Modeling of Rate Dependent Finite Deformation Viscoelastic Behavior of Foams

Abstract

The behavior of foams is typically rate-dependent and viscoelastic. In this paper, multiplicative decomposition of the deformation gradient and the second law of thermodynamics are employed to develop the differential constitutive equations for isotropic viscoelastic foams experiencing finite deformations, from a phenomenological point of view, i.e. without referring to micro-structural viewpoint. A model containing an equilibrium hyperelastic spring which is parallel to a Maxwell model has been utilized for introducing constitutive formulation. The deformation gradient tensor is decomposed into two parts: elastic deformation gradient tensor and viscoelastic deformation gradient tensor. A strain energy function is presented for the equilibrium spring as a function of the invariants of the left Cauchy-Green stretch tensor to obtain equilibrium stress components. Also, a strain energy function is presented for the intermediate spring as a function of the invariants of elastic deformation gradient tensor to determine overstress components. The constants of the strain energies are calculated by using nonlinear regulation numerical methods and by comparing with the experimental data obtained from uniaxial tension tests. The developed finite deformation constitutive equations are derived such that for every admissible process, the second law of thermodynamics is satisfied.