On the Initial Speed of Elastic-Plastic Boundaries in Longitudinal Wave Propagation in a Rod

[+] Author and Article Information
T. C. T. Ting

Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill.

J. Appl. Mech 38(2), 441-447 (Jun 01, 1971) (7 pages) doi:10.1115/1.3408795 History: Received October 14, 1969; Revised March 13, 1970; Online July 12, 2010


A study is given of elastic-plastic boundaries which start at the end x = 0 of a rod in one-dimensional wave propagation. The initial speed of the elastic-plastic boundaries at x = 0 and at any time, say t = t0 , is determined analytically for all possible combinations of the time derivative σt of the stress σ(0, t) before and after t = t0 . If σt at x = 0 is continuous and vanishes at t = t0 , all possible combinations of σtt before and after t = t0 are considered. The analysis also gives the number of regions involved, the derivatives in each region, and distinguishes elastic regions from plastic regions. These are useful guides for a numerical solution of general initial and boundary-value problems.

Copyright © 1971 by ASME
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