Axial stress waves in an elastic–perfectly-plastic bar

A bar, made from an elastic–perfectly plastic material, fixed at one end, suddenly has an axial load applied at the other end. After its sudden application, the load is held constant. If the load is less than half the yield load for the bar, and in the absence of damping, the load causes a stress wave to pass up and down the bar, all behaviour being elastic. At any point within the bar length, the stress varies, in a stepwise fashion, between zero, and twice the stress corresponding to the applied load. This is the classical elastic solution. However, if the load is greater than half the yield load, when the stress wave first hits the fixed end, yielding will occur, and a simple model is proposed in this paper to allow for yielding. The model incorporates two zones separated by the stress wave, as in the elastic solution, together with a third zone, concentrated, and adjacent to the fixed support, in which all plastic straining takes place. The paper describes and verifies the model, and presents the predictions that it gives for various levels of load.