Curvature-driven Interfacial Fracture in Growing Elastic Shells*

Biological interfaces can undergo instabilities that are triggered by growth. Especially interesting is the response of doubly curved growing interfaces. Motivated by the surgical problem of endograft seal zone stability, where a cylindrical membrane covered stent initially in contact with the inside of an artery losses contact, we study the stability of interfaces with varying curvatures under various loads. This computational study implements isotropic growth in a finite element model. The adhesive interface is modeled using cohesive zone mechanics (CZM). The load on the interface comes from growth as well as flow inside the lumen of the curved cylindrical shells. We perform a coupled fluid-structure-fracture simulation (FSFS).  We capitalize on our expertise with explicit dynamic approaches for solid mechanics/fracture and couple them with a Lattice-Boltzmann (LB) code to model fluid flow (CFD). Our data shows that singly curved interfaces, such as cylinders, lose stability uniformly and follow an edge-delamination mechanism. However, doubly curved interfaces, like a toroidal section of a bent cylinder, fail non-uniformly. The negative Gaussian curvature section is more sensitive to fracture compared to the spherical section. Our data can be used to better design endograft stents for optimal seal in vascular surgery.