Pore–gas interaction in foams at finite deformation using staggered solution techniques

In the present paper we investigate the significance of gas–solid interaction in foamed polymers. In particular, we consider the response of foams to large compressive deformations at high rates. A main feature of the paper concerns the representation of gas-filled foams as a two-phase porous material, where the interaction between the phases is modeled by means of a deformation dependent Darcian filter law. Thereby, a continuum mechanical coupling is obtained between the gas pressure and the deformation of the cellular network. It is proposed to resolve this coupling utilizing a staggered solution procedure similar to the staggered handling of the thermo-mechanically coupled problem. Two different types of decouplings are compared: the “undrained” decoupling where the gas flow is locally prescribed for each step in the solution of the momentum balance, and the “constant pressure” decoupling where the pressure is considered constant during the momentum balance step. The model is implemented in the finite element code LS-DYNA, and the paper is concluded by number of representative numerical simulations. A parametric study in terms of the permeability properties of foam is carried out to display the significance of the gas–solid interaction for a polymeric foam.