On copositive matrices and strong ellipticity for isotropic elastic materials

  • H. C. Simpson
  • S. J. Spector


Neural Network Complex System Nonlinear Dynamics Electromagnetism Elastic Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker, M., & J. L. Ericksen, Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids. J. Wash. Acad. Sci. 44 (1954), 33–35. Reprinted in Foundations of Elasticity Theory. Intl. Sci. Rev. Serv. New York: Gordon and Breach 1965.Google Scholar
  2. 2.
    Cottle, R. W., G. J. Habetler & C. E. Lemke, On classes of copositive matrices, Lin. Alg. Appl. 3 (1970), 295–310.Google Scholar
  3. 3.
    Gantmacher, F. R., The Theory of Matrices, New York: Chelsea 1960.Google Scholar
  4. 4.
    Gurtin, M. E., An Introduction to Continuum Mechanics. New York: Academic Press 1981.Google Scholar
  5. 5.
    Knowles, J. K., & E. Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch. Rational Mech. Anal. 63 (1977), 321–336.Google Scholar
  6. 6.
    Zee, L., & E. Sternberg, Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids. Arch. Rational Mech. Anal. 83 (1983), 53–90.Google Scholar
  7. 7.
    Truesdell, C., & W. Noll, The non-linear field theories of mechanics, Handbuch der Physik Vol. III/3. Berlin Heidelberg New York: Springer 1965.Google Scholar
  8. 8.
    Dunn, J. E., Elastic materials of coaxial type and inequalities sufficient to insure strong ellipticity. To appear: Int. J. Solids Structures.Google Scholar
  9. 9.
    Hadeler, K. P., On copositive matrices. Lin. Alg. Appl. 49 (1983), 79–89.Google Scholar
  10. 10.
    Sawyers, K. N., & R. S. Rivlin, On the speed of propagation of waves in a deformed compressible elastic material. Z. Angew. Math. Phys. 29 (1978), 245–251.Google Scholar
  11. 11.
    Simpson, H. C., & S. J. Spector, On barrelling instabilities in elasticity. To appear: J. Elasticity.Google Scholar

Copyright information

© Springer-Verlag GmbH & Co 1983

Authors and Affiliations

  • H. C. Simpson
    • 1
    • 2
  • S. J. Spector
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of TennesseeUSA
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondale

Personalised recommendations