Analysis of fracture in thin shells by overlapping paired elements

A finite element methodology for evolution of cracks in thin shells using mid-surface displacement and director field discontinuities is presented. We enrich the mid-surface displacement and director fields of a discrete Kirchhoff–Love quadrilateral element using a piecewise decomposition of element kinematics, which leads to a basis that is a variant of the one used in the extended finite element method. This allows considerable simplifications in the inclusion of the shell director field. A cohesive law is employed to represent the progressive release of the fracture energy. In contrast with previous works, we retain the original quadrature points after the formation of a crack, which, in combination with an elasto-plastic multiplicative decomposition of the deformation gradient, avoids the previously required internal variable mapping during crack evolution. Results are presented for large strain elastic and elasto-plastic crack propagation.