Time dependent large principal deformation of polymers

Abstract

A constitutive model which describes principal deformations of polymeric materials under small and large deformations is presented. It uses the kinetic theory of rubber elasticity as a starting point for the large deformation behaviour and generalizes this theory to include the effect of broad-spectral rate dependence. The constitutive model reduces to (phenomenological) small strain linear viscoelasticity under vanishing strains, while at long times the response corresponds to that of a rubber-elastic material. The behaviour of the model under constant strain rate is examined in both the loading and unloading mode. As a result of appealing to physical-molecular concepts it provides naturally for simulation of a rate dependent yield phenomenon through intrinsic relaxation behaviour without the specific introduction of a yield parameter or yield function. The effect of generalizing the rubber elasticity model to include compressibility is discussed. It is found that the strain energy functional cannot be generalized arbitrarily through an additive term containing the dilatational component. The investigation renders a material description, which, while possibly lacking in detail of species-specific behaviour, reproduces major features of nonlinear and large deformation viscoelastic characteristics. These general features make the model suitable for investigating the influence of rate dependent yielding and large deformation viscoelasticity in the solution of boundary value problems