Strong displacement discontinuities and Lagrange multipliers in the analysis of finite displacement fracture problems

The finite displacement formulation of a quadrilateral element containing an embedded displacement discontinuity is presented. The formulation is based on the kinematically optimal technique, and some known defects of this technique are addressed. Lagrange multipliers are adopted to ensure the corre...

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Bibliographic Details
Published in:Computational mechanics 2004-12, Vol.35 (1), p.54-71
Main Authors: Areias, P. M. A., C sar de S, J. M. A., Concei o Ant nio, C. A., Carneiro, J. A. S. A. O., Teixeira, V .M. P.
Format: Article
Language:English
Subjects:
Crack closure
Crack initiation
Displacement
Lagrange multiplier
Quadrilaterals
Robustness (mathematics)
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Summary:The finite displacement formulation of a quadrilateral element containing an embedded displacement discontinuity is presented. The formulation is based on the kinematically optimal technique, and some known defects of this technique are addressed. Lagrange multipliers are adopted to ensure the correct crack closure prior to initiation. Six additional degrees of freedom in each element allow the representation of the two states of the crack. A classical enhanced strain technique is employed to improve the bending performance of the element. Numerical examples illustrate both the robustness and the accuracy of the proposed solutions.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-004-0603-z