Dynamically accelerating cracks part 2: a finite length mode III crack in elastic material
Authors:
Tanya L. Leise and Jay R. Walton
Journal:
Quart. Appl. Math. 59 (2001), 601-614
MSC:
Primary 74R10
DOI:
https://doi.org/10.1090/qam/1866550
MathSciNet review:
MR1866550
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Abstract: We consider a dynamically accelerating, finite length, mode III crack in an infinite elastic body. This initial boundary value problem has the nature of a free boundary problem since the crack tip motion is a priori unknown and must be found as part of the solution after imposition of a fracture criterion. Using an analog to a Dirichlet-to-Neumann map, we reduce the fracture problem to integrodifferential equations along the boundary that, for simplicity, we combine with a stress intensity factor fracture criterion. This approach has the advantage of being applicable to cases of multiple cracks as well as, in principle, to mode I cracks and to cracks in viscoelastic materials.
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- Francesco Costanzo and Jay R. Walton, A numerical solution technique for a class of integro-differential equations in elastodynamic crack propagation problems, Comput. Methods Appl. Mech. Engrg. 162 (1998), no. 1-4, 19β48. MR 1645345, DOI https://doi.org/10.1016/S0045-7825%2897%2900328-9
F. Costanzo and J. R. Walton, Numerical simulations of a dynamically propagating crack with a nonlinear cohesive zone, Internat. J. Frac. 91, 373β389 (1999)
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- Avner Friedman and Yong Liu, Propagation of cracks in elastic media, Arch. Rational Mech. Anal. 136 (1996), no. 3, 235β290. MR 1423009, DOI https://doi.org/10.1007/BF02206556
A. A. Griffith, The phenomenon of rupture and flow in solids, Philos. Trans. Royal Soc. London A221, 163β198 (1920)
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B. V. Kostrov, Unsteady propagation of longitudinal shear cracks, Appl. Math. Mech. (PPM) 30, 1042β1049 (1966)
J. L. Rice, Mathematical analysis in mechanics of fracture, Fracture, Vol. 2 (H. Liebowitz, ed.), Academic Press, 1968, pp. 191β311
L. I. Slepyan, Principal of maximum energy dissipation rate in crack dynamics, J. Mech. Phys. Solids 41, 1019β1033 (1993)
- G. A. C. Graham and J. R. Walton (eds.), Crack and contact problems for viscoelastic bodies, CISM International Centre for Mechanical Sciences. Courses and Lectures, vol. 356, Springer-Verlag, Vienna, 1995. Papers from the Advanced School held in Udine, September 5β9, 1994. MR 1411683
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F. Costanzo and J. R. Walton, A study of dynamic crack growth in elastic materials using a cohesive zone model, Internat. J. Engrg. Sci. 35, 1085β1114 (1997)
F. Costanzo and J. R. Walton, A numerical solution technique for a class of integro-differential equations in elastodynamic crack propagation problems, Comp. Meth. Appl. Mech. Engrg. 162, 19β48 (1998)
F. Costanzo and J. R. Walton, Numerical simulations of a dynamically propagating crack with a nonlinear cohesive zone, Internat. J. Frac. 91, 373β389 (1999)
L. B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, 1990
Avner Friedman and Yong Liu, Propagation of cracks in elastic media, Arch. Rat. Mech. Anal. 136, 235β290 (1996)
A. A. Griffith, The phenomenon of rupture and flow in solids, Philos. Trans. Royal Soc. London A221, 163β198 (1920)
M. E. Gurtin, On the energy release rate in quasi-static elastic crack propagation, J. Elasticity 9, 187β195 (1979)
B. V. Kostrov, Unsteady propagation of longitudinal shear cracks, Appl. Math. Mech. (PPM) 30, 1042β1049 (1966)
J. L. Rice, Mathematical analysis in mechanics of fracture, Fracture, Vol. 2 (H. Liebowitz, ed.), Academic Press, 1968, pp. 191β311
L. I. Slepyan, Principal of maximum energy dissipation rate in crack dynamics, J. Mech. Phys. Solids 41, 1019β1033 (1993)
J. R. Walton, Dynamic viscoelastic fracture, Crack and Contact Problems for Viscoelastic Bodies (G.A.C. Graham and J. R. Walton, eds.), CISM Courses and Lectures No. 356, Springer-Verlag, Wien and New York, 1995, pp. 259β311
J. R. Walton and J. M. Herrmann, A new method for solving dynamically accelerating crack problems: part 1. The case of a semi-infinite mode III crack in elastic material revisited, Quart. Appl. Math. 50, 373β387 (1992)
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© Copyright 2001
American Mathematical Society
