A constitutive model in finite viscoelasticity with an entropy-driven material clock

Abstract

A constitutive model is derived for the nonlinear viscoelastic response in polymers under isothermal loading at finite strains. The model is based on the concept of transient networks, where the rates of breakage and reformation of active chains are assumed to depend on the specific entropy. The stress-strain relations are developed for arbitrary active chains and for arbitrary rates of loss and reformation. For Gaussian chains and nonaging networks, the constitutive relations are simplified and reduced to quasi-linear Volterra equations with entropy-dependent kernels. In this case, the governing equations contain only one new adjustable parameter compared to conventional linear models in finite viscoelasticity. The constitutive model with an entropy-driven internal clock is applied to describe shear-thickening in polymeric solutions. By comparison of numerical results with experimental data, it is demonstrated that the model adequately predicts the shear-thickening phenomenon.