Athermal Quasistatic Sheared Voronoi

Huang et al. · PRL 128, 178001 (2022) | Nguyen et al. · Nat. Commun. 16, 3260 (2025)
-- fps
γ 0.000 σ_xy — E/N — ⟨q⟩ — T1s total 0 T1s/Δγ 0 FIRE it. —
Stress σxy vs strain γ
About this model

Athermal quasistatic simple shear of the 2D Voronoi tissue model under Lees–Edwards boundaries. With K_A = 0 the energy is perimeter-only: E = Σ K_P (P_i − P_0)². Default box side L = √N so ⟨A⟩ = A₀ = 1.

Each strain step applies an affine shear x → x + Δγ·y, wraps under LEBC, then FIRE-minimises to mechanical equilibrium. Shear stress σ_xy is measured from the virial/analytical form (1/L²) Σ_e T_e dx_e dy_e / |e|, which does not spike at T1s. T1 events are detected by changes in the Delaunay edge set; the four cells of each T1 quartet flash red briefly.

Model Parameters
p₀target shape index
P₀/√A₀. Jamming transition at p₀* ≈ 3.813
3.78
Δγstrain step
Affine shear applied before each FIRE relax
0.0020
Presets
Solid (p₀=3.60)
Near-critical (p₀=3.81)
Strain-stiffening (p₀=3.90)
Fluid (p₀=4.00)
Simulation
N cells
Visualization
Cell edges
Cell centres
T1 flashes
Persistent T1 markers
References

Huang, J., Cochran, J., Fielding, S., Marchetti, M., & Bi, D. Shear-Driven Solidification and Nonlinear Elasticity in Epithelial Tissues. Phys. Rev. Lett. 128, 178001 (2022).

Nguyen, A. Q., Huang, J., & Bi, D. Origin of yield stress and mechanical plasticity in model biological tissues. Nat. Commun. 16, 3260 (2025).

Disclaimer
This demo was developed with assistance from AI coding tools. Forces use the analytical circumcenter-Jacobian chain rule (same as the SPV/Bi 2016 formulation); FIRE is capped at a few hundred iterations for interactive speed, so at strongly nonlinear configurations the relaxation may not reach the tolerance of a batch MATLAB run.