Abstract
It is shown that a static pure torsion can be imposed on a circular cylinder comprised of any homogeneous isotropic elastic material subject to suitable surface tractions alone if the material is incompressible, but such a pure torsion cannot generally be imposed if the material is compressible. Hence the static torsion is a universal deformation for an incompressible isotropic elastic material, but not for a compressible isotropic elastic material. The analysis of such a pure torsion is due to Rivlin (1947; 1948a; 1949a). A broader family of universal deformations of Ericksen & Rivlin (1954) is also discussed, where this larger family includes not only torsions but also extensions and inflations of a circular cylinder. The calculation of these and other universal exact solutions for finite elastic deformation represents a remarkable achievement in the mathematical theory of elasticity. The development here follows that of Truesdell & Noll (1965).
The picture of nature as a whole given us by mechanics may be compared to a black-and-white photograph: It neglects a great deal, but within its limitations, it can be highly precise.
Truesdell (1966)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Smith, D.R. (1993). Torsion of an Isotropic Elastic Circular Cylinder. In: An Introduction to Continuum Mechanics — after Truesdell and Noll . Solid Mechanics and Its Applications, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0713-8_13
Download citation
DOI: https://doi.org/10.1007/978-94-017-0713-8_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4314-6
Online ISBN: 978-94-017-0713-8
eBook Packages: Springer Book Archive