A stable hyperelastic model for foamed rubber

A hyperelastic strain energy function for foamed rubber that is based on the physical features of a typical uniaxial compression curve for foams and the behavior of a spherical pore in a spherical, incompressible Mooney-Rivlin matrix is presented. The model is unconditionally stable when positive moduli are used, and can represent most foam test data, including variable Poisson behavior during compression. This most general model has six parameters, including four moduli, a dimensionless parameter associated with buckling or plateau strain, and an initial porosity. The model will be described and its ability to fit compression response data for PDMS foams over a range of relative densities will be evaluated. Several potential extensions of this model will be discussed, including representation of the Mullins effect, representation of aging behavior, inclusion of matrix compressibility, and modeling the effect of pore gas response.