New Journal of Physics
New Journal of Physics
5 years ago

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

A geometrically controlled rigidity transition in a model for confluent 3D tissues
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 ##IMG## [http://ej.iop.org/images/1367-2630/20/2/022002/njpaaaa13ieqn1.gif] {${s}_{0}\equiv {S}_{0}/{\bar{V}}^{2/3}\approx 5.413$} with ##IMG## [http://ej.iop.org/images/1367-2630/20/2/022002/njpaaaa13ieqn2.gif] {$\bar{V}$} 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, ...

Publisher URL: http://iopscience.iop.org/1367-2630/20/2/022002

DOI: 10.1088/1367-2630/aaaa13

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