Fracture in Sheets Draped on Curved Surfaces

TL;DR

This paper demonstrates how fixed curvature profiles in elastic sheets can control crack initiation, growth, and paths, offering a geometric method to influence material failure across scales.

Contribution

It introduces a novel approach using curvature constraints to steer and suppress cracks, supported by analytical and phase-field models.

Findings

Curvature can stimulate or suppress crack growth.

Crack paths can be steered or halted by curvature.

Results are scale-independent for isotropic brittle materials.

Abstract

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, and unlike in previous studies on cracked plates and shells, we constrained flat elastic sheets to adopt fixed curvature profiles. 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 analytical model captures crack behavior at the onset of propagation, while a two-dimensional phase-field model with an added curvature term successfully captures the crack's path. Because the curvature-induced stresses are independent of material parameters for isotropic, brittle media, our results apply across scales.