Wave propagation in a pre-stressed highly elastic body: two exact solutions for Boussinesq problems
✍ Scribed by L.M. Brock
- Book ID
- 104293898
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 171 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0165-2125
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✦ Synopsis
Two problems of wave propagation induced by surface loads in a compressible neo-Hookean half-space, initially at rest under a uniform pre-stress, are considered. One problem concerns a plane-strain situation, the other, one of axial symmetry. An accepted general procedure, that of superposing infinitesimal deformations upon the possibly large deformations due to pre-stress, is carried out completely in terms of tractable exact solutions for both the surface behavior and the full field, and analytical expressions for all wave speeds.
The results show that for a tensile pre-stress above a critical value, a negative Poisson effect occurs; for compressive pre-stresses, Rayleigh waves disappear at a critical value. Indeed, all wave speeds in the deformed configuration (effective wave speeds), as well as the solutions, for both problems are clearly sensitive to material properties and to both the magnitude and nature (compressive or tensile) of the pre-stress. In particular, the constraint imposed by plane strain appears to enhance this sensitivity.