Nonlinear augmented finite element method for arbitrary cracking in large deformation plates and shells

This article presents a nonlinear augmented finite element method (N-AFEM) for the analysis of arbitrary crack initiation and propagation in large deformation plates and shells. The FE formulations for plate/shell elements and a shell-like cohesive zone element, both with explicit consideration of geometric nonlinearity, have been derived in detail. The geometrically nonlinear shell-like cohesive element has the essential feature of 3D but with crack displacements directly extracted from midplane shell element nodes, which enables an accurate description of crack propagation in shells and plates under large deformation. Furthermore, a novel augmentation process that can explicitly account for the discontinuous displacement fields of cracked elements without the need of extra nodes or nodal DoFs has been develop based on a nonlinear Newton-Raphson method. The numerical performance of the N-AFEM in modeling a number of benchmark shell/plate fracture problems demonstrates that the method is efficient, accurate, and robust.