Numerical modeling of large strain behavior of polymeric crushable foams

This paper describes a constitutive law modeling isotropic polymeric foam materials. Focus has been placed on modeling the relative density dependency effect on polymeric foams subjected to large deformations using uniaxial and hydrostatic compressive hardening laws. The constitutive model is written in terms of the rotated Kirchhoff stress and of its conjugate logarithmic, or Hencky, strain measure. A numerical scheme for solving the constitutive model is described and implemented using both the finite element and the element-free Galerkin methods, in a Total Lagrangian finite strain framework. The imposition of the unilateral contact with friction and the essential boundary conditions are obtained by applying the Augmented Lagrangian method. Numerical examples are presented in order to attest the performance of the proposed constitutive model.