Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On static similarity deformations for isotropic materials


Author: James M. Hill
Journal: Quart. Appl. Math. 40 (1982), 287-291
MSC: Primary 73B10; Secondary 73G05
DOI: https://doi.org/10.1090/qam/678199
MathSciNet review: 678199
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Abstract: For static deformations of isotropic materials satisfying the principle of material indifference, the governing equations remain invariant under arbitrary orthogonal rotations of the material and spatial coordinate systems. Moreover, the basic equations are also invariant under the same change of length scale for both coordinate systems. The general functional form of the similarity deformation corresponding to these invariances is deduced. Although these invariances involve seven arbitrary constants, it is shown that by an appropriate selection of coordinates only three arbitrary constants are involved in an essential way.


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

  • [1] W. W. Klingbeil and R. T. Shield, On a class of solutions in plane finite elasticity, Z. angew. Math. Phys. 17, 489-511 (1966) MR 0211658
  • [2] Z. Wesolowski, Finite deformations of an elastic wedge and cone (in Polish), Mechanika Teoretyczna i Stosowana 7, 195-204 (1969)
  • [3] W. Langlois, Slow viscous flow, Macmillan Co., New York (1964) MR 0173436
  • [4] G. W. Bluman and J. D. Cole, Similarity methods for differential equations, Applied Mathematical Sciences 13, Springer-Verlag, New York (1974) MR 0460846
  • [5] J. M. Hill, Some partial solutions of finite elasticity, Ph.D. Thesis, University of Queensland (1972)
  • [6] M. Singh and A. C. Pipkin, Note on Ericksen's problem, Z. angew. Math. Phys. 16, 706-709 (1965)
  • [7] J. L. Ericksen, Deformations possible in every isotropic incompressible perfectly elastic body, Z. angew. Math. Phys. 5, 466-486 (1954) MR 0066873

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DOI: https://doi.org/10.1090/qam/678199
Article copyright: © Copyright 1982 American Mathematical Society

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