eXtended Finite Element Method (XFEM) in Abaqus - Simulia

61 Pages·2011·3.06 MB·English

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• Introduction
• BBaassiicc XXFFEEMM CCoonncceeppttss
• Modeling Approaches
• Stationary cracks
• Contour integgral calculation
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• Static
• Implicit dynamic
• Low cycle fatigue
• XFEM used with other Analysis Techniques
• Global/local modeling approach
• Co-Simulation
• EElleemmeennttss, OOuuttppuuttss aanndd ootthheerrss
• Demonstration
IInnttrroodduuccttiioonn
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IInnttrroodduuccttiioonn
• Strong technology exists in Abaqus:
• IInntteerrffaacciiaall ccrraacckkss wwiitthh VVCCCCTT aanndd ccoohheessiivvee eelleemmeenntt tteecchhnniiqquueess
• Smeared crack approach to continuum damage initiation and evolution
in the bulk materials
• Some difficulties exist:
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1st introduced by Belyschko and Black in 1999.
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• Makes modeling of cracks easier and accurate
• Allows crack to be modeled independent of the mesh
• Allows simulation of initiation and propagation of a
ddiissccrreettee ccrraacckk aalloonngg aann aarrbbiittrraarryy,, ssoolluuttiioonn-ddeeppeennddeenntt
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BBaassiicc XXFFEEMM CCoonncceeppttss
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BBaassiicc XXFFEEMM CCoonncceeppttss
• is an extension of the conventional finite element method based on the concept of partition of unity;
• allows the presence of discontinuities in an element by enriching degrees of freedom with special
displacement functions
Nodal displacement vectors
Nodal enriched degree of
DDiissppllaacceemmeenntt vveeccttoorr ffrreeeeddoomm vveeccttoorr
JJump ffunctiion
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Asymptotic crack-tip
functions
Shape functions
Nodal enriched degree of
ffrreeeeddoomm vveeccttoorr
BBaassiicc XXFFEEMM CCoonncceeppttss
Applies to nodes whose
Applies to all nodes in shape function support is
tthhee mmooddeell ccuutt bbyy tthhee ccrraacckk ttiipp
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ww. Applies to nodes whose
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cut by the crack interior
BBaassiicc XXFFEEMM CCoonncceeppttss
Level set method
• Is a numerical technique for describing a crack and tracking the motion
ooff tthhee ccrraacckk
• Couples naturally with XFEM and makes possible the modeling of 3D
arbitrary crack growth without remeshing
s | • Requires two level sets for a crack:
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level sets gives the crack front
• UUsseess ssiiggnneedd ddiissttaannccee ffuunnccttiioonnss ttoo ddeessccrriibbee tthhee ccrraacckk ggeeoommeettrryy
• No explicit representation of the crack is needed and the crack is entirely
described by nodal data
BBaassiicc XXFFEEMM CCoonncceeppttss
• Calculating Φ and Ψ
•• TThhee nnooddaall vvaalluuee ooff tthhee ffuunnccttiioonn ΦΦ iiss tthhee ssiiggnneedd ddiissttaannccee ooff tthhee nnooddee ffrroomm
the crack face
• Positive value on one side of the crack face, negative on the other
s | • The nodal value of the function Ψ is the signed distance of the node from
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NNodde ΦΦ ΨΨ
1 +0.25 −1.5
1 2
22 +00.2255 −11.00 00.55
3 4
3 −0.25 −1.5
44 −00.2255 −11.00
1.5