Thin Hyperelastic sheets of compressible material: Field equations, airy stress function and an application in fracture mechanics
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OpenAlex topics: Elasticity and Material Modeling · Elasticity and Wave Propagation · Contact Mechanics and Variational Inequalities
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References (31)
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1. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity. Cambridge University Press, Cambridge (1927) (reprinted by Dover Publications, New York, 1944).
2. J.E. Adkins, A.E. Green and G.C. Nicholas, Two-dimensional theory of elasticity for finite deformation. Phil. Trans. Roy. Soc. A 247 (1954) 279?306.10.1098/rsta.1954.0019 ↗
3. J.E. Adkins and A.E. Green, Plane problems in second-order elasticity theory. Phil. Trans. Roy. Soc. A 239 (1957) 557?576.
4. A.E. Green and J.E. Adkins, Large Elastic Deformation and Nonlinear Continuum Mechanics, Oxford university Press, Oxford (1960).
5. W.H. Yang, Stress concentration in a rubber sheet under axially symmetric stretching, J. Appl. Mech. 34 (1967) 942?946.10.1115/1.3607860 ↗
6. F.S. Wong and R.T. Shield, Large plane deformations of thin elastic sheets of Neo-Hookean material. ZAMP 20 (1969) 176?199.
7. M.M. Carroll, Finite strain in compressible isotropic elasticity. J. Elasticity 18 (1988) 65?92.10.1007/BF00042141 ↗
8. P.G. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity. North-Holland (1988).
9. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1977) 337?403.10.1007/BF00279992 ↗
10. J.K. Knowles and Eli Sternberg, Large deformations near a tip of an interface-crack between two Neo-Hookean sheets. J. Elasticity 13 (1983) 257?293.10.1007/BF00042997 ↗
11. 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?98.10.1007/BF00115539 ↗
12. 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?138.10.1007/BF00115540 ↗
13. 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?174.10.1007/BF00115541 ↗
14. J.K. Knowles and Eli Sternberg, An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack. J. Elasticity 3 (1973) 67?107.10.1007/BF00045816 ↗
15. J.K. Knowles and Eli Sternberg, Finite-deformation analysis of the elastostatic field near the tip of a crack: reconsideration and higher order results. J. Elasticity 4 (1974) 201?233.10.1007/BF00049265 ↗
16. 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?99.10.1007/BF00043706 ↗
17. K. Ch. Le, On the singular elastostatic field induced by a crack in a Hadamard material. Quart. J. Mech. App. Math. 45 (1992) 101?117.10.1093/qjmam/45.1.101 ↗
18. K. Ch. Le and H. Stumpf, The singular elastostatic field due to a crack in rubberlike materials. J. Elasticity 32 (1993) 183?222.10.1007/BF00131660 ↗
19. J.K. Knowles, The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. Int. J. Fracture 13 (1977) 611?639.10.1007/BF00017296 ↗
20. J.K. Knowles and Eli Sternberg, Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example. J. Elasticity 10 (1980) 81?110.10.1007/BF00043136 ↗
21. J.K. Knowles and Eli Sternberg, Anti-plane shear fields with discontinuous deformation gradients near the tip of a crack in finite elastostatics. J. Elasticity 11 (1981) 129?164.10.1007/BF00043857 ↗
22. R.C. Abeyaratne and J.S. Yang, Localized shear discontinuities near the tip of a mode I crack. J. Elasticity 17 (1987) 93?102.10.1007/BF00043018 ↗
23. S.A. Silling, Numerical studies of loss of ellipticity near singularities in an elastic material. J. Elasticity 19 (1988) 213?239.10.1007/BF00045617 ↗
24. S.A. Silling, Consequences of the Maxwell relation for anti-plane shear deformation of an elastic solid. J. Elasticity 19 (1988) 241?284.10.1007/BF00045618 ↗
25. S.S. Antman, Existence of solutions of the equilibrium equations for nonlinearly elastic rings and arches. Indiana University Mathematics Journal 20 (1970) 281?302.10.1512/iumj.1971.20.20025 ↗
26. S.S. Antman, Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders. Arch. Rational Mech. Anal. 83 (1983) 1?52.10.1007/BF00281086 ↗
27. P. Podio Guidugli and G. Vergara Caffarelli, Extreme elastic deformations. Arch. Rational Mech. Anal. 115 (1991) 311?328.10.1007/BF00375278 ↗
28. 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.
29. A.M. Tarantino, On extreme thinning at the notch-tip of a Neo-Hookean sheet. (1995) Forthcoming paper.
30. A.E. Green and J.E. Adkins, Large Elastic Deformations. Clarendon Press, Oxford (1970).
31. J.R. Rice, Mathematical analysis in the mechanics of fracture. In Fracture, Vol. II, Chapter 3. Academic Press, New York (1968).