Modeling auxetic foams through semi-rigid rotating triangles

Abstract

Auxetic foams have been widely studied in view of their superior properties and many useful applications and various models have been developed to help explain the auxetic behavior in such foams. One such model involves the description of auxetic foams in terms of rotating units (e.g. the joints where different cell walls meet), a mechanism, which has also been observed experimentally. In the models, the rotating units are taken, to a first approximation, to be representable through rotating rigid triangles, which correspond to the 2D projection of these rotating units and although this model has been improved significantly since it was first proposed, current models still do not fully capture all the deformations that may occur in real foams. In this work, we propose an extended model which not only allows for relative rotation of the units (joints), represented by non-equilateral triangular units, but also for differing amount of material at the joints as well as deformation of the joints themselves, a scenario that is more representative of real auxetic foams. This model shows that, by permitting deformation mechanisms other than rotation of the triangles, the predicted extent of auxeticity decreases when compared to the equivalent idealized rotating rigid triangles model, thus resulting in more plausible predictions of the Poisson's ratios. Furthermore, it is shown that in the manufacturing process, a minimum compression factor, which is dependent on the amount of materials at the joints, is required to obtain an auxetic foam from a conventional foam, as one normally observed in experimental work on foams.