  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.
