Numerical investigations on the deformation styles and stress distributions of hyperelastic/viscoelastic spheres during water entry

Abstract

This paper investigates the water entry physics of hyperelastic/viscoelastic spheres, including their deformation styles and stress distributions. For this purpose, elastic spheres entering water are modeled by combining neo-Hookean hyperelasticity and Prony series viscoelasticity models in a structured framework, and the fluid flow is determined by numerically solving the Navier–Stokes equations. Based on the experimental results, the numerical method of the fluid–structure interaction problem is validated. The results show that after water entry, the elastic spheres present five typical deformation styles in a single sphere deformation period, resulting in a nested cavity. In addition, the stress distributions of the elastic sphere surface mainly experience four typical stages in a single deformation period. A quantitative analysis of the stress is performed to describe the variation in the stress with the dimensionless displacement of a curved path at every stage. Moreover, the stress peak of the elastic sphere surface migrates from the bottom to the top of the sphere during a single deformation period and increases with the increases in the material shear modulus and impact velocity.