Towards understanding the geometry effects on fracture in thin elastic shells

TL;DR

This paper investigates how the geometry of thin elastic shells influences fracture behavior, using phase-field simulations and theoretical derivations to understand crack evolution and toughness variations.

Contribution

It introduces a theoretical framework linking shell geometry to fracture mechanics by deriving the configurational force for crack extension in thin shells.

Findings

Shell shape significantly influences crack evolution.

Curvature contributes to non-conservative forces affecting fracture.

Theoretical insights can guide design optimization of shell structures.

Abstract

We examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.