ABSTRACT
Solutions to some dynamic elasto-plastic problems (mostly one-dimensional) are presented in this chapter to bring out the effect of the dynamic or inertia terms. Ideally, the two formulations described in Chapter 6 should be used, namely, the Eulerian and updated Lagrangian formulations. However, for the problems described in this chapter, the total Lagrangian formulation in steps of loading and unloading is convenient. In each step, the three governing equations need to be solved: (i) equation of motion, (ii) stress-strain relation and (iii) strain-displacement relation. A simplified approach will be used to solve these problems. First, the problem of longitudinal stress wave propagation in a rod shall be discussed. This problem was first solved independently by von Karman (1942) and Taylor (1942).
