Abstract
This paper presents a boundary element method (BEM) analysis of linear elastic fracture mechanics in two-dimensional solids. The most outstanding feature of this new analysis is that it is a single-domain method, and yet it is very accurate, efficient and versatile: Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched, internal or edged type with a straight or curved shape. Loading can be of in-plane or anti-plane, and can be applied along the no-crack boundary or crack surface. Furthermore, the body-force case can also be analyzed. The present BEM analysis is an extension of the work by Pan and Amadei (1996a) and is such that the displacement and traction integral equations are collocated, respectively, on the no-crack boundary and on one side of the crack surface. Since in this formulation the displacement and/or traction are used as unknowns on the no-crack boundary and the relative crack displacement (i.e. displacement discontinuity) as unknown on the crack surface, it possesses the advantages of both the traditional displacement BEM and the displacement discontinuity method (DDM) and yet gets rid of the disadvantages associated with these methods when modeling fracture mechanics problems. Numerical examples of calculation of stress intensity factors (SIFs) for various benchmark problems were conducted and excellent agreement with previously published results was obtained.
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References
Aliabadi, M.H. (1997). Boundary element formulations in fracture mechanics. Applied Mechanics Review 50, 83–96.
Amadei, B. and Pan, E. (1992). Gravitational stresses in anisotropic rock masses with inclined strata. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 29, 225–236.
Ammons, B.A. and Vable, M. (1996). Boundary element analysis of cracks. International Journal of Solids and Structures 33, 1853–1865.
Blandford, G.E., Ingraffea, A.R. and Liggett, J.A. (1981). Two-dimensional stress intensity factor computations using the boundary element method. International Journal for Numerical Methods in Engineering 17, 387–404.
Chang, C. and Mear, M.E. (1995). A boundary element method for two dimensional linear elastic fracture analysis. International Journal of Fracture 74, 219–251.
Chen, Y.Z. (1995). Hypersingular integral equation approach for the multiple crack problem in an infinite plate. Acta Mechanica 108, 121–131.
Civelek, M.B. and Erdogan, F. (1982). Crack problems for a rectangular sheet and an infinite strip. International Journal of Fracture 19, 139–159.
Crouch, S.L. and Starfield, A.M. (1983). Boundary Element Methods in Solid Mechanics, George Allen and Unwin Publishers, London.
Dumir, P.C. and Mehta, A.K. (1987). Boundary element solution for elastic orthotropic half-plane problems. Computers and Structures 26, 431–438.
Eshelby, J.D., Read, W.T. and Shockley, W. (1953). Anisotropic elasticity with applications to dislocations theory. Acta Metallurgica 1, 251–259.
Gandhi, K.R. (1972). Analysis of an inclined crack centrally placed in an orthotropic rectangular plate. Journal of Strain Analysis 7, 157–162.
Gray, L.J., Martha, L.F. and Ingraffea, A.R. (1990). Hypersingular integrals in boundary element fracture analysis. International Journal for Numerical Methods in Engineering 29, 1135–1158.
Hong, H.K. and Chen, J.T. (1988). Derivations of integral equations of elasticity. Journal of Engineering Mechanics 114, 1028–1044.
Itou, S. (1994). Stress intensity factors around a crack parallel to a free surface of a half-plane. International Journal of Fracture 67, 179–185.
Lee, J.S. (1995). Boundary element method for electroelastic interaction in piezoceramics. Engineering Analysis with Boundary Elements 15, 321–328.
Lekhnitskii, S.G. (1963). Theory of Elasticity of an Anisotropic Body, Holden Day, San Francisco.
Leung, A.Y.T. and Su, R.K.L. (1995). Body-force linear elastic stress intensity factor calculation using fractal two level finite element method. Engineering Fracture Mechanics 51, 879–888.
Liu, N. and Altiero, N.J. (1991). Multiple cracks and branch cracks in finite plane bodies. Mechanics Research Communications 18, 233–244.
Liu, N. and Altiero, N.J. (1992). An integral equation method applied to mode III crack problems. Engineering Fracture Mechanics 41, 587–596.
Liu, N., Altiero, N.J. and Sur, U. (1990). An alternative integral equation approach applied to kinked cracks in finite plane bodies. Computer Methods in Applied Mechanics and Engineering 84, 211–226.
