Geometric Frustration and Solid-Solid Transitions in Model 2D Tissue

Michael Moshe, Mark J. Bowick, M. Cristina Marchetti

Research output: Contribution to journalArticlepeer-review


We study the mechanical behavior of two-dimensional cellular tissues by formulating the continuum limit of discrete vertex models based on an energy that penalizes departures from a target area A0 and a target perimeter P0 for the component cells of the tissue. As the dimensionless target shape index s0=(P0/A0) is varied, we find a transition from a soft elastic regime for a compatible target perimeter and area to a stiffer nonlinear elastic regime frustrated by geometric incompatibility. We show that the ground state in the soft regime has a family of degenerate solutions associated with zero modes for the target area and perimeter. The onset of geometric incompatibility at a critical s0c lifts this degeneracy. The resultant energy gap leads to a nonlinear elastic response distinct from that obtained in classical elasticity models. We draw an analogy between cellular tissues and anelastic deformations in solids.

Original languageAmerican English
Article number268105
JournalPhysical Review Letters
Issue number26
StatePublished - 29 Jun 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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