Propagation of nonlinear waves along a viscoelastic bar

Various types of nonlinear waves propagating along a viscoelastic bar are considered. The rheological equation of state has strong physical and geometric nonlinearities, and nonisothermal effects are included. Both weak (isentropic) and shock waves of loading and unloading are investigated. It is shown that, for certain rubber-like materials, stable shock waves of extension can exist along with the shock waves of compression at very large strains. We then consider the strike of a viscoelastic bar of finite length against a rigid obstacle. Numerical solutions to this problem illustrate the influence of stress relaxation on nonlinear wave processes. A model for sticking and bouncing off is formulated and the mass-averaged velocity of the bar at the moment when it bounces off the obstacle is calculated.