Inertia effect of deformation in amorphous solids: A dynamic mesoscale model

Shear transformation (ST), as the fundamental event of plastic deformation of amorphous solids, is commonly considered as transient in time and thus assumed to be an equilibrium process without inertia. Such an approximation however poses a major challenge when the deformation becomes non-equilibrium, e.g., under the dynamic and even shock loadings. To overcome the challenge, this paper proposes a dynamic mesoscale model for amorphous solids that connects microscopically inertial STs with macroscopically elastoplastic deformation. By defining two dimensionless parameters: strain increment and intrinsic Deborah number, the model predicts a phase diagram for describing the inertia effect on deformation of amorphous solids. It is found that with increasing strain rate or decreasing ST activation time, the significant inertia effect facilitates the activation and interaction of STs, resulting in the earlier yield of plasticity and lower steady-state flow stress. We also observe that the externally-applied shock wave can directly drive the activation of STs far below the global yield and then propagation along the wave-front. These behaviors are very different from shear banding in the quasi-static treatment without considering the inertia effect of STs. The present study highlights the non-equilibrium nature of plastic events, and increases the understanding of dynamic or shock deformation of amorphous solids at mesoscale.