Wave motion in relaxation-testing of nonlinear elastic media

Relaxation testing is a fundamental tool for mechanical characterization of viscoelastic materials. Inertial effects are usually neglected when analysing these tests. However, relaxation tests involve sudden stretching of specimens, which causes propagation of waves whose effects may be significant. We study wave motion in a nonlinear elastic model specimen and derive expressions for the conditions under which loading may be considered to be quasi-static. Additionally, we derive expressions for wave properties such as wave speed and the time needed to reach a steady-state wave pattern. These expressions can be used to deduce nonlinear elastic material properties from dynamic experiments.