Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Plastic Wave Propagation

[+] Author and Article Information
R. J. Clifton

Division of Engineering, Brown University, Providence, R. I.

J. Appl. Mech 35(4), 782-786 (Dec 01, 1968) (5 pages) doi:10.1115/1.3601306 History: Received January 08, 1968; Revised May 23, 1968; Online September 14, 2011


Assuming a one-dimensional rate independent theory of combined longitudinal and torsional plastic wave propagation in a thin-walled tube, restrictions are obtained on the possible speeds of elastic-plastic boundaries. These restrictions are shown to depend on the type of discontinuity at the boundary and on whether loading or unloading is occurring. The range of unloading (loading) wave speeds for the case when the nth time derivative of the solution is the first derivative that is discontinuous across the boundary is the complement of the range of unloading (loading) wave speeds for the case when the first discontinuity is in the (n + 1)th time derivative. Thus all speeds are possible for elastic-plastic boundaries corresponding to either loading or unloading. The general features of the discontinuities associated with loading and unloading boundaries are established, and examples are presented of unloading boundaries overtaking simple waves.

Copyright © 1968 by ASME
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