Numerical evaluation of the viscoelastic and viscoplastic behavior of composites

This paper is concerned with the development of homogenization methods in order to obtain the effective material parameters of viscoelastic and viscoplastic composites. In the case of a viscoelastic behavior, the constitutive laws at the heterogeneous scale are transposed into a LAPLACE-CARSON domain where the equations become similar to those of linear elasticity and classical homogenization procedures can be applied. Afterward, the results have to be converted by an inverse transformation. Mostly, this procedure is combined with analytical or semi-analytical models such as the self-consistent or Mori-Tanaka model. Since the application of this approach is limited to simple structured composites it is not suitable for materials with a complex internal architecture. In order to avoid this limitation, this paper is focused on the development of a homogenization procedure which is based on the LAPLACE-CARSON transformation and a numerical solution of the field problem. For heterogeneous material with viscoplastic or nonlinear viscoelastic properties, an additional linearization step is required. A new algorithm is proposed in order to combine this affine formulation with the numerical homogenization method. Finally, these procedures are used to estimate the effective material behavior of different types of composites. With that, the accuracy of the results and efficiency of the methodologies is assessed