Stability of Deformation of an Elastic Layer

  • Y. C. Chen
  • K. R. Rajagopal


Ericksen [1] proved all universal deformations of isotropic compressible elastic materials to be homogeneous. He also proved inhomogeneous universal deformations possible if the isotropic elastic material is incompressible (cf.Ericksen [2]). Recently, interest has grown in the study of inhomogeneous, not universal deformations of isotropic incompressible elastic materials. The importance of such deformations and the need to study is them discussed in some detail by Rajagopal & Carroll [3].


Compact Support Equilibrium Solution Elastic Layer Uniaxial Extension Isotropic 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.
    Ericksen, J. L., Deformations possible in every compressible isotropic perfectly elastic material, J. Math. Phys. 34, 126–128 (1955).MathSciNetGoogle Scholar
  2. 2.
    Ericksen, J. L., Deformations possible in every isotropic incompressible perfectly elastic body, Z. Angew. Math. Phys. 5, 466–486 (1954).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Rajagopal, K. R., & Carroll, M. M., Non-homogeneous deformations of non-linear elastic wedges, submitted for publication.Google Scholar
  4. 4.
    Rajagopal, K. R., & Wineman, A. S., New exact solutions in non-linear elasticity, Intl. J. Eng. Science 23, 216–234, (1985).MathSciNetGoogle Scholar
  5. 5.
    Fosdick, R. L., & MacSithigh, G. P., Minimization in incompressible nonlinear elasticity theory, J. Elasticity, 16, 267–301 (1986).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Morrey, C. B., Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin-Heidelberg-New York, 1966.MATHGoogle Scholar
  7. 7.
    Rajagopal, K. R., & Wineman, A. S., On a class of deformations of a material with nonconvex stored energy function, J. Struct. Mech. 12, 471–482 (1985).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Y. C. Chen
    • 1
    • 2
  • K. R. Rajagopal
    • 1
    • 2
  1. 1.Department of Theoretical MechanicsCornell UniversityIthacaUSA
  2. 2.Department of Mechanical EngineeringUniversity of PittsburghPittsburghUSA

Personalised recommendations