Micromechanical modeling coupling time-independent and time-dependent behaviors for heterogeneous materials

Homogenization methods were developed to relate microstructure and local deformation mechanisms to overall behavior. The well-known self-consistent scheme was successfully developed to describe mechanical interactions for elastic, elastoplastic and viscoplastic behaviors. When complex space–time couplings and non-linearity are involved, new estimations have to be established. This paper addresses to local behavior exhibiting elastic, anelastic and inelastic strains. A new estimation of mechanical interactions is proposed. It uses an incremental representation of the behavior and is based on translated fields techniques and self-consistent approximation. First, the case of a purely anelastic (Kelvin–Voigt) heterogeneous medium is treated. The solution of the anelastic heterogeneous problem is then used to solve the complete problem where the local behavior is described through a Burger element. Results obtained with the present modeling are compared with results obtained with other models found in literature in the case of linear behavior. They show that a good description of the time-dependent spatial interactions is obtained. Thanks to this incremental approach, the present modeling can be easily used for non linear behavior.