Role of inertia in the rheology of amorphous systems: A finite-element-based elastoplastic model

A simple finite-element analysis with varying damping strength is used to model the athermal shear rheology of densely packed glassy systems at a continuum level. We focus on the influence of dissipation on bulk rheological properties. Our numerical studies, done over a wide range of damping coefficients, identify two well-separated rheological regimes along with a crossover region controlled by a critical damping. In the overdamped limit, inertial effects are negligible and the rheological response is well described by the commonly observed Herschel-Bulkley equation. In stark contrast, inertial vibrations in the underdamped regime prompt a significant drop in the mean-stress level, leading to a nonmonotonic constitutive relation. The observed negative slope in the flow curve, which is a signature of mechanical instability and thus permanent shear banding, arises from the sole influence of inertia, in qualitative agreement with the recent molecular dynamics study of Nicolas et al., Phys. Rev. Lett. 116, 058303 (2016).