Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A principal stress contour for nonlinear elastic deformations


Author: Jingyu Shi
Journal: Quart. Appl. Math. 52 (1994), 439-448
MSC: Primary 73G05; Secondary 73C50
DOI: https://doi.org/10.1090/qam/1292196
MathSciNet review: MR1292196
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Abstract: We seek special principal stress contours, for a nonlinear elastic plane deformation, on which both the principal stresses are constant and the principal axes do not change directions. It is found that they must be straight lines and that the lines must be parallel to one another or intersect at one point. It is also shown that the principal stress contours in the deformation for the straightening of a circular arc are such straight lines.


References [Enhancements On Off] (What's this?)

  • [1] R. W. Ogden, Principal stress and strain trajectories in nonlinear elastostatics, Quart. Appl. Math. 44, 255-264 (1986)
  • [2] R. W. Ogden, Non-linear elastic deformations, Ellis Horwood, Chichester, 1984
  • [3] E. Varley and E. Cumberbatch, The finite deformation of an elastic material surrounding an elliptical hole, Finite Elasticity 27, ASME, 41-64 (1977)
  • [4] E. Varley and E. Cumberbatch, Finite deformations of elastic materials surrounding holes, J. Elasticity 10, 341-405 (1980)
  • [5] A. J. M. Spencer, Continuum Mechanics, Longman, London, 1980

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Additional Information

DOI: https://doi.org/10.1090/qam/1292196
Article copyright: © Copyright 1994 American Mathematical Society


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