# Oscillatory Instabilities in Frictional Granular Matter

## TL;DR

This paper reveals a new oscillatory instability mechanism in frictional granular matter, differing fundamentally from non-frictional glasses, with implications for understanding plasticity, failure, and earthquake physics.

## Contribution

It identifies a novel oscillatory instability mechanism in frictional granular materials, expanding the understanding of their plastic responses beyond traditional eigenvalue-based instabilities.

## Key findings

- Frictional granular matter exhibits complex eigenvalues leading to oscillatory instabilities.
- These instabilities differ from those in non-frictional glasses, which involve real eigenvalue vanishing.
- The study discusses potential relevance to earthquake physics.

## 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.