Odd moduli of disordered odd elastic lattices

TL;DR

This paper investigates how bond disorder affects the odd elastic properties of triangular and honeycomb lattices, revealing a crossover from affine response to rigidity percolation, with robustness varying based on lattice fine-tuning.

Contribution

It introduces an effective medium theory combined with simulations to analyze the impact of disorder on odd elastic moduli in lattices, highlighting the transition mechanisms involved.

Findings

Odd moduli exhibit a crossover from affine response to rigidity percolation.

Oddness remains robust against disorder in general, except for fine-tuned honeycomb lattices.

Disorder influences the stability and transition behavior of odd elastic properties.

Abstract

We study the effects of bond disorder on triangular and honeycomb lattices where each spring has a probability p to be odd elastic. Using an effective medium theory and numerical simulations, we uncover the behavior of odd moduli in the presence of disorder, which we interpret as a crossover between the affine response of the passive elastic backbone, and a rigidity percolation transition in the odd elastic components. Though oddness is generally robust against disorder even at low p, we find that fine-tuned features of an odd elastic honeycomb lattice are not robust against disorder.