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The formation of shear shock waves in the brain has been proposed as one ofthe plausible explanations for deep intracranial injuries. In fact, suchsingular solutions emerge naturally in soft viscoelastic tissues under dynamicloading conditions. To improve our understanding of the mechanical processes athand, the development of dedicated computational models is needed. The presentstudy concerns three-dimensional numerical models of incompressibleviscoelastic solids whose motion is analysed by means of shock-capturing finitevolume methods. More specifically, we focus on the use of the artificialcompressibility method, a technique that has been frequently employed incomputational fluid dynamics. The material behaviour is deduced from theFung--Simo quasi-linear viscoelasiticity theory (QLV) where the elasticresponse is of Yeoh type. We analyse the accuracy of the method and demonstrateits applicability for the study of nonlinear wave propagation in soft solids.The numerical results cover accuracy tests, shock formation and wavediffraction.

Computation of viscoelastic shear shock waves using finite volume schemes with artificial compressibility