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

  • Erdogan S. Suhubi (a1) and Alan Jeffrey (a1)

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.

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References

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1Eringen, A. C. and Suhubi, E. S.. Elastodynamics 1. Finite motions (New York: Academic Press, 1974).
2Jeffrey, A.. The propagation of weak discontinuities in quasilinear hyperbolic systems with discontinuous coefficients. I. Fundamental theory. Applicable Anal. 3 (1973), 79100.
3Jeffrey, A.. The propagation of weak discontinuities in quasilinear hyperbolic systems with discontinuous coefficients. II. Special cases and applications. Applicable Anal. 3 (1974), 359375.
4Collins, W. D.. One-dimensional nonlinear wave propagation in incompressible elastic materials. Quart. J. Mech. Appl. Math. 19 (1966), 259328.
5Jeffrey, A. and Teymur, M.. Formation of shock waves in hyperelastic solids. Acta Mech. 20 (1974), 133149.
6Jeffrey, A. and Tin, S.. Waves over obstacles on a shallow seabed. Proc. Roy. Soc. Edinburgh Sect. A 71 (1974), 181192.

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