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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 85
PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING
Edited by: B.H.V. Topping
Paper 51

An Enriched Meshfree Method for Multiple Cracks in Three Dimensions

T. Rabczuk1, S. Bordas2 and G. Zi3

1Mechanical Engineering Department, University of Canterbury, Christchurch, New Zealand
2Civil Engineering Department, University of Glasgow, United Kingdom
3Department of Civil & Environmental Engineering, Korea University, Seoul, Korea

Full Bibliographic Reference for this paper
T. Rabczuk, S. Bordas, G. Zi, "An Enriched Meshfree Method for Multiple Cracks in Three Dimensions", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 51, 2007. doi:10.4203/ccp.85.51
Keywords: eXtended Element Free Galerkin Method (XEFG), discontinuous enrichment, cohesive cracks, Lagrange multipliers, dynamic fracture, large deformations, high velocity impact, meshfree methods.

Summary
This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, branching, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations, for statics and dynamics.

The novelty of the methodology fashioned in this work is that only an extrinsic discontinuous enrichment and no near-tip/asymptotic enrichment is required. Instead, a Lagrange multiplier field is added along the crack front to close the crack. This decreases the computational cost and removes difficulties involved with a branch enrichment.

Numerical examples treated a crack branching problem, twisting of a chalk bar and, finally, a Taylor bar impact with very large deformation and fragmentation. The results are compared to experimental data, and other simulations from the literature to show the robustness and accuracy of the method.

The contribution only highlights the most salient features of the method, and the interested readers are encouraged to consult references [2,1] for details.

References
1
S. Bordas, T. Rabczuk, and G. Zi. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, submitted, 2007. doi:10.1016/j.engfracmech.2007.05.010
2
T. Rabczuk, S. Bordas, and G. Zi. A three dimensional meshfree method for static and dynamic multiple crack nucleation/propagation with crack path continuity. Computational Mechanics, in press, 2007. doi:10.1007/s00466-006-0122-1

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