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Ordinary and Strong Ellipticity in the Equilibrium Theory of Incompressible Hyperelastic Solids


Zee, Layne (1983) Ordinary and Strong Ellipticity in the Equilibrium Theory of Incompressible Hyperelastic Solids. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jzka-ce91.


In this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three-dimensional field equations in the nonlinear equilibrium theory of incompressible, homogeneous and isotropic, hyperelastic solids. The resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain-energy density with respect to the deformation invariants or the principal stretches. The conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the Baker-Ericksen inequalities and possess a positive shear modulus at infinitesimal deformations. Various implications of these ellipticity conditions for special classes of materials and deformations are explored.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mechanics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sternberg, Eli
Thesis Committee:
  • Sternberg, Eli (chair)
  • Brennen, Christopher E.
  • Keller, Herbert Bishop
  • Knowles, James K.
  • Miklowitz, Julius
Defense Date:30 July 1982
Funding AgencyGrant Number
Earle C. Anthony FellowshipUNSPECIFIED
Office of Naval Research (ONR)N00014-75-C-0196
Record Number:CaltechETD:etd-11012005-130640
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4358
Deposited By: Imported from ETD-db
Deposited On:01 Nov 2005
Last Modified:16 Apr 2021 22:21

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PDF (Zee_l_1983.pdf) - Final Version
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