An efficient augmented finite element method for arbitrary cracking and crack interaction in solids

W. Liu, Q. D. Yang, S. Mohammadizadeh, X. Y. Su

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


SUMMARY: This paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra-elemental discontinuities in 2D solids. The augmented finite element method (A-FEM) employs four internal nodes to account for the crack displacements due to an intra-elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece-wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A-FEM's high-fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A-FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust.

Original languageEnglish (US)
Pages (from-to)438-468
Number of pages31
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - Aug 10 2014


  • Composites
  • Damage
  • Finite element methods
  • Fracture
  • Stability

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis


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