zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A higher-order scheme for two-dimensional quasi-static crack growth simulations. (English) Zbl 1173.74470
Summary: An efficient scheme for the simulation of quasi-static crack growth in two-dimensional linearly elastic isotropic specimens is presented. The crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step. In a local coordinate system each such extension is represented as a polynomial of some, user specified, degree,$ n$. The coefficients of the polynomial describing an extension are found by requiring that the mode II stress intensity factor is equal to zero at certain points of the extension. If a crack grows from a pre-existing crack so that a kink develops, the leading term describing the crack shape close to the kink will, in a local coordinate system, be proportional to $x^{3/2}$. We therefore allow the crack extensions to contain such a term in addition to the monomial terms. The discontinuity in the crack growth direction at a kink, the kink angle, is determined by requiring that the mode II stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack. To implement the scheme, accurate values of the stress intensity factors and $T$-stress are needed in each step of the simulation. These fracture parameters are computed using a previously developed integral equation of the second kind.

74S30Other numerical methods in solid mechanics
74R10Brittle fracture
74H35Singularities, blowup, stress concentrations (dynamical problems in solid mechanics)
Full Text: DOI
[1] Friedman, A.; Hu, B.; Velazquez, J. J. L.: The evolution of stress intensity factors in the propagation of two dimensional cracks. Eur. J. Appl. math. 11, 453-471 (2000) · Zbl 0969.74056
[2] Belytschko, T.; Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. methods engrg. 45, 601-620 (1999) · Zbl 0943.74061
[3] Bittencourt, T. N.; Wawrzynek, P. A.; Ingraffea, A. R.; Sousa, J. L.: Quasi-automatic simulation of crack propagation for 2D LEFM problems. Engrg. fracture mech. 55, 321-334 (1996)
[4] Boselli, J.; Pitcher, P. D.; Gregson, P. J.; Sinclair, I.: Numerical modelling of particle distribution effects on fatigue in al-sicp composites. Mater. sci. Engrg. A 300, 113-124 (2001)
[5] Bouchard, P. O.; Bay, F.; Chastel, Y.: Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput. methods appl. Mech. engrg. 192, 3887-3908 (2003) · Zbl 1054.74724
[6] Bush, M. B.: The interaction between a crack and a particle cluster. Int. J. Fracture 88, 215-232 (1997)
[7] Datsishin, O. P.; Marchenko, G. P.: Quasistatic edge crack growth with non-self-balancing stresses at the edges. Sov. mater. Sci. 27, 379-385 (1991)
[8] Dobroskok, A.: On a new method for iterative calculation of crack trajectory. Int. J. Fracture 111, L41-L46 (2001)
[9] Heintz, P.: On the numerical modelling of quasi-static crack growth in linear elastic fracture mechanics. Int. J. Numer. methods engrg. 65, 174-189 (2006) · Zbl 1111.74043
[10] Huang, R.; Sukumar, N.; Prévost, J. H.: Modeling quasi-static crack growth with the extended finite element method part II: Numerical applications. Int. J. Solids struct. 40, 7539-7552 (2003) · Zbl 1064.74163
[11] Knight, M. G.; Wrobel, L. C.; Henshall, J. L.; De Lacerda, L. A.: A study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique. Int. J. Fracture 114, 47-61 (2002)
[12] Lee, S. H.; Yoon, Y. C.: Numerical prediction of crack propagation by an enhanced element-free Galerkin method. Nucl. engrg. Des. 227, 257-271 (2004)
[13] Mogilevskaya, S. G.: Numerical modeling of 2-D smooth crack growth. Int. J. Fracture 87, 389-405 (1997)
[14] Phongthanapanich, S.; Dechaumphai, P.: Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis. Finite elem. Anal. des. 40, 1753-1771 (2004)
[15] Rashid, M. M.: The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis. Comput. methods appl. Mech. engrg. 154, 133-150 (1998) · Zbl 0939.74071
[16] Silveira, N. P. P.; Guimarães, S.; Telles, J. C. F.: A numerical Green’s function BEM formulation for crack growth simulation. Engrg. anal. Bound. elem. 29, 978-985 (2005) · Zbl 1182.74236
[17] Stolarska, M.; Chopp, D. L.; Moës, N.; Belytschko, T.: Modelling crack growth by level sets in the extended finite element method. Int. J. Numer. methods engrg. 51, 943-960 (2001) · Zbl 1022.74049
[18] Stone, T. J.; Babuška, I.: A numerical method with a posteriori error estimation for determining the path taken by a propagating crack. Comput. methods appl. Mech. engrg. 160, 245-271 (1998) · Zbl 0932.74070
[19] Tabbara, M. R.; Stone, C. M.: A computational method for quasi-static fracture. Comput. mech. 22, 203-210 (1998) · Zbl 0927.74072
[20] Yan, X.: Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements. Appl. math. Modell. 30, 489-508 (2006) · Zbl 05623766
[21] Englund, J.: Efficient algorithm for edge cracked geometries. Int. J. Numer. methods engrg. 66, 1791-1816 (2006) · Zbl 1110.74864
[22] J. Englund, A Nyström scheme with rational quadrature applied to edge crack problems, Commun. Numer. Methods Engrg., available online 19 October 2006.
[23] Erdogan, F.; Sih, G. C.: On the crack extension in plates under plane loading and transverse shear. J. basic engrg. 85, 519-527 (1963)
[24] Sih, G. C.: Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fracture 10, 305-321 (1974)
[25] Nuismer, R. J.: An energy release rate criterion for mixed mode fracture. Int. J. Fracture 11, 245-250 (1975)
[26] Broberg, K. B.: Cracks and fracture. (1999)
[27] Gol’dstein, R. V.; Salganik, R. L.: Brittle fracture of solids with arbitrary cracks. Int. J. Fracture 10, 507-523 (1974)
[28] Melin, S.: Accurate data for stress intensity factors at infinitesimal kinks. Trans. ASME J. Appl. mech. 61, 467-470 (1994) · Zbl 0800.73343
[29] Amestoy, M.; Leblond, J. B.: Crack paths in plane situations-II. Detailed form of the expansion of the stress intensity factors. Int. J. Solids struct. 29, 465-501 (1992) · Zbl 0755.73072
[30] Leblond, J. B.: Crack paths in plane situations-I. General form of the expansion of the stress intensity factors. Int. J. Solids struct. 25, 1311-1325 (1989) · Zbl 0703.73062
[31] Oleaga, G. E.: On the path of a quasi-static crack in mode III. J. elasticity 76, 163-189 (2004) · Zbl 1060.74059