COMPUTATIONAL HOMOGENIZATION METHOD AND REDUCED DATABASE MODEL FOR HYPERELASTIC HETEROGENEOUS STRUCTURES

Abstract

A nonconcurrent multiscale homogenization method is proposed to compute the response of structures made of heterogeneous hyperelastic materials. The method uses a database describing the effective strain energy density function (potential) in the macroscopic right Cauchy-Green strain tensor space. Each value of the database is computed numerically by means of the finite element method on a representative volume element, the corresponding macroscopic strains being prescribed as boundary conditions. An interpolation scheme is then introduced to provide a continuous representation of the potential, from which the macroscopic stress and elastic tangent tensors can be derived during macroscopic structures calculations. To efficiently compute the interpolations at the macroscopic scale, the full database is reduced by a tensor product approximation. Several extensions are provided to handle issues related to finite strains. The accuracy of the method is tested through different numerical tests involving composites at finite strains with isotropic or anisotropic microstructures. Second-order accuracy is achieved during the macroscopic Newton-Raphson iterations.