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On the failure of ellipticity of the equations for finite elastostatic plane strain. (English) Zbl 0351.73061


MSC:

74B20 Nonlinear elasticity
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[1] J. K. Knowles & Eli Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material, Journal of Elasticity, 5 (1975), 3–4, 341. · Zbl 0323.73010 · doi:10.1007/BF00126996
[2] P.J. Blatz & 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
[3] C. Truesdell & W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, Vol. III/3, Springer, Berlin, 1965. · Zbl 0779.73004
[4] R.J. Knops & L.E. Payne, Uniqueness theorems in linear elasticity, Springer Tracts in Natural Philosophy, Vol. 19, Springer, Berlin, 1971. · Zbl 0224.73016
[5] M.E. Gurtin, The linear theory of elasticity, in Handbuch der Physik, Vol. VIa/2, Springer, Berlin, 1972. · Zbl 0317.73002
[6] R.A. Toupin & B. Bernstein, Sound waves in deformed perfectly elastic materials. Acoustoelastic effect, The Journal of the Acoustical Society of America, 33 (1961), 2, 216. · doi:10.1121/1.1908623
[7] Fritz John, Plane strain problems for a perfectly elastic material of harmonic type, Communications on Pure and Applied Mathematics, XIII (1960), 239. · Zbl 0094.37001
[8] J.K. Knowles & Eli Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics, International Journal of Solids and Structures, 11 (1975), 1173. · Zbl 0348.73009 · doi:10.1016/0020-7683(75)90107-9
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