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On the Finite Motions Generated by a Mode I Propagating Crack

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Abstract

The motion field surrounding a rapidly propagating crack, loaded symmetrically about the plane of the crack, is investigated. The problem is formulated within the framework of finite elastodynamics for thin slabs composed of compressible hyperelastic material. Writing the motion equations, the initial and the internal boundary conditions, with respect to a coordinate system that translates with the moving crack tip, we perform an asymptotic local analysis for a traction-free straight crack that suddenly grows at constant velocity. Moreover, the asymptotic Piola–Kirchhoff and Cauchy stress fields are computed, and we discuss the order of singularity of the dynamic stresses.

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References

  1. E.H. Yoffe, The moving Griffith crack. Phil. Mag. Ser. 7 42 (1951) 739-750.

    MATH  MathSciNet  Google Scholar 

  2. K.B. Broberg, The propagation of a brittle crack. Arkiv Fysik 18 (1960) 159-192.

    MathSciNet  Google Scholar 

  3. B.R. Baker, Dynamic stresses created by a moving crack. J. Appl. Mech. E 29 (1962) 449-458.

    Google Scholar 

  4. F. Nilsson, Dynamic stress intensity factors for finite strip problems. Internat. J. Fracture Mech. 8 (1972) 403-411.

    Google Scholar 

  5. L.B. Freund, Crack propagation in an elastic solid subjected to general loading-I. Constant rate of extension. J. Mech. Phys. Solids 20 (1972) 129-140.

    Article  MATH  ADS  Google Scholar 

  6. L.B. Freund, Crack propagation in an elastic solid subjected to general loading-II. Non-uniform rate of extension. J. Mech. Phys. Solids 20 (1972) 141-152.

    Article  MATH  ADS  Google Scholar 

  7. L.B. Freund, Crack propagation in an elastic solid subjected to general loading-III. Stress wave loading. J. Mech. Phys. Solids 21 (1973) 47-61.

    Article  MATH  ADS  Google Scholar 

  8. L.B. Freund, Crack propagation in an elastic solid subjected to general loading-IV. Obliquely incident stress pulse. J. Mech. Phys. Solids 22 (1974) 137-146.

    Article  MATH  ADS  Google Scholar 

  9. J.K. Knowles and E. Sternberg, An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack. J. Elasticity 3 (1973) 67-107.

    Article  MathSciNet  Google Scholar 

  10. J.K. Knowles and E. Sternberg, Finite-deformation analysis of the elastostatic field near the tip of a crack: reconsideration and higher order results. J. Elasticity 4 (1974) 201-233.

    MATH  MathSciNet  Google Scholar 

  11. R.A. Stephenson, The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials. J. Elasticity 12 (1982) 65-99.

    Article  MATH  MathSciNet  Google Scholar 

  12. J.K. Knowles and E. Sternberg, Large deformations near a tip of an interface-crack between two Neo-Hookean sheets. J. Elasticity 13 (1983) 257-293.

    Article  MATH  MathSciNet  Google Scholar 

  13. J.K. Knowles, The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. Internat. J. Fracture 13 (1977) 611-639.

    Article  MathSciNet  Google Scholar 

  14. P.H. Geubelle and W.G. Knauss, Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case. J. Elasticity 35 (1994) 61-98.

    Article  MATH  Google Scholar 

  15. P.H. Geubelle and W.G. Knauss, Finite strains at the tip of a crack in a sheet of hyperelastic material: II. Special bimaterial cases. J. Elasticity 35 (1994) 99-138.

    Article  Google Scholar 

  16. P.H. Geubelle and W.G. Knauss, Finite strains at the tip of a crack in a sheet of hyperelastic material: III. General bimaterial case. J. Elasticity 35 (1994) 139-174.

    Article  Google Scholar 

  17. H. Stumpf and K.Ch. Le, Variational principles of nonlinear fracture mechanics. Acta Mech. 83 (1990) 25-37.

    Article  MATH  MathSciNet  Google Scholar 

  18. K.Ch. Le, On the singular elastostatic field induced by a crack in a Hadamard material. Quart. J. Mech. Appl. Math. 45 (1992) 101-117.

    MATH  MathSciNet  Google Scholar 

  19. K.Ch. Le and H. Stumpf, The singular elastostatic field due to a crack in rubberlike materials. J. Elasticity 32 (1993) 183-222.

    Article  MATH  MathSciNet  Google Scholar 

  20. A.M. Tarantino, Thin hyperelastic sheets of compressible material: field equations, Airy stress function and an application in fracture mechanics. J. Elasticity 44 (1996) 37-59.

    Article  MATH  MathSciNet  Google Scholar 

  21. A.M. Tarantino, The singular wedge problem in nonlinear elastostatic plane stress theory. Quart. Appl. Math. 57 (1999) 433-451.

    MATH  MathSciNet  Google Scholar 

  22. D. Broek, Elementary Engineering Fracture Mechanics. Sijthoff & Noordhoff, The Netherlands (1978).

    MATH  Google Scholar 

  23. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity. Cambridge Univ. Press, Cambridge (1927) (reprinted by Dover, New York, 1944).

    MATH  Google Scholar 

  24. P.G. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity. North-Holland, Amsterdam (1988).

    Google Scholar 

  25. P.G. Ciarlet and G. Geymonat, Sur les lois de comportement en élasticité non-linéaire compressible. C. R. Acad. Sci. Paris Sér. II 295 (1982) 423-426.

    MATH  MathSciNet  Google Scholar 

  26. A.A. Griffith, The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. London A 221 (1921) 163-197.

    ADS  Google Scholar 

  27. J.R. Rice, A path-independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. 35(2) (1968) 379-388.

    MathSciNet  Google Scholar 

  28. L.B. Freund, Energy flux into the tip of an extending crack in an elastic solid. J. Elasticity 2 (1972) 341-349.

    Article  Google Scholar 

  29. M.E. Gurtin and C. Yatomi, On the energy release rate in elastodynamical crack propagation. Arch. Rational Mech. Anal. 74 (1980) 231-247.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. A.M. Tarantino, Dynamic crack propagation in sheets of compressible neo-Hookean material under general in-plane loading. Quart. Appl. Math. (2000) (accepted for publication).

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  1. Dipartimento di Scienze dell'Ingegneria, Università di Modena e Reggio Emilia, via Campi 213/B, 41100, Modena, Italy

    Angelo Marcello Tarantino

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  1. Angelo Marcello Tarantino
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Tarantino, A.M. On the Finite Motions Generated by a Mode I Propagating Crack. Journal of Elasticity 57, 85–103 (1999). https://doi.org/10.1023/A:1007673212904

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