Cavity expansion in nonlinear viscoelastic solids: A nonlinear dynamic study

Abstract

Dynamic cavity expansion has been studied for hyperelastic materials since the work of Knowles and Jakub in 1965. It has recently drawn new attention for potential applications in measuring the mechanical properties of soft polymer or biological tissues. These soft materials, however, are intrinsically rate-dependent, and the study of dynamic cavitation in nonlinear viscoelastic solid is relatively scarce. In this article, we utilize the established two-potential nonlinear viscoelastic framework to study the cavity behavior in infinite solid. Differently, we further introduced the surface energy into account and pay extra attention to the oscillation of the cavity surface based on nonlinear dynamics. The cavity behavior and stress change under a monotonically increasing pressure, creep experiment, and relaxation experiment are investigated. Considering surface effects, we notice the cavity surface has an oscillation process of expansion and shrink before infinitely large expansion before rupture. The oscillation amplitude gradually diminishes with time due to the energy consumption of viscosity. Regarding the viscoelastic material as a system with diminishing shear modulus, we analyze the stability of the cavity surface and find it can be either a stable center point or an unstable saddle point. The results of this study are helpful for understanding the cavitation phenomenon in viscoelastic solids caused by dynamic loading.