×

zbMATH — the first resource for mathematics

Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. (English) Zbl 1194.74358
Summary: New enrichment functions are proposed for crack modelling in orthotropic media using the extended finite element method (XFEM). In this method, Heaviside and near-tip functions are utilized in the framework of the partition of unity method for modelling discontinuities in the classical finite element method. In this procedure, by using meshless based ideas, elements containing a crack are not required to conform to crack edges. Therefore, mesh generation is directly performed ignoring the existence of any crack while the method remains capable of extending the crack without any remeshing requirement. Furthermore, the type of elements around the crack-tip remains the same as other parts of the finite element model and the number of nodes and consequently degrees of freedom are reduced considerably in comparison to the classical finite element method. Mixed-mode stress intensity factors (SIFs) are evaluated to determine the fracture properties of domain and to compare the proposed approach with other available methods. In this paper, the interaction integral (M-integral) is adopted, which is considered as one of the most accurate numerical methods for calculating stress intensity factors.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74B05 Classical linear elasticity
PDF BibTeX Cite
Full Text: DOI
References:
[1] Some Basic Problems on the Mathematical Theory of Elasticity. Noordhoof: Groningen, 1953 (Translated by Radok JRM).
[2] Stress Concentration Around Holes. Pergamon Press: Oxford, 1961. · Zbl 0124.18303
[3] Theory of an Anisotropic Elastic Body. Holden-Day: San Francisco, 1963.
[4] Sih, International Journal of Fracture Mechanics 1 pp 189– (1965)
[5] Tupholme, Journal of Engineering and Mathematics 8 pp 57– (1974) · Zbl 0275.73061
[6] Viola, Engineering Fracture Mechanics 34 pp 1155– (1989)
[7] Anisotropic Elasticity, Theory and Applications. Oxford University Press: New York, Oxford, 1996.
[8] Lim, Engineering Fracture Mechanics 68 pp 403– (2001)
[9] Nobile, Composite Structures 68 pp 285– (2005)
[10] Belytschko, International Journal of Fracture Mechanics 45 pp 601– (1999)
[11] Moës, International Journal for Numerical Methods in Engineering 46 pp 131– (1999)
[12] Sukumar, International Journal for Numerical Methods in Engineering 48 pp 1549– (2000)
[13] Areias, International Journal for Numerical Methods in Engineering 63 pp 760– (2005)
[14] Sukumar, International Journal of Solids and Structures 40 pp 7513– (2003)
[15] Dolbow, Computer Methods in Applied Mechanics and Engineering 190 pp 6825– (2001)
[16] Zi, International Journal for Numerical Methods in Engineering 57 pp 2221– (2003)
[17] Mergheim, International Journal for Numerical Methods in Engineering 63 pp 276– (2005)
[18] Belytschko, International Journal for Numerical Methods in Engineering 58 pp 1873– (2003)
[19] Melenk, Computer Methods in Applied Mechanics and Engineering 139 pp 289– (1996)
[20] Sukumar, International Journal for Numerical Methods in Engineering 48 pp 1549– (2000)
[21] Dolbow, Computer Methods in Applied Mechanics and Engineering 190 pp 6825– (2001)
[22] Dolbow, International Journal of Solids and Structures 57 pp 7161– (2000)
[23] Belytschko, International Journal for Numerical Methods in Engineering 58 pp 1873– (2003)
[24] , . Crack analysis in orthotropic media using the extended finite element method. 2005, submitted.
[25] Asadpoure, Finite Elements in Analysis and Design (2006)
[26] Kim, International Journal of Solids and Structures 40 pp 3967– (2003)
[27] Rice, Journal of Applied Mechanics, Transactions 35 pp 379– (1968)
[28] An extended finite element method with discontinuous enrichment for applied mechanics. Ph.D. Thesis, Theoretical and Applied Mechanics, Northwestern University, Evanston, IL, U.S.A., 1999.
[29] Aliabadi, Composites Science and Technology 58 pp 1697– (1998)
[30] Jernkvist, Picea abies. Engineering Fracture Mechanics 68 pp 565– (2001)
[31] Atluri, Fracture Mechanics of Composites 593 pp 86– (1975)
[32] Wang, International Journal of Fracture 16 pp 247– (1980)
[33] Kim, Engineering Fracture Mechanics 69 pp 1557– (2002)
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.