Decoding mechanics by just looking (and not deforming)

How does one determine whether or not a frictional particle packing or biological cells tiling a surface is a rigid material? To answer this question, one typically deforms the material. Rigid materials resist deformations, while floppy ones do not. And yet, constraint-counting methods, relying solely on contact network topology, can identify rigid structures within a frictional particle packing. Additionally, the geometry of cell shapes can help determine whether or not a confluent biological tissue is rigid. Newer examples of “looking but not deforming” mechanics will be discussed, such as area-conserving loops embedded within a fiber network to drive nonlinear compression mechanics as well as convexity-driven rigidity transitions more generally, with an eye towards illuminating the universal design principles for materials that can readily toggle between ultra-responsive and ultra-robust mechanics.