Chapter 5 - Rigid Unloading Approximation

Abstract

This chapter discusses rigid unloading in detail. At times, the elastic–plastic wave propagation containing unloading processes are discussed based on the assumption of elastic unloading. In such cases, unloading disturbances propagate with elastic wave velocity. If the elastic wave velocity is much larger than the plastic wave velocity, then relative to the plastic wave velocity, the elastic wave velocity can be approximately regarded as infinite. When unloading problems are dealt with, this is corresponding to that of the elastic–plastic body once unloading is regarded as a rigid body but the inertia effect of rigid part should be still taken into account. By such a “rigid unloading” assumption, the elastic–plastic wave propagation problems containing unloading processes usually can be simplified a lot. The chapter discusses rigid unloading in infinite bars as well as in finite bars. If the shock waves form in a gradually increasing hardening plastic material, wherein the shock wave velocity varies with shock intensity, it becomes complicated. The authors discuss rigid unloading in such a case. It is shown that the rigid unloading analysis averages the original discontinuous distribution of residual strain obtained in the elastic–plastic wave analysis so that its distribution is continuous.