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

W. Liu, Qingda Yang, S. Mohammadizadeh, X. Y. Su

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

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
Pages (from-to)438-468
Number of pages31
JournalInternational Journal for Numerical Methods in Engineering
Volume99
Issue number6
DOIs
StatePublished - Aug 10 2014

Fingerprint

Cracking
Cohesive Crack
Strong Discontinuity
Crack
Finite Element Method
Augmentation
Cracks
Condensation
Finite element method
Discontinuity
Arbitrary
Interaction
Internal
Exactness
Crack initiation
Piecewise Linear
Fidelity
Crack propagation
Damage
Propagation

Keywords

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

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

An efficient augmented finite element method for arbitrary cracking and crack interaction in solids. / Liu, W.; Yang, Qingda; Mohammadizadeh, S.; Su, X. Y.

In: International Journal for Numerical Methods in Engineering, Vol. 99, No. 6, 10.08.2014, p. 438-468.

Research output: Contribution to journalArticle

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