A microstructure-based hyperelastic model for open-cell solids

Mesoscopic continuum hyperelastic models for open-cell solids subject to large elastic deformations are derived from the architecture of the cellular body and the microscopic responses of the cell walls. These models are valid for general structures, with randomly oriented cell walls, made from an arbitrary isotropic nonlinear hyperelastic material, and subject to finite triaxial stretches. Their analyses provide global descriptors of the cellular structure, such as nonlinear stretch and shear moduli, and Poisson's ratio. Comparisons with numerical simulations show that the mesoscopic models capture well the mechanical responses under large strain deformations of three-dimensional periodic structures and of two-dimensional honeycombs made from a neo-Hookean material