Abstract
A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path.
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References
M. Amestoy and J.B. Leblond, Crack paths in plane situations II: Detailed form of the expansions of the stress intensity factors. Internat. J. Solids Struct. 29(4) (1992) 465–501.
C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Internat. edn. McGraw-Hill, Singapore (1978).
M. Brokate and A. Khludnev, On crack propagation shapes in elastic bodies. Z. Angew. Math. Phys. 55 (2004) 318–329.
M. Buliga, Energy minimizing brittle crack propagation. J. Elasticity 52 (1999) 201–238.
M. Buliga, Brittle crack propagation based on an optimal energy balance. Rev. Roum. Math. Pures Appl. 45(2) (2001) 201–209.
B. Cotterell and J.R. Rice, Slightly curved or kinked cracks. Internat. J. Fracture 16(2) (1980) 155–169.
G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fracture: existence and approximation results. Arch. Rational Mech. Anal. 162(2) (2002) 101–135.
G.A. Francfort and C.J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure Appl. Math. LVI (2003) 1465–1500.
G.A. Francfort and J.J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8) (1998) 1319–1342.
L.B. Freund, Dynamic Fracture Mechanics, 2nd edn. Cambridge Univ. Press, Cambridge (1998).
R.V. Goldstein and R.L. Salganik, Brittle fracture of solids with arbitrary cracks. Internat. J. Fracture 10 (1974) 507.
A.A. Griffith, The phenomenon of rupture and flow in solids. Phylosoph. Trans. Roy. Soc. London A 221 (1920) 163–198.
G.R. Irwin, Analysis of stresses and strains near the end of a crack transversing a plate. J. Appl. Mech. 24 (1957) 361–364.
J.B. Leblond, Crack paths in plane situations I: General form of the expansion of the stress intensity factors. Internat. J. Solids Struct. 25(11) (1989) 1311–1325.
Z. Nehari, Conformal Mapping. Dover, New York (1975).
J.R. Rice, Mathematical analysis in the mechanics of fracture. In: H. Liebowitz (ed.), Fracture, An Advanced Treatise, Vol. 2. Academic Press, New York (1968) pp. 191–311.
G.C. Sih, Stress distribution near internal crack tips for longitudinal shear problems. J. Appl. Mech. (March 1965) 51–58.
T.J. Stone and I. Babuska, A numerical method with a posteriori error estimation for determining the path taken by a propagating crack. Comput. Methods Appl. Mech. Engrg. 160 (1998) 245–271.
C.H. Wu, Elasticity problems of a slender Z-crack. J. Elasticity 8(2) (1978) 235–257.
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Mathematics Subject Classifications (2000)
74R05, 74B05, 74G70.
Gerardo E. Oleaga: Supported by EU-Project “Front Singularities” University of Leipzig and the Max Planck Institute MIS. Partial support was also provided by the Spanish DGES project BFM2000-0605.
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Oleaga, G.E. On the Path of a Quasi-static Crack in Mode III. J Elasticity 76, 163–189 (2004). https://doi.org/10.1007/s10659-005-0297-2
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DOI: https://doi.org/10.1007/s10659-005-0297-2