Studies On The Constitutive Theory For Nonlinear Viscoelastic Materials With Damage

AbstractVscoelastic theory is a boundary science that depends on thedevelopment of mechanic and materia1 science, it is one of the importanparts of continuum mechanic. At present, many driportan developmenton the studies of viscoelastic theory have been made by the efforts ofin-country and out-coUntry scholars, linear viscoelasticity theory hasperfectly developed, but nonlinear viscoelastic theory has beendeveloping by the reason of difficulties in exPedent and mathematics.The mechanical property of material will gradually become bad underthe conditions of loading and surroundings, with the increasing ofdeformation, the micro-deIYctS will emerged in the material, then theywill gradually groW coalesce, join and make the material be destroyedultimately. For describing the mechanical behavior of nonlinearviscoe1astic material accUraely the effect of daInage in the material toconstitutive must be considered.In the present, the three-dimensional nonlinear viscoelasticconstitutive relations in Stieltjes convolution are given by aPplying theelasticity recovery correspondence principle in the viscoelasticity theoryBased on the anaIysis on the continuum thermodynamics for nonlinearviscoelastic material, and combining the SEM observations to thepolyPropylene test in the course of single-axis tension, the damageevolution equation for a class of materials as polpoers is obtained.Adopting the continuum damage method, on the basis of strainequivalent hypothesis, the nonlinear viscoelasticity constitutive relationof relaxation model with damage is obtained, and on the basis of strainenergy equivalent hyPothesis, the one of creep model with damage isobtained as well.For single-axis tension under different strain rates and constant amplitude cyclic strain, the nonlinear viscoelasticity constitutive relations without damage and these with damage are applied for describing the mechanics behavior of the class of materials as polymers. The result that the theory curves obtained by the nonlinear viscoelasticity constitutive relation with damage are be more agreeable with experimental data than those obtained by the one without damage is verified.