×

zbMATH — the first resource for mathematics

A method for dynamic crack and shear band propagation with phantom nodes. (English) Zbl 1113.74078
Summary: A new method for modelling of arbitrary dynamic crack and shear band propagation is presented. We show that by a rearrangement of the extended finite element basis and the nodal degrees of freedom, the discontinuity can be described by superposed elements and phantom nodes. Cracks are treated by adding phantom nodes and superposing elements on the original mesh. Shear bands are treated by adding phantom degrees of freedom. The proposed method simplifies the treatment of element-by-element crack and shear band propagation in explicit methods. A quadrature method for 4-node quadrilaterals is proposed based on a single quadrature point and hourglass control. The proposed method provides consistent history variables because it does not use a subdomain integration scheme for the discontinuous integrand. Numerical examples for dynamic crack and shear band propagation are provided to demonstrate the effectiveness and robustness of the proposed method.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Belytschko, International Journal for Numerical Methods in Engineering 58 pp 1873– (2003)
[2] Hansbo, Computer Methods in Applied Mechanics and Engineering 193 pp 3523– (2004) · Zbl 1068.74076
[3] Belytschko, International Journal for Numerical Methods in Engineering 45 pp 601– (1999)
[4] Moës, International Journal for Numerical Methods in Engineering 46 pp 131– (1999)
[5] Babuška, Computer Methods in Applied Mechanics and Engineering 191 pp 5595– (2002)
[6] Chessa, International Journal for Numerical Methods in Engineering 57 pp 1015– (2003)
[7] Ventura, International Journal for Numerical Methods in Engineering 54 pp 923– (2002)
[8] Rabczuk, International Journal for Numerical Methods in Engineering 61 pp 2316– (2004)
[9] Xu, Journal of Mechanics and Physics of Solids 42 pp 1397– (1994)
[10] Ortiz, International Journal for Numerical Methods in Engineering 44 pp 1267– (1999)
[11] Réthoré, International Journal for Numerical Methods in Engineering 63 pp 631– (2005)
[12] Areias, International Journal for Numerical Methods in Engineering 63 pp 760– (2005)
[13] Mergheim, International Journal for Numerical Methods in Engineering 63 pp 276– (2005)
[14] Stolarska, International Journal for Numerical Methods in Engineering 51 pp 943– (2001)
[15] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001)
[16] Areias, Computer Methods in Applied Mechanics and Engineering (2005)
[17] , . Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000. · Zbl 0959.74001
[18] Flanagan, International Journal for Numerical Methods in Engineering 17 pp 679– (1981)
[19] Daniel, International Journal for Numerical Methods in Engineering 64 pp 335– (2005)
[20] . Mechanics of Solid Materials. Cambridge University Press: Cambridge, 1990. ISBN 0 521 32853 5. · doi:10.1017/CBO9781139167970
[21] Thermodynamic Theory of Viscoplasticity. Academic Press: New York, 1971. · doi:10.1016/S0065-2156(08)70345-4
[22] Lemonds, Mechanics of Materials 5 pp 339– (1986)
[23] Zhou, Journal of the Mechanics and Physics of Solids 44 pp 1007– (1996)
[24] Li, International Journal of Solids and Structures 39 pp 1213– (2002)
[25] Peirce, Computers and Structures 18 pp 875– (1984)
[26] . Stability of rate dependent materials, submitted.
[27] Kalthoff, International Conference on Impact Loading and Dynamic Behavior of Materials 1 pp 185– (1987)
[28] Lee, Journal of Applied Mechanics 57 pp 104– (1990)
[29] Kalthoff, International Journal of Fracture 101 pp 1– (2000)
[30] Source Book on Maraging Steels. American Society for Metals, 1979.
[31] Evaluation of dissipation and damage in metal submitted to dynamic loading. Proceedings ICM 1, 1971.
[32] Belytschko, International Journal of Solids and Structures 32 pp 2547– (1995)
[33] Belytschko, International Journal for Numerical Methods in Engineering 39 pp 923– (1996)
[34] Ramulu, International Journal of Fracture 27 pp 187– (1985)
[35] Ravi-Chandar, International Journal of Fracture 90 pp 83– (1998)
[36] Sharon, Physical Review Letters 74 pp 5096– (1995)
[37] Sharon, Physical Review B 54 pp 7128– (1996)
[38] Fineberg, International Journal of Fracture 121 pp 55– (2003)
[39] John, Journal of Structural Engineering 116 pp 585– (1988)
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.