Summary
In this paper we consider plane deformations of an incompressible elastic material and we show that by a suitable choice of strain energy function we can find the class of deformations with constant local rotation angle. Although the form for the strain energy function is chosen in the first place for mathematical convenience it does correspond to physically reasonable behaviour and such a theory may be regarded as a first order theory. The class of solutions obtained are expressed in a parametric form involving an arbitrary function, simple choices of which correspond to the well known exact solutions of finite elasticity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Courant, R. and D. Hilbert, Methods of Mathematical Physics, vol. II, Interscience, New York 1962.
Truesdell, C. A. and R. A. Toupin, Handbuch der Physik, vol. III/1, Springer, Berlin 1960.
Green, A. E. and W. Zerna, Theoretical Elasticity, Clarendon Press, Oxford 1960.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Holden, J.T. A class of exact solutions for finite plane strain deformations of a particular elastic material. Appl. Sci. Res. 19, 171–181 (1968). https://doi.org/10.1007/BF00383920
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00383920