Nonlinear elasticity, viscosity and damage in open-cell polymeric foams

Of interest, in this work, is the behavior of open-cell polymer foams under compression. In a recent work by Del Piero and Pampolini (Continuum Mech Thermodyn 24:181-199, 2012), a model coupling nonlinear elasticity and viscosity was introduced to describe the response of a polyurethane foam subjected to uniaxial cyclic compression. Inelastic effects were attributed to the viscous properties of the foam, while strain localization and hysteresis were attributed to the nonconvexity of the strain energy density. But the model did not reproduce the response curves after the first loading-unloading cycle. Here, the model is extended by taking into account the damage of the foam. A simple phenomenological one parameter damage law is used to describe the damage occurring during the first loading cycle. An accurate identification procedure for the material constants is also developed, and the interaction of viscosity and damage in both monotonic and cyclic deformation processes is discussed. In spite of the one dimensional formulation, the model permits a precise analysis of the main phenomena which determine the complex behavior of the foam.