A computational homogenization scheme is developed to model heterogeneous hyperelastic materials undergoing large deformations. The homogenization scheme is based on a so-called computational continua formulation in which the macro-scale model is assumed to consist of disjoint unit cells. This formulation adds no higher-order boundary conditions and extra degrees of freedom to the problem. A computational procedure is presented to calculate the macroscopic quantities from the solution of the representative volume element boundary value problem. The proposed homogenization scheme is verified against a direct numerical simulation. It is also shown that the computational cost of the proposed model is lower than that of standard homogenization schemes.@en

The computational homogenization method enables to derive the overall behavior of heterogeneous materials from their local-scale response. In this method, a representative volume element (RVE) is assigned to a macroscopic material point and the constitutive law for the macroscopic model at that point is obtained by solving a boundary value problem for the RVE. However, the standard computational homogenization scheme cannot be used when strain localization occurs and does not account for dynamic effects at the local-scale. Furthermore, in the computational homogenization scheme, at each iteration, a boundary value problem should be solved for RVEs associated to the integration points of macroscopic elements which leads to high computational cost. When the problem is nonlinear (material and/or geometrical nonlinearities), the computational cost may become more than used for direct numerical simulation (DNS). This study aims at developing computational and numerical homogenization schemes which account for strain localization, dynamic effects at the local-scale and large deformations and strains. Furthermore, strategies are presented to decrease the computational cost while preserving accuracy. Different heterogeneous structures consisting of quasi-brittle materials, hyperelastic materials and polymer materials are studied and proper homogenization schemes are presented.@en