Ma, S.W. (1988). A central crack in a rectangular sheet where its boundary is subjected to an arbitrary anti-plane load. Engineering Fracture Mechanics 30, 435–443.
Ma, S.W. (1989). A central crack of mode III in a rectangular sheet with fixed edges. International Journal of Fracture 39, 323–329.
Ma, S.W. and Zhang, L.X. (1991). A new solution of an eccentric crack off the center line of a rectangular sheet for mode-III. Engineering Fracture Mechanics 40, 1–7.
Murakami, Y. (1987). Stress Intensity Factors Handbook, Pergamon Press, Oxford.
Noda, N.A. and Matsuo, T. (1993). Numerical solutions of singular integral equations having Cauchy-type singular kernel by means of expansion method. International Journal of Fracture 63, 229–245.
Pan, E. and Amadei, B. (1995). Stress concentration at irregular surfaces of anisotropic half-spaces. Acta Mechanica 113, 119–135.
Pan, E. and Amadei, B. (1996a). Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method. International Journal of Fracture 77, 161–174.
Pan, E. and Amadei, B. (1996b). A 3-D boundary element formulation of anisotropic elasticity with gravity. Applied Mathematical Modelling 20, 114–120.
Pan, E., Chen, C.S. and Amadei, B. (1997). A BEM formulation for anisotropic half-plane problems. Engineering Analysis with Boundary Elements 20, 185–195.
Portela, A., Aliabadi, M.H. and Rooke, D.P. (1992). The dual boundary element method: Effective implementation for crack problems. International Journal for Numerical Methods in Engineering 33, 1269–1287.
Sih, G.C., Paris, P.C. and Irwin, G.R. (1965). On cracks in rectilinearly anisotropic bodies. International Journal of Fracture 3, 189–203.
Snyder, M.D. and Cruse, T.A. (1975). Boundary-integral analysis of anisotropic cracked plates. International Journal of Fracture 11, 315–328.
Sollero, P. and Aliabadi, M.H. (1993). Fracture mechanics analysis of anisotropic composite laminates by the boundary element method. International Journal of Fracture 64, 269–284.
Sollero, P. and Aliabadi, M.H. (1995a). Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Composite structures 31, 229–233.
Sollero, P. and Aliabadi, M.H. (1995b). Dual boundary element analysis of anisotropic crack problems. In Boundary Elements XVII, C. A. Brebbia et al. (eds.) Computational Mechanics Publications, Southampton, 267–278.
Sollero, P., Aliabadi, M.H. and Rooke, D.P. (1994). Anisotropic analysis of cracks emanating from circular holes in composite laminates using the boundary element method. Engineering Fracture Mechanics 49, 213–224.
Stroh, A.N. (1958). Dislocations and cracks in anisotropic elasticity. The Philosophical Magazine 7, 625–646.
Suo, Z. (1990). Singularities, interfaces and cracks in dissimilar anisotropic media. Proceedings of the Royal Society (London), A427, 331–358.
Sur, U. and Altiero, N.J. (1988). An alternative integral equation approach for curved and kinked cracks. International Journal of Fracture 38, 25–41.
Tada, H., Paris, P.C. and Irwin, G.R. (1985). The Stress Analysis of Cracks Handbook, 2nd Edition, Paris Productions Incorporated, Missouri.
Telles, J.C.F. and Brebbia, C.A. (1981). Boundary element solution for half-plane problems. International Journal of Solids and Structures 17, 1149–1158.
Ting, T.C.T. (1992). Image singularities of Green's functions for anisotropic elastic half-spaces and bimaterials. Quarterly Journal of Mechanics and Applied Mathematics 45, 119–139.
Ting, T.C.T. and Barnett, D.M. (1993). Image force on line dislocations in anisotropic elastic half-spaces with a fixed boundary. International Journal of Solids and Structures 30, 313–323.
Tsamasphyros, G. and Dimou, G. (1990). Gauss quadrature rules for finite part integrals. International Journal for Numerical Methods in Engineering 30, 13–26.
Wei, L. and Ting, T.C.T. (1994). Explicit expressions of the Barnett-Lothe tensors for anisotropic materials. Journal of Elasticity 36, 67–83.
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Pan, E. A general Boundary Element Analysis of 2-D Linear Elastic Fracture Mechanics. International Journal of Fracture 88, 41–59 (1997). https://doi.org/10.1023/A:1007462319811
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DOI: https://doi.org/10.1023/A:1007462319811