Shear shock formation in incompressible viscoelastic solids

Experiments have shown that shear waves induced in brain tissue can develop into shock waves, thus providing a possible explanation of deep traumatic injuries. Here, we study the formation soft viscoelastic solids subject to an imposed velocity at their boundary. We consider plane shearing motion semi-infinite half-space, which corresponds spatially one-dimensional problem. Incompressible whose behaviour is described by Fung-Simo quasi-linear viscoelasticy theory (QLV) are considered, where elastic response either exponential or polynomial Mooney-Rivlin-Yeoh type. Waveform breaking occur blow-up acceleration leading one sufficient condition for shocks. A slow scale analysis based on small amplitude parameter yields damped Burgers-like equation, another condition. Numerical experiments performed using dedicated finite volume scheme show these estimates limited accuracy. Their validity restricted limit too, exact conditions known.