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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.

MSC:
74M20 Impact in solid mechanics
74J10 Bulk waves in solid mechanics
74J99 Waves in solid mechanics
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