#### IMSc Webinar

#### Convexity-induced rigidity transitions and compression stiffening of cells

#### Mahesh Gandikota

##### Syracuse University, USA

*Google meet link: meet.google.com/fiz-hdce-ayh*

A fundamental theorem in rigidity theory due to Cauchy states that all convex polyhedrons in three dimensions are rigid, i.e. the polyhedron cannot be deformed without changing the shape of at least one of its faces at some energy cost. However, a polygon in two dimensions remains floppy irrespective of its convexity and can be deformed with no energy cost. This property is consistent with Maxwell's constraint counting scheme. Numerical results show that under finite isotropic expansion, an area-conserving polygon rigidifies as it achieves convexity. This demonstrates a link between geometry and mechanics. Such a link is also seen in 2D spring networks. We then discuss the relevance of area-conserving polygons in modeling the elastic response of two systems - an animal cell and fibrin network embedded with inclusions.

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