Prestressed elasticity of amorphous solids

TL;DR

This paper develops mathematical tools to analyze how prestress influences the elasticity of amorphous solids, revealing effects like heterogeneity, stress distribution, and criteria for floppy modes, which are crucial for understanding their mechanical behavior.

Contribution

The paper introduces new mathematical methods to separate the effects of disorder and prestress in amorphous solids, advancing understanding of their elastic properties.

Findings

Prestress causes strong spatial heterogeneity in stress response.

Distribution of minimal dipole stiffness follows a power-law.

A new criterion for classifying floppy modes in prestressed solids.

Abstract

Prestress in amorphous solids bears the memory of their formation, and plays a profound role in their mechanical properties, from stiffening or softening elastic moduli to shifting frequencies of vibrational modes, as well as directing yielding and solidification in the nonlinear regime. Here we develop a set of mathematical tools to investigate elasticity of prestressed discrete networks, which disentangles the effects from disorder in configuration and disorder in prestress. Applying these methods to prestressed triangular lattices and a computational model of amorphous solids, we demonstrate the importance of prestress on elasticity, and reveal a number of intriguing effects caused by prestress, including strong spatial heterogeneity in stress-response unique to prestressed solids, power-law distribution of minimal dipole stiffness, and a new criterion to classify floppy modes.