ON THE INITIAL SLOPE OF ELASTIC-PLASTIC BOUNDARIES IN LONGITUDINAL WAVE PROPAGATION IN A ROD
STANFORD UNIV CA STANFORD
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In one dimensional wave propagation such as longitudinal waves in a rod, an elastic-plastic boundary may start at the end x 0 of the rod depending on the stresses prescribed at x 0. The initial slope of the elastic-plastic boundary at x 0 can be determined easily if the time derivative sigma sub t of the stress sigma on both sides of the elastic-plastic boundary are not zero. In this paper, the initial slope of the elastic-plastic boundary or boundaries is determined analytically when sigma sub t at x 0 is continuous and vanishes at time t t sub 0 while the second derivative sigma sub tt at t sub 0 may or may not be continuous. It is seen that an elastic region can be generated near the end of the rod even though the stress state at the end is continuously plastic.