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

Liang Wang, Xueshi Ma, Qingda Yang, Ryan L. Karkkainen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4509-4536
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Issue number20
StatePublished - Oct 30 2020


  • augmented finite element method
  • cohesive zone model
  • fracture
  • geometric nonlinearity
  • plate
  • shell

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


Dive into the research topics of 'Nonlinear augmented finite element method for arbitrary cracking in large deformation plates and shells'. Together they form a unique fingerprint.

Cite this