An efficient A-FEM for arbitrary cracking in solids

Qingda Yang, Wei Liu, Xian Yue Su

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper a new augmented finite element method (A-FEM) that can account for multiple, intra-elemental discontinuities in heterogeneous solids has been derived. It does not need the extra DoFs as in the extended finite element method (X-FEM), or the additional nodes as in the phantom node method (PNM). The new A-FEM employs four internal nodes to facilitate the calculation of subdomain stiffness and the crack displacements due to an intra-elemental discontinuity. It is shown that through a novel efficient solving algorithm the displacement DoFs associated with the internal nodes can be solved analytically as functions of the regular nodal DoFs for any piece-wise linear cohesive laws, which leads to a fully-condensed elemental equilibrium equation that is mathematically exact. The new formulation permits repeated elemental augmentation to include multiple interactive cracks within a single element, enabling a unified treatment of the evolution from a weak discontinuity, to a strong discontinuity, and to multiple intra-element discontinuities, all within a single element that employs standard DoFs only. The new A-FEM's capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples. It has been demonstrated that the new A-FEM achieved more than two orders of magnitude improvement in numerical accuracy, efficiency, and robustness, compared to the X-FEM.

Original languageEnglish
Title of host publication13th International Conference on Fracture 2013, ICF 2013
PublisherChinese Society of Theoretical and Applied Mechanics
Number of pages10
StatePublished - Jan 1 2013
Event13th International Conference on Fracture 2013, ICF 2013 - Beijing, China
Duration: Jun 16 2013Jun 21 2013


Other13th International Conference on Fracture 2013, ICF 2013


  • Augmented FEM
  • Cohesive model
  • Extended FEM
  • Fracture
  • Numerical simulation

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology


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