×

zbMATH — the first resource for mathematics

A simplified mesh-free method for shear bands with cohesive surfaces. (English) Zbl 1194.74536
Summary: A simple methodology to model shear bands as strong displacement discontinuities in a mesh-free particle method is presented. The shear band is represented as a set of sheared particles. A sheared particle is developed through enrichment by tangential displacement discontinuities. The representation of the shear band as set of cohesive segments provides a simple and versatile model of shear bands. The loss of material stability is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation law acting on the discontinuity surface. The method is implemented for two and three dimensions. Examples of shear band progression in rate-dependent and rate-independent materials are presented, including the Kalthoff problem, where the transition from brittle fracture to shear banding is studied.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bazant, Journal of Engineering Mechanics 111 pp 381– (1985)
[2] Lasry, International Journal of Solids and Structures 24 pp 581– (1988)
[3] Needleman, International Journal of Solids and Structures 32 pp 2571– (1995)
[4] Jirasek, Computer Methods in Applied Mechanics and Engineering 188 pp 307– (2000)
[5] Xu, Journal of the Mechanics and Physics of Solids 42 pp 1397– (1994)
[6] Camacho, International Journal of Solids and Structures 33 pp 2899– (1996)
[7] Ortiz, Computer Methods in Applied Mechanics and Engineering 61 pp 189– (1987)
[8] Zhou, International Journal for Numerical Methods in Engineering 59 pp 1– (2004)
[9] Yang, International Journal for Numerical Methods in Engineering 62 pp 1013– (2005)
[10] Falk, Journal de Physique IV 11 (PR5) pp 43– (2001)
[11] Moes, International Journal for Numerical Methods in Engineering 46 pp 133– (1999)
[12] Moes, Engineering Fracture Mechanics 69 pp 813– (2002)
[13] Gravouil, International Journal for Numerical Methods in Engineering 53 pp 2569– (2002)
[14] Belytschko, International Journal for Numerical Methods in Engineering 58 pp 1873– (2003)
[15] Ventura, International Journal for Numerical Methods in Engineering 62 pp 1463– (2005)
[16] Samaniego, International Journal for Numerical Methods in Engineering 62 pp 1857– (2005)
[17] Belytschko, Computer Methods in Applied Mechanics and Engineering 70 pp 59– (1988)
[18] Armero, International Journal of Solids and Structures 33 pp 2863– (1996)
[19] Oliver, International Journal of Plasticity 15 pp 319– (1999)
[20] Li, International Journal of Solids and Structures 39 pp 1213– (2002)
[21] Li, International Journal of Solids and Structures 37 pp 7185– (2000)
[22] Hao, Computer Methods in Applied Mechanics and Engineering 187 pp 401– (2000)
[23] Krysl, International Journal for Numerical Methods in Engineering 44 pp 767– (1999)
[24] Organ, Computational Mechanics 18 pp 225– (1996)
[25] Rabczuk, International Journal for Numerical Methods in Engineering 61 pp 2316– (2004)
[26] Rabczuk, Computer Methods in Applied Mechanics and Engineering
[27] Belytschko, International Journal for Numerical Methods in Engineering 48 pp 1359– (2000)
[28] Rabczuk, Computer Methods in Applied Mechanics and Engineering 193 pp 1035– (2004)
[29] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 229– (1994)
[30] Wang, International Journal for Numerical Methods in Engineering 40 pp 3839– (1997)
[31] Clifton, Scripta Metallugrica 18 pp 443– (1984)
[32] Wright, Journal of the Mechanics and Physics of Solids 44 pp 77– (1996)
[33] , . Nonlinear Finite Elements for Continua and Structures. Wiley: Chichester, 2000. · Zbl 0959.74001
[34] The Mechanics and Thermodynamics of Continuous Media. Springer: Berlin, 1997. · Zbl 0870.73004 · doi:10.1007/978-3-662-03389-0
[35] Grady, Mechanics of Materials 17 pp 289– (1994)
[36] Minnaar, Journal of the Mechanics and Physics of Solids 46 pp 2155– (1998)
[37] Plasticity. Cambridge University Press: Cambridge, U.K., 2004.
[38] Dolbow, International Journal for Numerical Methods in Engineering 46 pp 925– (1999)
[39] Chen, Computer Methods in Applied Mechanics and Engineering 181 pp 117– (2000)
[40] Hughes, International Journal for Numerical Methods in Engineering 15 pp 1413– (1980)
[41] Flory, Transactions of the Faraday Society 57 pp 829– (1961)
[42] Brooks, Computer Methods in Applied Mechanics and Engineering 32 pp 199– (1982)
[43] Hughes, Computer Methods in Applied Mechanics and Engineering 73 pp 173– (1989)
[44] Kalthoff, International Conference on Impact Loading and Dynamic Behavior of Materials 1 pp 185– (1987)
[45] Kalthoff, International Journal of Fracture 101 pp 1– (2000)
[46] Zhou, Journal of the Mechanics and Physics of Solids 44 pp 981– (1996)
[47] Ravi-Chandar, International Journal of Fracture 101 pp 33– (2000)
[48] Batra, International Journal of Fracture 101 pp 99– (2000)
[49] Zhou, Journal of the Mechanics and Physics of Solids 44 pp 1007– (1996)
[50] Batra, International Journal of Fracture 105 pp 161– (2000)
[51] . A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures. Proceedings 7th International Symposium on Ballistics, 1983.
[52] Diez, Mechanics of Cohesive-Frictional Materials 5 pp 87– (2000)
[53] Rabczuk, International Journal for Numerical Methods in Engineering 63 pp 1559– (2005)
[54] Finite Element Technology, Damage Modeling, Contact Constraints and Fracture Analysis. Doutoramento, FEUP–Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n 4200-465 Porto, Portugal, 2003. www.fe.up.pt.
[55] Miehe, Computer Methods in Applied Mechanics and Engineering 192 pp 473– (2003)
[56] , . Self-organization in the initiation of adiabatic shear bands. Acta Materialia 1998.
[57] Xue, International Journal of Impact Engineering (2003)
[58] , , . Shear localization in dynamic deformation of materials: microstructural evolution and self-organization. Material Science and Engineering 2001.
[59] , . High-strain-rate deformation of granular silicon carbide. Acta Materialia 1998.
[60] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001)
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.