Mean-field/FMBEM homogenization of 3-D particulate composites

Abstract

An approach to homogenization of particulate composite materials is proposed. The mean-field assumption for averaging over phases is combined with numerical calculations of strain-concentration tensors, thus making it independent from the analytical Eshelby solution for ellipsoidal inclusions. The fast multipole boundary element method (FMBEM) is applied to 3-D elasticity and two-phase composites. As opposed to the finite element method (FEM), this method allows for easy modeling of large structures without the need to discretize volumes. Single-inhomogeneity problems are solved, and the calculated strain concentration tensors are used in the averaging formula under the assumption of the Mori–Tanaka approach. An interpolative scheme involving the inverse Mori–Tanaka assumption, known from the literature, is also applied to increase the accuracy of the approximation for higher volume fractions of particles. Examples include composites with spherical and cubic particles, and hybrid materials with auxetic components. The results are consistent with analytical solutions and RVE/FEM models.