Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical loadings

J. Jung, B. C. Do, Qingda Yang

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper, a thermal-mechanical augmented finiteelement method (TM-AFEM) has been proposed, implemented and validated for steady-state and transient, coupled thermal-mechanical analyses of complex materials with explicit consideration of arbitrary evolving cracks. The method permits the derivation of explicit, fully condensed thermal- mechanical equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node quadrilateral two-dimensional (2D) element and a 4-node tetrahedron three-dimensional (3D) element. It has been demonstrated, through several numerical examples that the new TM-AFEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 2D and 3D solids under coupled thermal- mechanical loading conditions. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

Original languageEnglish (US)
Article number20150282
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume374
Issue number2071
DOIs
StatePublished - Jul 13 2016

Fingerprint

equilibrium equations
Cracking
crack propagation
tetrahedrons
integrity
finite element method
Crack
derivation
cracks
Finite Element Method
Cracks
Finite element method
composite materials
Arbitrary
Interaction
interactions
Multiscale Modeling
Numerical Accuracy
Exactness
Triangular pyramid

Keywords

  • Augmented finite-element method
  • Cohesive zone models
  • Composites
  • Fracture

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Engineering(all)

Cite this

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N2 - In this paper, a thermal-mechanical augmented finiteelement method (TM-AFEM) has been proposed, implemented and validated for steady-state and transient, coupled thermal-mechanical analyses of complex materials with explicit consideration of arbitrary evolving cracks. The method permits the derivation of explicit, fully condensed thermal- mechanical equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node quadrilateral two-dimensional (2D) element and a 4-node tetrahedron three-dimensional (3D) element. It has been demonstrated, through several numerical examples that the new TM-AFEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 2D and 3D solids under coupled thermal- mechanical loading conditions. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

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