Extracting non-linear viscoelastic material properties from violently-collapsing cavitation bubbles

Abstract

Determination of high strain-rate constitutive material parameters from highly compliant, non-linear materials including hydrogels and soft tissues remains a significant challenge. To address this challenge we recently developed a laser-based Inertial Microcavitation Rheometry (IMR) technique, capable of constitutively characterizing soft materials at ultra-high strain-rates (O(103)∼O(108)s−1). This technique utilizes spatially-focused, and temporally-resolved, single cavitation bubbles in conjunction with a theoretical framework for determining the non-linear viscoelastic material properties of the surrounding soft material.Here, by advancing our spatiotemporal imaging capability and tracking the motion of native material features close to the inertially cavitating bubble, we find significant deviation from the IMR predicted material displacements at a critical material Mach number of 0.08, marking the transition to violent collapse. Interestingly, this critical Mach number appears to be almost independent of the material properties of the surrounding hydrogel. We show that through proper temporal resolution of the cavitation dynamics, all of the highly nonlinear viscoelastic properties of the surrounding material can still be uniquely determined from just the first expansion and collapse cycle alone, as long as the local Mach number is below the critical threshold. Furthermore, we show that the inclusion of a higher order strain stiffening term on the rate-dependent non-linear spring can lead to better estimation of the material properties and full recovery of the equilibrium shear modulus, which was not possible with previous nonlinear neo-Hookean Kelvin–Voigt model formulations. Thus, the developments presented here significantly expand the applicability and robustness of IMR for accurately determining the rate-dependent, finite deformation constitutive behavior of soft materials.