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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.

74M20 Impact in solid mechanics
74J10 Bulk waves in solid mechanics
74J99 Waves in solid mechanics
Full Text: DOI
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