Rigidity percolation in a random tensegrity via analytic graph theory.

Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers, and membranes. These structures are known loosely as tensegrities, since these cable-like elements have the highly nonlinear property of supporting only extensile tension. Marginally rigid systems are of particular interest because the number of structural constraints permits both flexible deformation and the support of external loads.