The transition from acceleration wave to shock wave. (English) Zbl 0734.73013
Summary: In certain circumstances the amplitude of an acceleration wave is predicted by singular surface theory to become infinite after only a finite distance of propagation and it is widely believed that this corresponds to the formation of a shock wave, though no proof appears to have been given. We prove that this is so for one-dimensional motions of an elastic half-space by utilizing an exact solution obtained from simple wave theory. This result is extended to dilatational cylindrical and spherical wave propagation in an elastic material.
MSC:
| 74M20 | Impact in solid mechanics |
| 74J10 | Bulk waves in solid mechanics |
| 74J99 | Waves in solid mechanics |
References:
| [1] | Green, W. A., Arch. Rational Mech. Anal., 16, 79-88 (1964) · Zbl 0124.41702 |
| [2] | Coleman, B. D.; Gurtin, M. E., Arch. Rational Mech. Anal., 19, 239-265 (1965) · Zbl 0244.73017 |
| [3] | Varley, E., Arch. Rational Mech. Anal., 19, 215-225 (1965) · Zbl 0136.22101 |
| [4] | Varley, E.; Dunwoody, J., J. Mech. Phys. Solids, 13, 17-28 (1965) · Zbl 0123.20303 |
| [5] | Lindsay, K. A.; Straughan, B., Arch. Rational Mech. Anal., 68, 53-87 (1978) · Zbl 0399.76078 |
| [6] | Chen, P. J., Growth and Decay of Waves in Solids, (Handbuch der Physik, Vol. VIa/3 (1973), Springer: Springer Berlin) |
| [7] | McCarthy, M. F., Singular surfaces and waves, (Eringen, A. C., Continuum Physics (1975), Academic Press: Academic Press New York) · Zbl 0485.73091 |
| [8] | Fu, Y. B.; Scott, N. H., Q. J. Mech. Appl. Math., 42, 23-39 (1989) · Zbl 0686.73024 |
| [9] | Fu, Y. B.; Scott, N. H., Arch. Rational Mech. Anal., 108, 11-34 (1989) · Zbl 0691.73017 |
| [10] | Whitham, G. B., Linear and Nonlinear Waves (1974), Wiley: Wiley New York · Zbl 0373.76001 |
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