2019/07/15 by Chockalingam Senthilnathan, Tal Cohen, Senthilnathan, Chockalingam +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Medicine · #Automotive and Human Injury Biomechanics #Cellular Mechanics and Interactions #Elasticity and Material Modeling #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.1907.06760
openalex publication_date 2019/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.