Anisotropic Plasticity Model for Foams and Honeycombs

Abstract

A three‐dimensional plasticity model is developed for foams and honeycombs. The model accounts for the transverse isotropy of foams and the orthotropy of honeycombs by incorporating a shift on stress that provides a yield surface in the form of a sphere with the centroid shifted from the origin in the principal stress space. To model the extensive strains that occur at constant stress, an elastic‐perfectly plastic formulation is used until a critical plastic volumetric strain is reached. Then the initiation of lockup is represented as an isotropic hardening function of plastic volumetric strain. Both elastic and plastic constants are given as functions of the initial density of the cellular material. With lockup, the elasticity tensor transforms to that of the parent solid. To account for strain‐rate effects, the plateau stresses and the hardening parameter are taken as functions of volumetric strain rate. For each material, experimental data are given for various densities and illustrative plots are given to show how well the model represents these data.