The transition from acceleration wave to shock wave.

*(English)*Zbl 0734.73013Summary: 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 |

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\textit{Y. B. Fu} and \textit{N. H. Scott}, Int. J. Eng. Sci. 29, No. 5, 617--624 (1991; Zbl 0734.73013)

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