Journal of Elasticity

, Volume 11, Issue 2, pp 197–206 | Cite as

On the anti-plane shear problem in finite elasticity

  • Morton E. Gurtin
  • Roger Temam
Article

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References

  1. [1]
    Ericksen, J. L., Equilibrium of bars. J. Elasticity 5 (1975) 191–201.Google Scholar
  2. [2]
    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.Google Scholar
  3. [3]
    Knowles, J. K., On finite anti-plane shear for incompressible elastic materials. J. Australian Math. Soc. 19(B) (1976) 400–415.Google Scholar
  4. [4]
    Knowles, K. K., A note on anti-plane shear for compressible materials in finite elastostatics. J. Australian Math. Soc. 20(B) (1977) 1–7.Google Scholar
  5. [5]
    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.Google Scholar
  6. [6]
    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.Google Scholar
  7. [7]
    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.Google Scholar
  8. [8]
    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.Google Scholar
  9. [9]
    Truesdell, C. and W., Noll, The non-linear field theories of mechanics. Handbuch der Physik. III/3. Berlin: Springer-Verlag, 1965.Google Scholar
  10. [10]
    Lions, J. L. and E., Magenes, Nonhomogeneous boundary value problems and applications. Berlin: Springer-Verlag, 1972.Google Scholar
  11. [11]
    Ekeland, I. and R., Temam, Convex Analysis and Variational Problems. Amsterdam: North-Holland, New York: Elsevier, 1976.Google Scholar
  12. [12]
    Aubert, G. and R., Tahraoui, Theoremes d'existence en calcul des variations. J. Diff. Eqts. 33 (1979) 1–15.Google Scholar
  13. [13]
    Ball J. M., Constitutive inequalities and existence theorems in nonlinear elastostatics. Nonlinear Analysis and Mechanics: Heriot-Watt Shmposium 1, 187–241. London: Pitman.Google Scholar

Copyright information

© Sijthoff & Noordhoff International Publishers 1981

Authors and Affiliations

  • Morton E. Gurtin
    • 1
  • Roger Temam
    • 2
  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Departement MathématiqueUniversité de Paris-SudOrsayFrance

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