Curvature-induced fracture mode coupling in doubly curved shells

Classical shell fracture theories predominantly consider cracks aligned with principal curvature directions in cylindrical and spherical shells under tensile mode or pressure loading, leaving the fracture behavior of arbitrarily oriented cracks in doubly curved shells under general loading poorly understood. Here, we introduce a semi-analytical framework based on Reissner shallow-shell theory to investigate isotropic shells with positive, zero, and negative Gaussian curvature. The formulation computes stress intensity factors, energy release rates, and crack-lip displacements for arbitrarily inclined through-thickness cracks in spheres, ellipsoids, cylinders, hyperboloids, and minimal surfaces under general mechanical loading. We show that shell curvature couples opening, sliding, and tearing, allowing a single loading component to activate multiple fracture modes, unlike in flat plates. This coupling depends strongly on crack orientation and the normal, parallel, and torsional components of the shell curvature. Ellipsoids exhibit weak coupling, hyperboloids generally exhibit the strongest coupling, and cylinders display the most complex orientation-dependent responses. Moreover, in-plane shear can induce crack closure in hyperboloidal shells, suggesting a potential geometric mechanism for enhanced damage resistance. These findings elucidate the role of local curvature in fracture-mode coupling and provide a mechanistic foundation for the analysis of shellular (meta-)structures with engineered curvature distributions.