Viscoelastic Constitutive Relation Of One Kind Polymer Material

In classical rate-independent viscosity, the finite viscoelasticity was commonly supposed to bedecomposed into elastic and viscous parts, which was described through their respectivecontrolling constitutive laws. However, there are still existing two issues remain unsettled, manyrational interpretation on the decomposition of the deformation into elastic and viscous parts andsome disputes on the choice of objective stress rate. This paper discusses a new method toformulate a new viscoelastic constitutive model for one kind polymeric material at finitedeformation. This model proposed is based on the multiplicative decomposition of the deformationgradient, which can be decomposed into elastic and viscous parts. Although the form in this thesis,consistence with the decomposition of Lee, the essence is different. First of all, we introduce thedevelopment of the viscoelastic constitutive models of the finite deformation and the main work ofthis Master’s thesis. Then, viscoelastic models of small deformation serve as a starting point for thedevelopment of the viscoelastic constitutive models of finite deformation, which also exhibits theviscoelastic of polymeric behavior. Some basic knowledge theory of the continuity mediummechanical of finite deformation was given. Using this new method, in this thesis, the constitutivemodel of small deformation is extended to make the model applicable in finite deformation. Ournew method is making the process of finite deformation is decomposed into a series of sub-processes of small deformation. The rotations of stress in sub-processes are determined by elasticconstitutive equation. The changes in the principal stress are calculated by using the spring anddashpot constructions. Then, a viscoelastic constitutive model, which satisfies the principle ofobjectivity, a new form of the viscoelastic formulation for the finite deformation is presented forthe isotropic polymeric materials. Such form of constitutive model in principle can be suitable for arange of strain-rates. Finally, we using this new constitutive relation, to calculate the finitedeformation of polymer material, and as an application, the simple shear deformation is computedto show that the proposed model can describe the viscoelastic behavior for polymers at finitedeformations.The advantage of this thesis is that the objectivity of the stress rate and decomposition of theviscoelastic finite deformation are dealt with in integrating the constitutive equation, which are alsosatisfied in the finite deformation of viscoelastic constitutive equation, we needn’t to choose whichkind of objective stress rate.