Continuum mechanics of a cellular tissue model

Raz Kupferman*, Ben Maman, Michael Moshe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider a two-dimensional cellular vertex model, modeling the mechanics of epithelial tissues. The energy of a planar configuration penalizes deviations in each cell from a reference perimeter P0 and a reference area A0. We study the variational limit of this model as the cell size tends to zero, obtaining a continuum variational model. For P02/A0 below a critical threshold, which corresponds to an isoperimetric constraint, the system is residually-stressed—there are no zero-energy states. For P02/A0 above this threshold, the zero-energy states are highly degenerate, allowing in particular for the formation of microstructures, which are not captured by formal long-wavelength expansions.

Original languageAmerican English
Article number104085
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Oct 2020

Bibliographical note

Publisher Copyright:
© 2020


  • Cellular models
  • Incompatible elasticity
  • Γ-convergence


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