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Large Plane Deformations of Thin Elastic Sheets of Neo-Hookean Material


Wong, Felix Shek Ho (1969) Large Plane Deformations of Thin Elastic Sheets of Neo-Hookean Material. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/M380-M034.


Large plane deformations of thin elastic sheets of neo-Hookean material are considered and a method of successive substitutions is developed to solve problems within the two-dimensional theory of finite plane stress. The first approximation is determined by linear boundary value problems on two harmonic functions, and it is approached asymptotically at very large extensions in the plane of the sheet. The second and higher approximations are obtained by solving Poisson equations. The method requires modification when the membrane has a traction-free edge.

Several problems are treated involving infinite sheets under uniform biaxial stretching at infinity. First approximations are obtained when a circular or elliptic inclusion is present and when the sheet has a circular or elliptic hole, including the limiting cases of a line inclusion and a straight crack or slit. Good agreement with exact solutions is found for circularly symmetric deformations. Other examples discuss the stretching of a short wide strip, the deformation near a boundary corner which is traction-free, and the application of a concentrated load to a boundary point.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Engineering Science and Applied Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering
Minor Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Shield, Richard T.
Thesis Committee:
  • Unknown, Unknown
Defense Date:26 July 1968
Additional Information:Title varies in the 1969 Caltech commencement program: Large Plane Deformations of Elastic Sheets of Neo-Hookean Material
Funding AgencyGrant Number
Ford FoundationUNSPECIFIED
Record Number:CaltechTHESIS:02222016-101835821
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9571
Deposited On:22 Feb 2016 21:37
Last Modified:06 May 2024 23:05

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