Representative volume element and effective elastic properties of open cell foam materials with random microstructures

This work is devoted to the problem of the numerical simulation of effective elastic properties of open-cell foam materials. The Laguerre tessellation procedure is used for the construction of skeletons of random foam microstructures with prescribed distributions of cell diameters. A four-parametric approximation of the ligament shapes in the open-cell foams is proposed. A version of the finite element method, based on the Timoshenko beam finite element, is developed for calculating stresses and strains in the foam ligaments and the solution of the homogenization problem. The size of the representative volume element for reliable calculations of the effective elastic properties of the foam materials is evaluated on the basis of a series of numerical experiments. The dependences of the effective elastic properties of the open-cell foams on cell size distributions and on ligament shapes are obtained and analyzed.