×

zbMATH — the first resource for mathematics

Dislocations by partition of unity. (English) Zbl 1078.74665
Summary: A new finite element method for accurately modelling the displacement and stress fields produced by a dislocation is proposed. The methodology is based on a local enrichment of the finite element space by closed-form solutions for dislocations in infinite media via local partitions of unity. This allows the treatment of both arbitrary boundary conditions and interfaces between materials. The method can readily be extended to arrays of dislocations, 3D problems, large strains and nonlinear constitutive models. Results are given for an edge dislocation in a hollow cylinder and in an infinite medium, for the cases of a glide plane intersecting a rigid obstacle and an interface between two materials.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
PDF BibTeX Cite
Full Text: DOI
References:
[1] Babuska, International Journal for Numerical Methods in Engineering 40 pp 727– (1997)
[2] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001)
[3] Sukumar, Computer Methods in Applied Mechanics and Engineering 90 pp 6183– (2001)
[4] Moës, International Journal for Numerical Methods in Engineering 53 pp 2549– (2002)
[5] Chessa, International Journal for Numerical Methods in Engineering 53 pp 1957– (2002)
[6] Chessa, ASME Journal of Applied Mechanics 70 pp 10– (2003)
[7] Devincre, Philosophical Transactions of the Royal Society of London A 355 pp 2003– (1997)
[8] Dislocations and mechanisms revealed by computer simulation. In et al (eds). Strength of Metals and Alloys, Proceedings of ICSMA 8, vol. 1. Pergamon: Oxford, 1988; 312.
[9] Duesdery, Critical Reviews in Solid State and Materials Sciences 17 pp 1– (1991)
[10] Veyssière, Revue de Physique Appliquee 23 pp 431– (1988)
[11] Devincre, Materials Science and Engineering A 309-310 pp 211– (2001)
[12] Kubin, Solid State Phenomena 23-24 pp 455– (1992)
[13] Schwarz, Journal of Applied Physics 85 pp 108– (1999)
[14] Schwarz, Modelling and Simulation in Materials Science and Engineering 11 pp 609– (2003)
[15] Zbib, International Journal of Mechanical Sciences 40 pp 113– (1998)
[16] Van Der Giessen, Modelling and Simulation in Materials Science and Engineering 3 pp 689– (1995)
[17] Zbib, International Journal of Plasticity 18 pp 1133– (2002)
[18] Groh, Philosophical Magazine Letters 83 pp 303– (2003)
[19] Lemarchand, Journal of the Mechanics and Physics of Solids 49 pp 1969– (2001)
[20] Theory of Crystal Dislocations. Dover Publications: New York, 1967.
[21] Lubarda, Acta Metallurgica et Materialia 41 pp 625– (1993)
[22] Reid, Phase Transitions 69 pp 309– (1999)
[23] Taylor, Proceedings of the Royal Society of London 145 pp 362– (1934)
[24] Boundary problems. Dislocations in Solids, (ed.). North-Holland: Amsterdam, New York, Oxford, 1979; 167-221.
[25] Koehler, Physical Review 60 pp 397– (1941)
[26] Dislocation Based Fracture Mechanics. World Scientific: Singapore, New Jersey, London, Hong Kong, 1996.
[27] Stazi, Computational Mechanics 31 pp 38– (2003)
[28] Peach, Physical Review 80 pp 436– (1950)
[29] Theory of Dislocations (2nd edn). Wiley: New York, 1982.
[30] Cools, ACM Transactions on Mathematical Software 23 pp 1– (1997)
[31] Chessa, International Journal for Numerical Methods in Engineering 57 pp 1015– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.