Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying, both experimentally and numerically, the case of a rod confined isotropically into a disc, we show that the emergence of the complexity is associated with a well-defined underlying statistical measure that determines the energy distribution of sub-elements, 'branches', of the rod. This result suggests that branches act as the 'microscopic' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system.