Universal mechanical instabilities in the energy landscape of amorphous solids: evidence from athermal quasistatic expansion

TL;DR

This study uses simulations to reveal universal mechanical instabilities in amorphous solids during quasi-static expansion, showing that failure involves saddle-node bifurcations with characteristic eigenvalue behavior and finite-size scaling of plastic events.

Contribution

It demonstrates the universality of failure mechanisms and eigenvalue behavior in amorphous solids under different quasi-static deformation protocols.

Findings

Eigenvalues vanish as a square-root at instabilities

Plastic events cause pressure and energy jumps

Finite-size scaling of plastic events shows universality

Abstract

Using numerical simulations, we study the failure of an amorphous solid under quasi-static expansion starting from a homogeneous high-density state. During the volume expansion, we demonstrate the existence of instabilities manifesting via saddle-node bifurcation in which a minimum meets a saddle. During all such events, the smallest eigenvalue of the Hessian matrix vanishes as a square-root singularity. The plastic instabilities are manifested via sudden jumps in pressure and energy, with the largest event happening when a cavity appears, leading to the yielding of the material. We show that during cavitation and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show sub-extensive finite-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our study reveals universality in the fundamental characteristics during mechanical failure in amorphous solids under any quasi-static deformation protocol.