Abstract
The buckling of a crack in an incompressible elastic solid subjected to a crack-parallel compression is studied by using a small-deformation-superposed-on-large-deformation analysis. It is found that for a general incompressible material there exists at least one and at most a finite number of buckling loads. For a Mooney material, a unique buckling load corresponding to a crack-parallel stretch ratio of 0.544 is found to exist.
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Wu, C. H., “Plane-strain buckling of a crack in a harmonic solid subjected to crack-parallel compression”, to appear in J. Appl. Mech., 46 (1979) 597–604.
Green, A. E., Rivlin, R. S. and Shield, R. T., “General theory of small elastic deformations superposed on large elastic deformations”, Proc. Roy. Soc. A, 211 (1952) 128–154.
Wilks, E. W., “On the stability of a circular tube under end thrust”, Quart. J. Mech. and Appl. Math., 8 (1955) 88–100.
Green, A. E. and Spencer, A. J. M., “The stability of a circular cylinder under finite extension and torsion”, J. Math. and Phys., 37 (1959) 316–338.
Corneliussen, A. H. and Shield, R. T., “Finite deformation of elastic membranes with application to the stability of an inflated and extended tube”, Arch. Rational Mech. and Analysis, 7 (1961) 273–304.
Sawyer, K. N. and Rivlin, R. S., “Bifurcation conditions for a thick elastic plate under thrust”, Int. J. Solids Structures, 10 (1974) 483–501.
Sensenig, C. B., “Instability of thick elastic solids”, Comm. Pure and Appl. Math., 17 (1964) 451–491.
Bromberg, E., “Buckling of a very thick rectangular block”, Comm. Pure and Appl. Math., 23 (1970) 511–528.
Luré, A. I., “Bifurcation of equilibrium of a perfectly elastic body”, PPM, 30 (1966) 718–731.
Biot, M. A., Mechanics of incremental deformations, John Wiley & Sons 1965.
John, F., “Plane strain problems for a perfectly elastic material of harmonic type”, Comm. Pure and Appl. Math., 13 (1960) 239–296.
Knowles, J. K. and Sternberg, E., “On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics”, Int. J. Solids Structures, 11 (1975) 1173–1201.
Knowles, J. K. and Sternberg, E. “On the failure of ellipticity of the equations for finite elastostatic plane strain”, Archive for Rational Mech. Ana., 63 (1977) 321–336.
Wong, F. S. and Shield, R. T., “Large plane deformations of thin elastic sheets of neo-Hookean material”, ZAMP, 20 (1969) 176–199.
Wu, C. H., “Large finite strain membrane problems”, Q. Appl. Math., 36 (1978) 347–359.
Lekhnitskii, S. G., Theory of elasticity of an anisotropic elastic body, Holden-Day, Inc. 1963.
Green, A. E. and Zerna, W., Theoretical elasticity, Oxford University Press 1963.
Coleman, B. D. and Noll, W., “On the thermostatics of continuous media”, Arch. Rational Mech. and Analysis, 4 (1959), 97–128.
Sih, G. C. and Liebowitz, H., “Mathematical theories of brittle fracture”, in Fracture, Vol. II, edited by Liebowitz.
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Supported by U.S. Army Research Office-Durham under Grant DAAG-29-76-G-0272.
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Wu, C.H. Plane-strain buckling of cracks in incompressible elastic solids. J Elasticity 10, 163–177 (1980). https://doi.org/10.1007/BF00044501
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DOI: https://doi.org/10.1007/BF00044501