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Nonlinear evolution of shear waves into shocks in incompressible elasticmaterials is investigated using the framework of large deformationelastodynamics, for a family of loadings and commonly used hyperelasticmaterial models. Closed form expressions for the shock formation distance arederived and used to construct non-dimensional phase maps that determine regimesin which a shock can be realized. These maps reveal the sensitivity of shockevolution to the amplitude, shape, and ramp time of the loading, and to theelastic material parameters. In light of a recent study (Espindola et al.,2017), which hypothesizes that shear shock formation could play a signicantrole in Traumatic Brain Injury (TBI), application to brain tissue is consideredand it is shown that the size matters in TBI research. Namely, for realisticloadings, smaller brains are less susceptible to formation of shear shocks.Furthermore, given the observed sensitivity to the imparted waveform and theconstitutive properties, it is suggested that the non-dimensional maps canguide the design of protective structures by determining the combination ofloading parameters, material dimensions, and elastic properties that can avoidshock formation.

Shear shock evolution in incompressible soft solids