Macroscopic Properties of Open-Cell Foams Based on Micromechanical Modelling

Abstract

This paper presents a micromechanical analysis for the assessment of macroscopic behaviour of threedimensional open-cell solid foams. The analysis is based on material properties of a solid phase and topological arrangement of cell structure. A foam structure consists of idealized tetrahedral unit cells, which are built of four identical half-struts forming a diamond-like structure and identified as Plateau borders. Such a unit cell represents the essential microstructural features of foam. An analytical formulation of force-displacement relations for struts can be found by considering the affinity of node displacements in tensile, bending, and shear deformation. The elements of the stiffness matrix for a single cell are expressed as functions of the compliance coefficients for stretching and bending of struts. The effective elastic constants for metallic foam considered as isotropic material are determined as functions of foam relative density and compared with available results. In this paper we define an energy-based limit condition of linear elasticity for open-cell foams and calculate the critical energy density pertinent to a particular orthogonal energy state accounting for elementary interactions in a microstructure. The study based on the assumption of linear elasticity leads to simple analytical formulas. Nevertheless, it should be stressed that the proposed theoretical basis of micromechanical modelling could be also applied for the analysis of nonlinear elastic behaviour, plasticity, and failure of foams. Such problems require, however, a more complex numerical approach.