Counter-intuitive results in acousto-elasticity |
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| Authors: | AL Gower M Destrade RW Ogden |
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| Institution: | 1. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland;2. School of Mechanical & Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland;3. School of Mathematics and Statistics, University of Glasgow, Scotland, United Kingdom |
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| Abstract: | We present examples of body wave and surface wave propagation in deformed solids where the slowest and the fastest waves do not travel along the directions of least and greatest stretch, respectively. These results run counter to commonly accepted theory, practice, and implementation of the principles of acousto-elasticity in initially isotropic solids. For instance, we find that in nickel and steel the fastest waves are along the direction of greatest compression, not greatest extension (and vice-versa for the slowest waves), as soon as those solids are deformed. Further, we find that when some materials are subject to a small-but-finite deformation, other extrema of wave speeds appear in non-principal directions. Examples include nickel, steel, polystyrene, and a certain hydrogel. The existence of these “oblique”, non-principal extremal waves complicates the protocols for the non-destructive determination of the directions of extreme strains. |
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| Keywords: | Acousto-elasticity Surface waves Non-principal waves |
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