Microscopic and Macroscopic Instabilities in Polymeric Foams

The compressive response of cellular solids, including solid foams, exhibits a stress plateau that extents to high macroscopic strains, producing a high energy absorption capacity under low-level stresses. This behavior combined with their low density makes foams excellent candidates for impact mitigation and blast protection applications. The initial limit stress, depending on the mechanical behavior of the underlying solid material and the microstructure, can be attributed to yielding, buckling, and/or brittle fracture. In the case of flexible polymeric foams it is well-known that their compressive response is governed by elastic buckling. However, depending on the underlying microstructure and loading conditions different modes of instabilities may occur, from microscopic ones at the cell level to global (long wavelength) buckling. Here we use micromechanical models of random foams in order to predict the onset of instability and associated mode and connect it to the key foam morphological characteristics. In particular, we show how the critical stresses and buckling modes are affected by the foam (a) density, (b) anisotropy, (c) polydispersity, and (d) ligament cross-sectional area. Random foam topologies based on tessellations are dressed with solid to march a target relative density. Simulations for different densities reveal a quadratic relation with the foam critical stress. Our results also show that a strong amount of anisotropy alters the buckling mode from a microscopic one, corresponding to isotropic foams, to a long-wavelength mode that is accompanied by a limit-load type response.  Random foam models with increasing amounts of polydispersity are used in simulations to examine the effect of the cell-size variation on the foam’s nonlinear response. Our results indicate that polydisperse foams have a monotonically increasing response with no limit load. In this case, however, this response is not produced by uniform compaction of foam cells, but by the increased localized deformation of the larger cells within the microstructure. The effect of the shape of the ligaments' cross-sectional area on the response is also examined.    

Finally, we compare our numerical results against experimentally measured compressive responses and deformed configurations of polymeric foams. Our predictive random foam modeling framework is shown to capture different types of instabilities and the associated modes for a range of different microstructures. Furthermore, the numerical responses are in good agreement with the corresponding experimental ones but do however somewhat overestimate the critical stresses. This is attributed to our defect-free morphologies of random foams that still remain idealized versions of commercial polymeric foams.