The formation of shear shock waves in the brain has been proposed as one of the plausible explanations for deep intracranial injuries. In fact, such singular solutions emerge naturally in soft viscoelastic tissues under dynamic loading conditions. To improve our understanding of the mechanical processes at hand, the development of dedicated computational models is needed. The present study concerns three-dimensional numerical models of incompressible viscoelastic solids whose motion is analysed by means of shock-capturing finite volume methods. More specifically, we focus on the use of the artificial compressibility method, a technique that has been frequently employed in computational fluid dynamics. The material behaviour is deduced from the Fung--Simo quasi-linear viscoelasiticity theory (QLV) where the elastic response is of Yeoh type. We analyse the accuracy of the method and demonstrate its applicability for the study of nonlinear wave propagation in soft solids. The numerical results cover accuracy tests, shock formation and wave diffraction.

翻译：在脑部形成剪切冲击波已被提出作为深部颅内损伤的一种合理解释。事实上，这种奇异解在动态加载条件下的软粘弹性组织中自然出现。为加深对相关力学过程的理解，需要开发专用的计算模型。本研究涉及不可压缩粘弹性固体的三维数值模型，其运动通过激波捕捉有限体积方法进行分析。具体而言，我们聚焦于人工可压缩性方法的应用——该技术已广泛用于计算流体动力学领域。材料行为基于Fung-Simo准线性粘弹性理论（QLV）推导，其中弹性响应为Yeoh类型。我们分析了该方法的精度，并论证了其在软固体非线性波传播研究中的适用性。数值结果涵盖精度测试、激波形成及波衍射现象。