Buckled Bundles and Beyond

Defects can elastically buckle 2D crystalline membranes (like graphene) into 3D shapes. Using a combination of numerical simulations and continuum elasticity theory we show how the same is true for columnar structures (like nanotubes or protein fibers). This discovery builds upon the recently uncovered mapping between the inter-filament spacing in bundles and the metric properties of a curved surface. We show that shape instabilities are controlled by a single material-dependent parameter that characterizes the ratio of bending to cohesion energies. Along with a host of previously unknown shape equilibria—the filamentous analogs to the conical and saddlelike shapes of defective membranes—we find a profoundly asymmetric response to positive and negative disclinations in the infinite length limit that is without parallel to the membrane analog.