Title: Non-linear elasticity of the vertex model and rigidity on curved geometries

Speaker: Arthur Hernandez (University of Leiden)

Abstract:

The vertex model is known to exhibit a transition between solid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. An asymmetry in the linear elastic response is identified at the rigidity transition between compression and dilation. We show that the asymmetry extends away from the transition point for finite strains, and implies that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the effective strain on cell shape due to curvature and write a prediction for the rigidity transition in a curved geometry. The shift of the rigidity transition due to geometry is validated by simulation work done by Sussman. Our work provides a new metric for predicting rigidity of curved tissues, as well as another way to test the vertex model’s ability to describe the mechanics of real biological tissues. Time permitting, I will discuss related extensions to other floppy mechanical systems.

This seminar will take place in room D1.116