A comparative study of Maxwell viscoelasticity at large strains and rotations

Abstract We present a new Eulerian large-strain model for Maxwell viscoelasticity using a logarithmic co-rotational stress rate and the Hencky strain tensor. This model is compared to the small-strain model without co-rotational terms and a formulation using the Jaumann stress rate. Homogeneous isothermal simple shear is examined for Weissenberg numbers in the interval [0.1; 10]. Significant differences in shear stress and energy evolution occur at Weissenberg numbers >0.1 and shear strains >0.5. In this parameter range, the Maxwell–Jaumann model dissipates elastic energy erroneously and thus should not be used. The small-strain model ignores finite transformations, frame indifference and self-consistency. As a result, it overestimates shear stresses compared to the new model and entails significant errors in the energy budget. Our large-strain model provides an energetically consistent approach to simulating non-coaxial viscoelastic deformation at large strains and rotations.