Computational homogenization of linear viscoelastic materials: a simplified approach

Several methods have been proposed for numerical homogeniation of linear viscoelastic materials, mainly based on Laplace transform or on multilevel (FE^2) approaches. In this paper, we introduce a much simpler technique based on a discrete representation of the effective relaxation tensor related to the homogeneous medium, which can then be used to evaluate the constitutive law in the form of a convolution product. In practice, calculations on the RVE reduce to 3 transient simulations in 2D and 6  in 3D. More details in

 A.B. Tran, J. Yvonnet, Q.-C. He, C. Toulemonde, J. Sanahuja, A simple computational homogenization method for structures made of linear heterogeneous viscoelastic material. Comput. Methods Appl. Mech. Eng. 200 (45-46):2956-2970 (2011).