Wave reflection in slightly compressible, finitely deformed elastic media |
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Authors: | A Chattopadhyay G A Rogerson |
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Institution: | (1) Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India, IN;(2) Department of Computer and Mathematical Sciences, University of Salford, Salford M5 4WT, UK, GB |
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Abstract: | Summary In this paper, the reflection of a plane wave at an incrementally traction-free boundary of a half-space composed of nearly
incompressible elastic material is considered. It is shown that two distinct cases exist, these being dependent on the underlying
primary deformation. In the first case, the appropriate slowness sections are each approximately elliptical, and the corresponding
reflection phenomena closely mirrors that associated with the corresponding linear isotropic theory. Specifically, an angular
range of direction of incident wave exists, for which both a quasi-longitudinal and quasi-shear wave are reflected, the former
being replaced by a surface wave outside this angular range. In the second case, the outer slowness section is re-enrant and,
in addition to the scenarios previously mentioned, it is possible for two quasi-shear waves to be reflected. Numerical illustrations
of reflection coefficients are presented in respect of a modified Varga material and the case of increasing bulk modulus is
investigated.
Received 17 January 2000; accepted for publication 22 February 2000 |
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Keywords: | elasticity pre-stress waves reflection finite strain |
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