Effect of Poisson ratio on cellular structure formation

TL;DR

This paper investigates how the Poisson ratio influences cellular structure formation in soft media, revealing phase transitions driven by elastic interactions and screening effects.

Contribution

It introduces an analytical model showing that Poisson ratio affects phase transitions in cellular arrangements via elastic interaction screening.

Findings

Elastic interactions decay exponentially due to screening.

Phase transitions occur from paraelastic to ferroelastic and anti-ferroelastic phases.

Poisson ratio determines the decay length of effective interactions.

Abstract

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long-ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a function of Poisson ratio.