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

Abstract

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).

Deformation and flow of amorphous solids: Insights from elastoplastic models

“…(Note that the effect of a delay in signal propagation had already been contemplated in an effective way by Lin et al (2014a), while, for the same purpose, Papanikolaou (2016) introduced a pinning delay in his EPM based on the depinning framework.) It was then possible to investigate the influence of the damping strength on the rheology of the elastoplastic system, which was indeed done by Karimi and Barrat (2016). Using a Maxwellian fluid description for blocks in the plastic regime and an unstructured mesh, these researchers found trends qualitatively very similar to what is observed in MD when the friction coefficient is varied.…”

Rheology of granular flows across the transition from soft to rigid particles

“…This is related to hysteresis, whose understanding needs to focus on the relation between elastoplasticity and jamming in systems prepared far from the steady sheared limit. A second perspective would be to bridge the gap with recent studies investigating the effect of inertia on the rheology of amorphous soft systems, in the limit S 1 [43,44].…”

Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids

“…In this respect, recent studies on atomistic simulations of glasses under deformation [26,27] argue, on the contrary, that inertial effects drive the system to a "new underdamped universality class", rather than taking it away from criticality. On the other hand, the same kind of atomistic approach [28], as well as more coarse grained method [29], have signaled a strong contrast of the finiteshear-rate rheology between the overdamped and the underdamped cases; with no signs of universal behavior in the latter. Strongly inertial underdamped systems tend to produce, in particular, a non-monotonic flow curve and the associated localization of the deformation [28,29].…”

“…On the other hand, the same kind of atomistic approach [28], as well as more coarse grained method [29], have signaled a strong contrast of the finiteshear-rate rheology between the overdamped and the underdamped cases; with no signs of universal behavior in the latter. Strongly inertial underdamped systems tend to produce, in particular, a non-monotonic flow curve and the associated localization of the deformation [28,29].…”