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

Abstract

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.

Modeling dynamic cracks initiation and propagation with the local to global approach

“…Yang and colleagues [28][29][30][31] proposed augmented finite element method (A-FEM) that can deal with discontinuous displacement fields without adding extra nodes/DoFs. In A-FEM, internal nodes are introduced at element boundaries cut by cracks to facilitate stiffness and crack displacement calculation, but those internal nodes are condensed at element level, which do not appear in global problem.…”

On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method

“…By embedding discontinuities inside elements, the AFEM simplifies their modelling because they no longer need to conform to the elements boundaries as required in the finite element method (FEM). The AFEM has been widely used in structural analysis to model cracks, with successful applications, including unstable crack propagation [8], crack growth under thermomechanical loading [9], dynamic crack propagation [10], three-dimensional studies of composite materials [11] or the large deformation of cracked shells [12]. The method was implemented as a user element in Abaqus and proved to be 50 times faster than the phantom-node method (PNM) natively implemented in this software [13].…”