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19.—Propagation of Weak Discontinuities in a Layered Hyperelastic Half-space

Published online by Cambridge University Press:  14 February 2012

Erdogan S. Suhubi  and
Alan Jeffrey
Erdogan S. Suhubi
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon Tyne
Alan Jeffrey
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon Tyne
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Synopsis

This paper investigates the one-dimensional propagation of weak discontinuities, that is acceleration waves, in a homogeneous and isotropic half-space composed of an arbitrary number of non-linearly hyperelastic layers. The transmission and reflection coefficients are evaluated in terms of the initial condition at the boundary, and the steepening of the waves to form a shock is discussed. The results are specialised to the case of periodic layering.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 3 , 1976 , pp. 209 - 221
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

REFERENCES

1Eringen, A. C. and Suhubi, E. S.. Elastodynamics 1. Finite motions (New York: Academic Press, 1974).Google Scholar
2Jeffrey, A.. The propagation of weak discontinuities in quasilinear hyperbolic systems with discontinuous coefficients. I. Fundamental theory. Applicable Anal. 3 (1973), 79–100.CrossRefGoogle Scholar
3Jeffrey, A.. The propagation of weak discontinuities in quasilinear hyperbolic systems with discontinuous coefficients. II. Special cases and applications. Applicable Anal. 3 (1974), 359–375.CrossRefGoogle Scholar
4Collins, W. D.. One-dimensional nonlinear wave propagation in incompressible elastic materials. Quart. J. Mech. Appl. Math. 19 (1966), 259–328.CrossRefGoogle Scholar
5Jeffrey, A. and Teymur, M.. Formation of shock waves in hyperelastic solids. Acta Mech. 20 (1974), 133–149.CrossRefGoogle Scholar
6Jeffrey, A. and Tin, S.. Waves over obstacles on a shallow seabed. Proc. Roy. Soc. Edinburgh Sect. A 71 (1974), 181–192.Google Scholar