A method for multiple crack growth in brittle materials without remeshing
Tóm tắt
A method for modelling the growth of multiple cracks in linear elastic media is presented. Both homogeneous and inhomogeneous materials are considered. The method uses the extended finite element method for arbitrary discontinuities and does not require remeshing as the cracks grow; the method also treats the junction of cracks. The crack geometries are arbitrary with respect to the mesh and are described by vector level sets. The overall response of the structure is obtained until complete failure. A stability analysis of competitive cracks tips is performed. The method is applied to bodies in plane strain or plane stress and to unit cells with 2–10 growing cracks (although the method does not limit the number of cracks). It is shown to be efficient and accurate for crack coalescence and percolation problems. Copyright © 2004 John Wiley & Sons, Ltd.
Từ khóa
Tài liệu tham khảo
Melenk JM, 1996, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering, 39, 289, 10.1016/S0045-7825(96)01087-0
Osher S, 1998, Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations, Journal of Computational Physics, 79, 12, 10.1016/0021-9991(88)90002-2
Sethian JA, 1999, Level Sets Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science
LawlerJ.Hybrid fiber‐reinforcement in mortar and concrete. Ph.D. Thesis Department of Civil and Environmental Engineering Northwestern University December2001.
Kachanov M, 1985, A simple technique of stress analysis in elastic solids with many cracks, International Journal of Fracture, 28, R11, 10.1007/BF00033702
Rubinstein A, 1985, Macrocrack interaction with semi‐infinite microcrack array, International Journal of Fracture, 27, 113, 10.1007/BF00040390
Freij‐Ayoub R, 1997, The dislocation approximation for calculating crack interaction, International Journal of Fracture, 86, L57
Chen YZ, 1984, General case of multiple cracks problems in an infinite plate, Engineering Fracture Mechanics, 20, 591, 10.1016/0013-7944(84)90034-1
Bazant ZP, 1998, Fracture and Size Effect in Concrete and Other Quasi‐brittle Materials
Stazi FL, 2002, An extended finite element method with higher‐order elements for curved cracks, Computational Mechanics, 31, 38, 10.1007/s00466-002-0391-2
Nguyen QS, 1985, Endomagement, fatigue, rupture—Sur le problème en vitesse de propagation de fissure et de déplacement en rupture fragile ou ductile. Note de Nguyen Quoc Son et Claude Stolz, présentée par Paul Germain, Comptes‐Rendus de l'Académie des Sciences de Paris, 301, 661
Nguyen QS, 1990, Energy methods in fracture mechanics: stability bifurcation and second variations, European Journal of Mechanics – A/Solids, 2, 157
Suo XZ, 1989, Sur une formulation mathématique de la dérivée seconde de l'énergie potentielle en théorie de la rupture fragile, Comptes‐Rendus de l'Académie des Sciences de Paris, 308, 1119
Bazant ZP, 1991, Stability of Structures
Tada H, 1973, The Stress Analysis of Cracks Handbook
BudynE.Multiple crack growth by the extended finite element method. Ph.D. Thesis Department of Mechanical Engineering Northwestern University June2004.