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Knowles, J. K.; Sternberg, Eli

On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics. (English) Zbl 0422.73038

J. Elasticity 8, 329-379 (1978).
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Cited in 80 Documents

MSC:

74B20 Nonlinear elasticity
35J60 Nonlinear elliptic equations

Keywords:

equilibrium fields; discontinuous displacement gradients; continuous displacements; finite plane deformations; anisotropic; compressible elastic solids; elastostatic shocks
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References:

[1] J. K.Knowles and EliSternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material, Journal of Elasticity, 5 (1975), 341. · Zbl 0323.73010 · doi:10.1007/BF00126996
[2] J. K.Knowles and EliSternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain, Archive for Rational Mechanics and Analysis, 63 (1977), 4, 321.
[3] P. J.Blatz and W. L.Ko, Application of finite elastic theory to the deformation of rubbery materials, Transactions of the Society of Rheology, 6 (1962), 223. · doi:10.1122/1.548937
[4] J. W.Rudnicki and J. R.Rice, Conditions for the localization of deformation in pressure-sensitive dilatant materials, Journal of the Mechanics and Physics of Solids, 23 (1975), 371. · doi:10.1016/0022-5096(75)90001-0
[5] J. R.Rice, The localization of plastic deformation, in Theoretical and Applied Mechanics, Proceedings of the 14th IUTAM Congress, Delft, The Netherlands, 1976, North Holland, Amsterdam, 1976. · Zbl 0368.73036
[6] R.Hill and J. W.Hutchinson, Bifurcation phenomena in the plane tension test, Journal of the Mechanics and Physics of Solids, 23 (1975), 239. · Zbl 0331.73048 · doi:10.1016/0022-5096(75)90027-7
[7] R.Courant and K. O.Friedrichs, Supersonic flow and shock waves, Interscience, New York, 1948. · Zbl 0041.11302
[8] J. K.Knowles, The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids, International Journal of Fracture, 13 (1977), 611. · doi:10.1007/BF00017296
[9] P. D.Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, in Regional Conference Series in Mathematics, No. 11, Society for Industrial and Applied Mathematics, Philadelphia, 1973. · Zbl 0268.35062
[10] J. D.Eshelby, The elastic energy-momentum tensor, Journal of Elasticity, 5 (1975), 321. · Zbl 0323.73011 · doi:10.1007/BF00126994
[11] J. R.Rice, A path-independent integral and the approximate analysis of strain concentrations by notches and cracks, Journal of Applied Mechanics, 35 (1968), 2, 379.
[12] T. Y.Thomas, Plastic flow and fracture in solids, Academic Press, New York, 1961. · Zbl 0095.38902
[13] A.Nadai, Theory of flow and fracture of solids, Vol. 1, Second Edition, McGraw-Hill, New York, 1950.
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