A Phenomenological Constitutive Model for Rigid Polymeric Foam

An orthotropic rate independent plasticity and viscoplasticity constitutive law for rigid low density polymeric foams is presented. A multi-surface yield criterion is used in the constitutive model to represent the envelope of failure surfaces given by Gibson et. al. (1989) for cellular materials. An inelastic flow direction is selected to simulate the near zero “plastic Poisson’s ratio” observed in many experimental tests. A special orthotropic hardening law is also developed that captures the extreme stiffening due to densification at very large strains. Details involving loading and unloading conditions and discrete algorithms for numerical implementation are discussed. The rate dependencies are modeled by a power law viscoplasticity relation. The model is implemented in the finite element code DYNA3D and is used to simulate experimental results.