Determination of the Unloading Boundary in Transverse Impact of an Elastic-Plastic String

Abstract

When a thin, elastic-plastic wire is transversely impacted, both longitudinal and transverse loading waves propagate. For certain types of excitation, unloading waves also propagate, and they overtake and interact with the loading waves. These interactions occur on moving boundaries, and a knowledge of the locations of these boundaries is needed for the solution of wave-propagation problems of this kind. An analytical technique and a numerical technique for the solution of such problems in long wires is presented. Examples, including response to impact by a finite mass, are given to illustrate the techniques. For finite length wires, the techniques will determine the initial portion of the solution.