Computer Simulation of Mechanical and Physical Properties of Carbon Foam Materials

摘要

The project is devoted to the problem of the numerical simulation of the effective elastic, thermo and electro conductive properties of open-cell foam materials. The Laguerre tessellation procedure is applied for the construction of skeletons of random foam microstructures with prescribed distributions of the cell diameters. A four-parametric approximation of the ligament shapes in the open-cell foams is proposed. For simulation of the elastic properties of open -cell foams, a version of the finite element method based on the Timoshenko beam finite element is developed. The method is used for calculation of stresses and strains in the foam ligaments and the solution of the homogenization problem. The size of the representative volume element (RVE) for reliable calculations of the effective elastic properties of the foam materials is evaluated on the basis of 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. The problem simulation of the effective electro and thermo conductive properties of open-cell foam materials with slim highly conductive ligaments has a specific feature. Its solution depends on two small parameters: the ratio of the typical length and the crosssection size of the ligaments. Principle terms of the asymptotic solutions (with respect to these parameters) for the fields inside the ligaments are obtained and used in the framework of a finite element method for the numerical simulation of the fields inside the representative volume element of the foam material. Effective conductivity constants of the foams are obtained by averaging the detailed fields in the ligaments over the RVE. The number of cells inside the RVE for reliable calculations of the effective conductivities is indicated. Dependences of the effective conductive properties on the details of the foam microstructure are obtained and analyzed.