A geometrically controlled rigidity transition in a model for confluent 3D tissues

Matthias Merkel, M. Lisa Manning

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that specifies cell shapes. Here, we generalize this model to 3D and find a rigidity transition that is similarly controlled by the preferred surface area S 0: the model is solid-like below a dimensionless surface area of with being the average cell volume, and fluid-like above this value. We demonstrate that, unlike jamming in soft spheres, residual stresses are necessary to create rigidity. These stresses occur precisely when cells are unable to obtain their desired geometry, and we conjecture that there is a well-defined minimal surface area possible for disordered cellular structures. We show that the behavior of this minimal surface induces a linear scaling of the shear modulus with the control parameter at the transition point, which is different from the scaling observed in particulate matter. The existence of such a minimal surface may be relevant for biological tissues and foams, and helps explain why cell shapes are a good structural order parameter for rigidity transitions in biological tissues.

Original languageEnglish (US)
Article number022002
JournalNew Journal of Physics
Issue number2
StatePublished - Feb 2018


  • biological tissues
  • constraint counting
  • jamming
  • residual stresses
  • rigidity transition
  • solid-fluid transition
  • vertex model

ASJC Scopus subject areas

  • General Physics and Astronomy


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