Modelling of a visco-hyperelastic polymeric foam with a continuous to discrete relaxation spectrum approach

The prediction of compressive properties of foams at large strains and in a wide range of strain rates is still an open issue. In this work we propose a visco-hyperelastic formulation, suitable for large finite strain applications, for the prediction of the compressive response of foams that takes into account the viscoelasticity of the polymer, nonlinear damping, nonlinear behaviour of the cellular structure and effect of gas permeability through the pores at high strain rates. A mathematical expression of the continuous relaxation spectrum is proposed to model the viscoelastic behaviour of the polymer. The relaxation spectrum is then discretized with the desired accuracy required for the subsequent numerical simulations. The model parameters are identified by coupling dynamic measurements at small strain with static ones at large strain. The results are validated by comparing numerical predictions with experimental data from compressive tests up to 50% strain performed at strain rates spanning over 6 degrees of magnitude.