Odd moduli of disordered odd elastic lattices

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.