Shear shock waves in quasi-incompressible soft solids have been observed experimentally only twelve years ago. They differ from compression shock waves because their nonlinearity is cubic instead of quadratic. Velocities of shear waves are small, of the order of the meter per second, and thus induce a strong nonlinear behavior over small distances. This allows to counter-balance the quite strong absorption in such media. To our knowledge, these shear shock waves have been studied only for plane waves. However, focusing is a fundamental phenomenon in the wave physics and its applications. This is why our objective is to investigate the focusing of shear waves theoretically, numerically, and experimentally. This work was in particular motivated by a potential application in biomechanics. We have hypothesized that shear shock waves could play a role in the formation of some traumatic brain injuries, the geometry of the skull producing the focusing effect. These hypotheses have governed our studies for the choice of the different parameters such as the frequency, the amplitude and the geometry. The focusing has been demonstrated in a biological tissue-mimicking gel. Comparisons with the theoretical and numerical model have shown a good agreement. Further studies should concern the possible formation of lesions by shear shock waves.
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