On wave propagation problems in which occurs

Author:
T. C. T. Ting

Journal:
Quart. Appl. Math. **31** (1973), 275-286

DOI:
https://doi.org/10.1090/qam/99700

MathSciNet review:
QAM99700

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Abstract | References | Additional Information

Abstract: The combined longitudinal and torsional plastic waves in a thin-walled tube of rate-independent isotropic work-hardening material are used to illustrate the problems involved when the situation occurs. Two examples are presented. In the first example, the stress paths in the plane for the fast and slow simple waves are examined in the region near the singular point where . For , where is a nondimensional material constant defined in the paper, there is *no* stress path passing through the singular point other than the -axis itself. For , there is a family of stress paths emanated from which span an angle of with the -axis. In any case, the stress paths for the fast and slow simple waves are *not* orthogonal to each other at the singular point. In the second example, a study is made of the propagation of the plastic wave front into the tube which is initially prestressed at the stress state . It is shown that the solution in the region next to a region of constant state is *not* necessarily a simple wave solution. In fact, an unloading can occur at the plastic wave front which changes its speed from to at the onset of the unloading.

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Additional Information

DOI:
https://doi.org/10.1090/qam/99700

Article copyright:
© Copyright 1973
American Mathematical Society