Effective conductive properties of open-cell foams

The work is devoted to the problem of simulation of the effective electro and thermoconductive properties of open-cell foam materials with slim highly conductive ligaments. The solution of this problem depends on two small parameters: the ratio of the typical length and the cross-section size of the ligaments, and the ratio of the conductivities of the host medium and the ligaments. The principal 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 (RVE) of the foam material. The Laguerre tessellation procedure is applied for simulation of foam microstructures with various distributions of cell-sizes inside the RVE. Effective conductivity constants of the foams are obtained by averaging the detailed fields 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 of the foams on the shapes of the ligaments and the distribution law of the cell-sizes are obtained and analyzed.