On the ABAQUS FEA model of finite viscoelasticity

As the demand for fuel efficient cars intensifies, tyre manufacturers are trying harder to esti- mate accurately the energy dissipation of their products. However, the mechanics of tires is a most complex topic due to the variety of mechanical factors involved, such as structural inho- mogeneities, complicated geometries and nonlinear material behavior, including hyperelasticity, viscoelasticity and hypoelasticity, for example. Consequently, advanced finite element codes are often called upon to simulate the behavior of tires in real-world applications, and, in particular, to evaluate their energy efficiency. These commercial codes are often used as "black boxes", and the validity of the results is rarely questioned, even though they might provide a decisive argu- ment in favor of, or against, the viability of a given tire model. In this note we examine the current implementation of nonlinear viscoelastic effects in the ABAQUS Finite Element Analysis (FEA) package because we have noticed certain discrepan- cies in the model used.** In particular, the ABAQUS model leads to results that are not consis- tent with the thermomechanically-based Quasi-Linear Viscoelastic (QLV) model. In Section "Finite Viscoelasticity Models" we therefore present both models and highlight their main dif- ferences. We then investigate two prototype experiments, for which purpose we use the incom- pressible Yeoh material for the elastic part of the material response in each case. In Section "Simple Tension" we discuss the uniaxial tension test, while in Section "Simple Shear" the sim- ple shear test is examined. The ABAQUS model predicts somewhat different stress components for each of the considered motions and, more significantly, considerably larger dissipation rates than the QLV model.