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On induced discontinuities in a class of linear materials with internal state parameters. (English) Zbl 0617.73033
The governing differential equations of induced discontinuities behind longitudinal and transverse shock waves are derived for a class of linear materials with internal state parameters. These equations indicate that the behavior of the induced discontinuities depends, in particular, on the behavior of the shock amplitudes and nonlinearly on the wave surface geomeries. Solutions for the case of plane waves with initially flat profiles are obtained, and they indicate that the global behavior of the induced discontinuities need not be monotone depending on the interpretation of the material responses.

MSC:
74J99 Waves in solid mechanics
74M20 Impact in solid mechanics
35L67 Shocks and singularities for hyperbolic equations
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