Fracture in Sheets Draped on Curved Surfaces

Abstract

Curving a thin material, such as a rubber sheet, can trigger fundamental changes in its structure and behavior. In particular, conforming materials to rigid substrates with Gaussian curvature -- positive for spheres and negative for saddles -- has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters, and liquid crystal ripples. Here we show how curvature can likewise be used to control material failure and guide the paths of cracks. In our experiments, we constrain flat elastic sheets to adopt fixed curvature profiles, unlike in previous studies on cracked plates and shells. This constraint provides a geometric tool for controlling fracture behavior: curvature can stimulate or suppress the growth of cracks, and steer or arrest their propagation. A simple model captures crack behavior at the onset of propagation, while a 2D phase-field model successfully captures the crack's path. Since the stresses from curvature are independent of material parameters, our results apply from the nanoscale to geological strata.