A class of models to predict the normal force and torque under torsional loading of a viscoelastic liquid

Viscoelastic liquids exhibit diverse mechanical behavior and offers a tremendous challenge in modeling its nonlinear response. This work is concerned with the development of a class of constitutive equations for viscoelastic liquids, which can capture the nonlinear response, especially, under torsional loading. By extending a universal solution developed by Rivlin (1948) for elastic bodies under torsional loading to viscoelastic bodies, one can arrive at a constitutive equation that can simultaneously predict torque and normal force with a reasonable accuracy. In order to develop such a constitutive equation, a suitable thermodynamical framework developed by Rajagopal and Srinivasa (2000) is chosen because of the fact that it can be used to exploit the mentioned result of Rivlin. Consequently, a suitable rate-type constitutive equation is also derived in Section 5. The efficacy of the developed model is checked by comparing the predictions of the model with that of the experimental data for torsional deformation of asphalt. It is found that the predictions of the model agree reasonably with that of the experimental data.