3D finite element investigation of hyperelastic foam behavior. I. Voronoi closed-cell microstructures

The mechanical behavior of isotropic, elastomeric, Classical Voronoi closed-cell foams is investigated numerically using 3D finite element simulations under finite-strain uniaxial compression, and infinitesimal-strain shear and hydrostatic loading conditions. Foam microstructures with porosities ranging from 77% to 95% and narrow pore volume distributions were generated by subtracting irregular polyhedra, obtained from Voronoi tessellations of well dispersed seed points, from a cubic matrix. Severe finite-strain uniaxial compression, up to 95% nominal strain, was simulated using the Abaqus/Explicit solver. Parametric studies revealed that the compressive response of the foams scales proportionally with the factor (1−c)², where c denotes the porosity. Moreover, at high porosities (typically 90%), the influence of the base polymer's hyperelasticity reduces to its initial shear modulus μ₀, since the matrix undergoes only limited strain, whereas the effect of the polymer's large-strain behavior becomes significant at lower porosities (typically 77%). As a result, all stress–strain curves collapse onto a single master curve when the stress is normalized by μ₀(1−c)². The effect of internal gas pressure within the closed cells was also assessed numerically and compared against experimental data, validating the simple analytical model proposed by Gibson and Ashby (1997). At small strains, the shear modulus is accurately predicted by the Differential Hollow Sphere Assemblage (DHSA) originally developed for spherical voids. However, the same model was found to overestimate the bulk modulus, and a phenomenological correction is therefore proposed to enable rapid and more accurate estimation of this quantity.