LINEAR ELASTIC BEHAVIOR OF A LOW-DENSITY KELVIN FOAM WITH OPEN CELLS

A micromechanical analysis for the linear elastic behavior of a low-de nsity foam with open cells is presented, The foam structure is based o n the geometry of a Kelvin soap froth with pat faces. 14-sided polyhed ral cells contain six squares and eight hexagons. Four struts meet at every joint in the perfectly ordered, spatially periodic, open-cell st ructure. All of the struts and joints have identical shape. Strut-leve l force-displacement relations are expressed by compliances for stretc hing, bending, and twisting. We consider arbitrary homogeneous deforma tions of the foam and present analytic results for the force, moment, and displacement at each strut midpoint and the rotation at each joint . The effective stress-strain relations for the foam, which has cubic symmetry, are represented by three elastic constants, a bulk modulus, and two shear moduli, that depend on the strut compliances. When these compliances are evaluated for specific strut geometries, the shear mo duli are nearly equal and therefore the elastic response is nearly iso tropic. The variational results of Hashin and Shtrikman are used to ca lculate the effective isotropic shear modulus of a polycrystal that co ntain grains of Kelvin foam.