What do guitar strings and balloons have in common with biological networks and tissues?

Both guitar strings and balloons are floppy unless rigidified by geometrically induced self-stresses. Similar kinds of rigidity transitions have recently been described in biopolymer networks and models for biological tissues. Here, we propose a general approach to quantitatively describe such transitions. Based on a minimal length function, which scales linearly with intrinsic fluctuations in the system and quadratically with shear strain, we make concrete predictions about the elastic response of these materials, which we verify numerically and which are consistent with previous experiments. Our approach may provide a gateway towards connecting macroscopic elastic properties of disordered materials to their microscopic structure.