References
Ericksen, J. L., Equilibrium of bars. J. Elasticity 5 (1975) 191–201.
Knowles, J. K. and E., Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics. J. Elasticity 8 (1978) 329–379.
Knowles, J. K., On finite anti-plane shear for incompressible elastic materials. J. Australian Math. Soc. 19(B) (1976) 400–415.
Knowles, K. K., A note on anti-plane shear for compressible materials in finite elastostatics. J. Australian Math. Soc. 20(B) (1977) 1–7.
Knowles, J. K., 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.
Knowles, J. K. and E., Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material. J. Elasticity 5 (1975) 341–361.
Knowles, J. K. and E., Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch. Rational Mech. Anal. 63 (1977) 221–236.
Knowles, J. K. and E., Sternberg, Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example. J. Elasticity 10 (1980) 81–110.
Truesdell, C. and W., Noll, The non-linear field theories of mechanics. Handbuch der Physik. III/3. Berlin: Springer-Verlag, 1965.
Lions, J. L. and E., Magenes, Nonhomogeneous boundary value problems and applications. Berlin: Springer-Verlag, 1972.
Ekeland, I. and R., Temam, Convex Analysis and Variational Problems. Amsterdam: North-Holland, New York: Elsevier, 1976.
Aubert, G. and R., Tahraoui, Theoremes d'existence en calcul des variations. J. Diff. Eqts. 33 (1979) 1–15.
Ball J. M., Constitutive inequalities and existence theorems in nonlinear elastostatics. Nonlinear Analysis and Mechanics: Heriot-Watt Shmposium 1, 187–241. London: Pitman.
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Gurtin, M.E., Temam, R. On the anti-plane shear problem in finite elasticity. J Elasticity 11, 197–206 (1981). https://doi.org/10.1007/BF00043860
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DOI: https://doi.org/10.1007/BF00043860