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

References | Similar Articles | Additional Information

**[1]**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) MR**651119****[2]**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) MR**1154765****[3]**K. Ch. Le and H. Stumpf,*The singular elastostatic field due to a crack in rubberlike materials*, J. Elasticity**32**, 183-222 (1993) MR**1252075****[4]**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)**[5]**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)**[6]**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)**[7]**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) MR**1417808****[8]**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)**[9]**J. D. Achenbach and N. Nishimura,*Large deformations near a propagating crack tip*, Engineering Fracture Mechanics**23**, 183-199 (1986)**[10]**P. G. Ciarlet,*Mathematical Elasticity. Vol.*I:*Three-Dimensional Elasticity*, North-Holland, 1988 MR**936420****[11]**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) MR**695540****[12]**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) MR**719844****[13]**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) MR**0067673****[14]**J. E. Adkins and A. E. Green,*Plane problems in second-order elasticity theory*, Philos. Trans. Roy. Soc.**A 239**, 557-576 (1957) MR**0086487****[15]**L. B. Freund,*Energy flux into the tip of an extending crack in an elastic solid*, J. Elasticity**2**, 341-349 (1972)**[16]**M. E. Gurtin and C. Yatomi,*On the energy release rate in elastodynamicsl crack propagation*, Arch. Rational Mech. Anal.**74**, 231-247 (1980) MR**591223****[17]**A. M. Tarantino,*On the finite motions generated by a mode I propagating crack*, J. Elasticity**57**, 85-103 (1999) MR**1793292**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
74R05,
74B20,
74H99

Retrieve articles in all journals with MSC: 74R05, 74B20, 74H99

Additional Information

DOI:
https://doi.org/10.1090/qam/1848530

Article copyright:
© Copyright 2001
American Mathematical Society