A Numerical Study of Plane Longitudinal Waves in a Nonlinear Viscoelastic Material

A numerical study of plane longitudinal waves in a nonlinear viscoelastic material is presented. The constitutive relationship and the conservation equations, in Lagrangian form, are formulated in an explicit first-order finite-difference manner. The mechanical behavior of the material is described by means of state and orientation variables and the associated differential equations. With the use of the numerical procedure we model wave-propagation experiments in polymethyl methacrylate and derive a constitutive relationship for that material. We then use this constitutive equation in a numerical study of the evolution of steady-state waves and we show that the time for the formation of these waves is inversely proportional to magnitude of the imposed velocity.