Linear Elastic Behavior of a Low-Density Kelvin Foam With Open Cells

Abstract

A micromechanical analysis for the linear elastic behavior of a low-density foam with open cells is presented. The foam structure is based on the geometry of a Kelvin soap froth with flat faces: 14-sided polyhedral cells contain six squares and eight hexagons. Four struts meet at every joint in the perfectly ordered, spatially periodic, open-cell structure. All of the struts and joints have identical shape. Strut-level force-displacement relations are expressed by compliances for stretching, bending, and twisting. We consider arbitrary homogeneous deformations 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 moduli are nearly equal and therefore the elastic response is nearly isotropic. The variational results of Hashin and Shtrikman are used to calculate the effective isotropic shear modulus of a polycrystal that contain grains of Kelvin foam.

Design of Mechanical Properties of Open-Cell Porous Materials Based on μCT Study of Commercial Foams

“…Most of geometrical models proposed in literature base on the assumption of equal volume of pores of different shapes [18][19][20][21][22][23]. In commercial practice foams are very frequently manufactured with narrow pore size distributions, which was confirmed by experimental observations [24].…”

Local and regional mechanical characterisation of a collagen-glycosaminoglycan scaffold using high-resolution finite element analysis

“…Consequently, given the mean voxel density (0.055 from the CT images described in section 2.1) indicated voxel-level porosity (the voxel volumes are partially filled), a voxel-density calibration procedure was developed in order to provide voxel-level properties. Thus, as previous investigations have indicated the validity of cellular solid mechanics for representing constructs with a relative density below 0.15 [Li et al, 2003;Warren and Kraynik, 1997] and our voxels have a relative density of 0.055, the Gibson and Ashby equation [Gibson, 2005] was employed. The voxel modulus E v was related to the known material modulus E m of a strut by,…”

The Role of Foaming Agent in Structure and Mechanical Performance of Al Based Foams

“…In particular, remarkable absorbing ability of aluminium foams offers significant performance gains for crash protection of vehicle and other applications where effective utilisation of impact energy is required. Despite of the several models [1][2][3][4][5][6] based on the idealised cellular structure have been proposed, actual profile of the mechanical properties for real Al-foams is recognised to be far from that predicted theoretically. The reason of this discrepancy is a mesoscopic heterogeneity in density and other structural imperfections including cell morphology (thickness, curvature, length, etc.)…”