Wave propagation and uniqueness in prestressed elastic solids
- 13 August 1963
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 274 (1359) , 500-506
- https://doi.org/10.1098/rspa.1963.0146
Abstract
A homogeneous isotropic perfectly elastic body is subjected to a large static pure homogeneous deformation with two of the principal extension ratios equal. An infinitesimal deformation is superimposed on the large deformation. The conditions for strong ellipticity of the system of equilibrium equations for the infinitesimal deformation are obtained. These conditions are examined within the context of uniqueness or non-uniqueness of the displacement boundary-value problem for the infinitesimal deformation. It is found that the conditions of strong ellipticity are sufficient but not necessary for uniqueness.Keywords
This publication has 2 references indexed in Scilit:
- Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic EffectThe Journal of the Acoustical Society of America, 1961
- Implications Of Hadamard's Conditions For Elastic Stability With Respect To Uniqueness TheoremsCanadian Journal of Mathematics, 1956