Numerical estimation of effective elastic properties of elastomer composites under finite strains using spectral element method with CAE Fidesys

Estimation of effective properties of composite materials is one of the main problems for the composite mechanics. In this article, a method is developed by which the effective nonlinear elastic properties of elastomer composites (filled rubbers) are estimated under finite strains. The method is based on numerical solution of nonlinear elastic boundary-value problems for a representative volume element (RVE) of elastomer composite. Different boundary conditions are consequently applied to the RVE: nonperiodic (displacements of the RVE boundary) or periodic (restraints on displacements of corresponding points of opposite faces of RVE). An obtained stress field is averaged by volume after the solution of an elastic boundary-value problem. Effective properties are estimated as a quadratic dependence of the second Piola-Kirchhoff stress tensor upon the Green strain tensor. This article presents the results of numerical estimation of effective elastic properties of filled rubbers under finite strains. Numerical calculations were performed with the help of Fidesys Composite program module, which is a part of the domestic Fidesys CAE-system, using the finite element method and the spectral element method. Spectral element method is one of the most effective and modern finite element method version. High order piecewice-polynomial functions are reference functions in SEM. There is no need to rebuild or refine mesh to check solution mesh convergence, as mesh is kept in initial state and only element orders are changed. The subject of investigation was the filled elastomer effective properties dependence upon the filler particles special orientation and the filling degree. Graphs of these dependencies are given in the article. The obtained results show that the spectral element method is suitable for numerical solution of the effective properties estimation problem for composite materials. In addition, the results allow to estimate the influence of non-linear effects upon the mechanical properties of the composite. The correction for stress from taking the non-linearity into account is about 25% under the strain 15% in the case of uniaxial tension.