  Nonlinear evolution of shear waves into shocks in incompressible elastic
materials is investigated using the framework of large deformation
elastodynamics, for a family of loadings and commonly used hyperelastic
material models. Closed form expressions for the shock formation distance are
derived and used to construct non-dimensional phase maps that determine regimes
in which a shock can be realized. These maps reveal the sensitivity of shock
evolution to the amplitude, shape, and ramp time of the loading, and to the
elastic material parameters. In light of a recent study (Espindola et al.,
2017), which hypothesizes that shear shock formation could play a signicant
role in Traumatic Brain Injury (TBI), application to brain tissue is considered
and it is shown that the size matters in TBI research. Namely, for realistic
loadings, smaller brains are less susceptible to formation of shear shocks.
Furthermore, given the observed sensitivity to the imparted waveform and the
constitutive properties, it is suggested that the non-dimensional maps can
guide the design of protective structures by determining the combination of
loading parameters, material dimensions, and elastic properties that can avoid
shock formation.
