastic correspondence principle and the Laplace-Carson transform. Then, a classical asymptotic homogenization approach for composites with discontinuous material properties and perfect contact at the interface between the constituents is performed. In particular, we reach to the stress jump conditions from local problems and obtain the corresponding interface loads. Furthermore, we solve numerically the local problems in the Laplace-Carson domain, and compute the effective coefficients. Moreover, the inversion to the original temporal space is also carried out. Finally, we compare our results with those obtained from different homogenization approaches, such as the Finite-Volume Direct Averaging Micromechanics (FVDAM) and the Locally Exact Homogenization Theory (LEHT).
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