Dynamic crack propagation in sheets of compressible neo-Hookean material under general in-plane loading
Author:
Angelo Marcello Tarantino
Journal:
Quart. Appl. Math. 59 (2001), 479-492
MSC:
Primary 74R05; Secondary 74B20, 74H99
DOI:
https://doi.org/10.1090/qam/1848530
MathSciNet review:
MR1848530
Full-text PDF Free Access
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- Rodney A. Stephenson, The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials, J. Elasticity 12 (1982), no. 1, 65–99. MR 651119, DOI https://doi.org/10.1007/BF00043706
- K. C. Le, On the singular elastostatic field induced by a crack in a Hadamard material, Quart. J. Mech. Appl. Math. 45 (1992), no. 1, 101–117. MR 1154765, DOI https://doi.org/10.1093/qjmam/45.1.101
- K. Ch. Le and H. Stumpf, The singular elastostatic field due to a crack in rubberlike materials, J. Elasticity 32 (1993), no. 3, 183–222. MR 1252075, DOI https://doi.org/10.1007/BF00131660
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, 61–98 (1994)
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, 99–138 (1994)
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, 139–174 (1994)
- Angelo Marcello Tarantino, Thin hyperelastic sheets of compressible material: field equations, Airy stress function and an application in fracture mechanics, J. Elasticity 44 (1996), no. 1, 37–59. MR 1417808, DOI https://doi.org/10.1007/BF00042191
J. D. Achenbach and N. Nishimura, Effect of inertia on finite near-tip deformation for fast mode-III crack growth, J. Appl. Mech. 52, 281–286 (1985)
J. D. Achenbach and N. Nishimura, Large deformations near a propagating crack tip, Engineering Fracture Mechanics 23, 183–199 (1986)
- Philippe G. Ciarlet, Mathematical elasticity. Vol. I, Studies in Mathematics and its Applications, vol. 20, North-Holland Publishing Co., Amsterdam, 1988. Three-dimensional elasticity. MR 936420
- Philippe G. Ciarlet and Giuseppe Geymonat, Sur les lois de comportement en élasticité non linéaire compressible, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 295 (1982), no. 4, 423–426 (French, with English summary). MR 695540
- J. K. Knowles and Eli Sternberg, Large deformations near a tip of an interface-crack between two neo-Hookean sheets, J. Elasticity 13 (1983), no. 3, 257–293. MR 719844, DOI https://doi.org/10.1007/BF00042997
- J. E. Adkins, A. E. Green, and G. C. Nicholas, Two-dimensional theory of elasticity for finite deformations, Philos. Trans. Roy. Soc. London Ser. A 247 (1954), 279–306. MR 67673, DOI https://doi.org/10.1098/rsta.1954.0019
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L. B. Freund, Energy flux into the tip of an extending crack in an elastic solid, J. Elasticity 2, 341–349 (1972)
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- Angelo Marcello Tarantino, On the finite motions generated by a mode I propagating crack, J. Elasticity 57 (1999), no. 2, 85–103 (2000). MR 1793292, DOI https://doi.org/10.1023/A%3A1007673212904
R. A. Stephenson, The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials, J. Elasticity 12, 65–99 (1982)
K. Ch. Le, On the singular elastostatic field induced by a crack in a Hadamard material, Quart. J. Mech. Appl. Math. 45, 101–117 (1992)
K. Ch. Le and H. Stumpf, The singular elastostatic field due to a crack in rubberlike materials, J. Elasticity 32, 183–222 (1993)
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, 61–98 (1994)
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, 99–138 (1994)
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, 139–174 (1994)
A. M. Tarantino, Thin hyperelastic sheets of compressible material: field equations, Airy stress function and an application in fracture mechanics, J. Elasticity 44, 37–59 (1996)
J. D. Achenbach and N. Nishimura, Effect of inertia on finite near-tip deformation for fast mode-III crack growth, J. Appl. Mech. 52, 281–286 (1985)
J. D. Achenbach and N. Nishimura, Large deformations near a propagating crack tip, Engineering Fracture Mechanics 23, 183–199 (1986)
P. G. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity, North-Holland, 1988
P. G. Ciarlet and G. Geymonat, Sur les lois de comportement en élasticité non-linéaire compressible, C. R. Acad. Sci. Paris Sér. II 295, 423–426 (1982)
J. K. Knowles and Eli Sternberg, Large deformations near a tip of an interface-crack between two Neo-Hookean sheets, J. Elasticity 13, 257–293 (1983)
J. E. Adkins, A. E. Green, and G. C. Nicholas, Two-dimensional theory of elasticity for finite deformation, Philos. Trans. Roy. Soc. A 247, 279–306 (1954)
J. E. Adkins and A. E. Green, Plane problems in second-order elasticity theory, Philos. Trans. Roy. Soc. A 239, 557–576 (1957)
L. B. Freund, Energy flux into the tip of an extending crack in an elastic solid, J. Elasticity 2, 341–349 (1972)
M. E. Gurtin and C. Yatomi, On the energy release rate in elastodynamicsl crack propagation, Arch. Rational Mech. Anal. 74, 231–247 (1980)
A. M. Tarantino, On the finite motions generated by a mode I propagating crack, J. Elasticity 57, 85–103 (1999)
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© Copyright 2001
American Mathematical Society