Skeleton-and-bubble model of polyether-polyurethane elastic open-cell foams for finite element analysis at large deformations

Abstract

We formulate a new micromechanical model of elastic open-cell (EOC) foams. In this model, the usual skeleton of open-cell foams is supplemented by fitting a thin-walled bubble within each cavity of the skeleton, as a substitute for the membranes that occlude the “windows” of the foam cells in polyether-polyurethane EOC foams. The model has nine parameters; each parameter has a clear geometrical or mechanical significance, and its value may be readily estimated for any given foam. To calibrate the model, we carry out fully nonlinear, three-dimensional finite-element simulations of the experiments of Dai et al. (2011a), in which a set of five polyether-polyurethane EOC foams covering a range of commercially available relative densities was tested under compression along the rise direction, compression along a transverse direction, tension along the rise direction, simple shear combined with compression along the rise direction, and hydrostatic pressure combined with compression along the rise direction. We show that, with a suitable choice of the values of the parameters of the model, the model is capable of reproducing the most salient trends evinced in the experimental stress–stretch curves. Yet the model can no longer reproduce all of these trends if the bubbles be excluded from the model, and we conclude that the bubbles play a crucial role at large deformations. We also show that the stretch fields that obtain in our computational simulations are in good accord with the digital-image-correlation (DIC) measurements of Dai et al. For simple shear combined with compression along the rise direction, the DIC measurements of Dai et al. prove insufficient to our purposes, and we carry out DIC measurements of our own. To demonstrate the performance of the model in a typical application of polyether-polyurethane EOC foams, we carry out experiments and simulations of foam specimens loaded through a cylindrical punch and a spherical punch. We conclude the paper with a discussion of the contrasts and similarities between our model, in which the deformation is dominated by a phase transition, and the standard micromechanical model of EOC foams, in which the deformation is dominated by a bifurcation of equilibrium.