Effect of poisson ratio on cellular structure formation.

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 antiferroelastic phases as a function of the Poisson ratio.