Abstract
An extended finite element method (X-FEM) for classical kinetic friction laws in a multi-material arbitrary Lagrangian Eulerian (MMALE) formulation is presented. The velocities of the nodes containing more than one material in their support are updated through the nodal accelerations to account for the kinetic friction effects. Numerical results are presented and discussed.
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References
Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5): 601–620
Benson D (1992) Computational methods in Lagrangian and Eulerian hydrocodes. Comput Methods Appl Mech Eng 99: 235–394
Benson D (1995) A multi-material Eulerian formulation for the efficient solution of impact and penetration problems. Comput Mech 15: 558–571
Benson D (1997) A mixture theory for contact in multi-material Eulerian formulations. Comput Methods Appl Mech Eng 140: 59–86
Benson D (2002) Volume of fluid interface reconstruction methods for multi-material problems. Appl Mech Rev 55(2): 151–165
Benson D, Okazawa S (2004) Contact in a multi-material Eulerian finite element formulation. Comput Methods Appl Mech Eng 193: 4277–4298
Chessa J, Belytschko T (2004) Arbitrary discontinuities in space–time finite elements by level sets and x-fem. Int J Numer Methods Eng 61(15): 2595–2614
Chorin A, Hughes T, McCracken M, Marsden J (1978) Product formulas and numerical algorithms. Commun Pure Appl Math 31: 205–256
Fleming M, Chu Y, Moran B, Belytschko T (1997) Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng 40: 1483–1504
Krongauz Y, Belytschko T (1998) Efg approximation with discontinuous derivatives. Int J Numer Methods Eng 41: 1215–1233
Sukumar N, Moes N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modeling. Int J Numer Methods Eng 48(11): 1549–1570
Sukumar N, Chop D, Moes N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190(46–47): 6183–6200
Vitali E (2007) An extended finite element formulation for contact in multi-material arbitrary Lagrangian–Eulerian calculations. Ph.D. dissertation, University of California, San Diego
Vitali E, Benson D (2006) An extended finite element formulation for contact in multi-material arbitrary Lagrangian–Eulerian calculations. Int J Numer Methods Eng 67(10): 1420–1444
Vitali E, Benson D (2008) Contact with friction in multi-material arbitrary Lagrangian–Eulerian formulations using x-fem. Int J Numer Methods Eng 76(6): 893–921
Youngs D (1982) Time dependent multi-material flow with large fluid distorsion. Numer Methods Fluid Dyn, pp 273–285
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Army Research Organization; contract/grant number: DAAD19-02-1-0266.
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Vitali, E., Benson, D. Kinetic friction for multi-material arbitrary Lagrangian Eulerian extended finite element formulations. Comput Mech 43, 847–857 (2009). https://doi.org/10.1007/s00466-008-0351-6
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DOI: https://doi.org/10.1007/s00466-008-0351-6