Oscillatory Instabilities in Frictional Granular Matter

Abstract

Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to a vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e. the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations which are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the understanding of plasticity and failure in frictional granular materials. The possible relevance to earthquake physics is discussed.

Supplementary materials follows the main text Animation of the instability: https://vimeo.com/310132278

References in corpus (3)

• Theoretical perspective on the glass transition and amorphous materials
• Continuum limit of the vibrational properties of amorphous solids
• Breakdown of Nonlinear Elasticity in Stress-Controlled Thermal Amorphous Solids

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• Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain
• Transition from Static to Dynamic Friction in an Array of Frictional Disks
• Universal mechanical instabilities in the energy landscape of amorphous solids: evidence from athermal quasistatic expansion
• Interacting Faults in California and Hindu Kush
• Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime
• Oscillatory Instabilities in 3-Dimensional Frictional Granular Matter
• Shear-induced mixing of granular materials featuring broad granule size distributions
• Enhanced collective vibrations in granular materials