Anomalous elasticity of a cellular tissue vertex model

Area of Science:

• Physics
• Materials Science
• Biophysics

Background:

• Vertex models are used to simulate cellular tissues, with cell energy dependent on area and perimeter deviations from targets.
• The interplay between area and perimeter constraints introduces complex mechanical behaviors in these models.

Purpose of the Study:

• To investigate the mechanical response of a simplified vertex model undergoing deformation.
• To analyze the transition between fluid and rigid states and the breakdown of linear elasticity.

Main Methods:

• A mean-field approach was applied to a uniform network of regular polygons without topological changes.
• Analysis focused on the ground states and deformation responses of individual cells.
• Mechanical resistance was calculated and measured under various deformation protocols.

Main Results:

• The model demonstrated a transition from a fluid/compatible state to a rigid/incompatible state.
• Linear elasticity failed to describe the mechanical response at the onset of rigidity, where a single zero-energy ground state exists.
• A breakdown of reciprocity was observed, with different moduli for compressive and tensile loads, indicating energy functional nonanalyticity.

Conclusions:

• The complex elastic response arises from distinct reference states for area and perimeter.
• Critically compatible tissues offer new possibilities for designing mechanical metamaterials that challenge classical elasticity.
• Findings provide insights into the fundamental mechanics of deformable materials and metamaterials.