Effects of morphology and orientation on the behavior of two-dimensional hexagonal foams and application in a re-entrant foam anchor model

This study deals with the elastic behavior of regular (equal strut lengths) hexagonal foams, both convex and non-convex (re-entrant). Explicit constitutive relations are given based on the unit cell geometry and strut material properties. Sensitivity studies show the effects of unit cell architecture and loading direction on the structural properties of the unit cell. The effect of cell strut angle on the structural properties is clarified by considering the change in relative density of the foam that is related to changes in the strut angles. It is shown that the density varies dramatically with strut angle for fixed strut lengths, which significantly effects the interpretation of results. An important conclusion regarding the effect of foam orientation (or loading direction) is that what has been referred to as a negative Poisson's ratio for re-entrant foams is actually a negative Poisson's ratio effect. This effect can in fact be reversed by simply rotating the foam; for intermediate rotation angles the foam may demonstrate a positive Poisson's ratio deformation behavior. Hexagonal re-entrant foams do not have a unique value of Poisson's ratio since they are anisotropic. For demonstration, the elastic re-entrant foam constitutive relations are embedded into a finite element model to study a foam anchor between rigid parallel walls. The effect of the cell strut angle on the anchoring effectiveness of the foam is discussed. Foams with strut angles of 100° and 110° and equal relative densities are compared, and it is concluded that the foam with 100° strut angle provides better anchoring. This conclusion is based on the finding that the 100° foam is stiffer and has a stronger negative Poisson's ratio (lateral expansion under tension) effect than the 110° foam having the same relative density.