A new approach to yield prediction in cellular solids

Although there exists several yield criteria proposed in the literature for highly porous solid foams, they are all phenomenological in nature, rely on relatively long list of model parameters that require difficult experimentation not readily available to end user, and none of them can handle the anisotropy observed in commercially available solid foams. Present work offers a novel approach by hypothesizing that the yielding of stochastic foams is governed by the total elastic strain energy density. Resulting analytical framework that is based on transverse anisotropy and energy homogenization leads to a pressure-dependent yield criterion for solid foams. Besides accommodating anisotropy, this energy-based yield criterion renders an advantage by relying only on the elastic properties and uniaxial yield strengths of the material. Finite element analysis is presented for a periodic elongated tetrakaidecahedral cell model with 0.1 relative density to validate the proposed model and the dependence of yield behavior on strain energy density. Proposed yield criterion is also validated by extensive experimental data in a companion paper.