On the nature of pressure dependence in foams

Present study explores the physical background of pressure dependence observed in the yield behavior of solid foams by analyzing the partition of strain energy and stress distribution in the struts that make up the foam. To this end, transversely isotropic Kelvin foam models of three different relative densities are utilized in FE analysis to probe the yield surface along various biaxial and triaxial stress paths for a wide range of mean stress. From a macroscopic viewpoint, it is observed that in addition to well-documented quadratic dependence of yielding on mean stress there also exists a linear pressure dependence, which has not been properly addressed in the literature. Partition of strain energy at the time of macroscopic yielding into bending and stretch modes of deformation within struts provides a unique tool with which the dominant deformation mode that drives yielding can be identified as a function of the stress path followed. Analysis of FE results indicates that positive mean stress, as compared to negative mean stress, provides a strong configurational stability in deformation kinematics that limits bending mode and promotes the stretch mode of deformation in struts. Increasing the fraction of strain energy stored in stretch mode effectively increases the critical strain energy of yielding and, thereby, delays the onset of microscopic yielding. Negative mean stress, on the other hand, results in a weak configurational stability where bending mode is more prominent. Furthermore, it seems that the degree of this already weak stability quickly decays with the magnitude of negative mean stress and completely disappears when (and if) the stabilizing effect of joint stiffness is exceeded. We conclude that this contrasting behavior is the main source of (i) linear pressure dependence observed in the yield behavior as well as (ii) the stronger effect of linear pressure in low-density foams.