On Tensile Shock Waves in Rubber-Like Materials

The problem of generation of one-dimensional tensile shock waves in rubber-like materials is studied numerically and compared to the exact elastic nonlinear solution and the steady wave solution. It is shown that a rate-type semilinear visco-elastic model can describe the steepening of the wave during its propagation and a “thickness” of the wave is naturally incorporated. An energetic criterion for the numerical stability is discussed. The numerical results point out the uncertainty (difficulty) one may encounter in measuring the dynamic Young’s modulus and Maxwell-type viscosity coefficient.