Strain Stiffening Effects of Soft Viscoelastic Materials in Inertial Microcavitation

Abstract

Mechanical characterization of soft materials, e.g. hydrogels, tissues, and various polymeric specimens, at high strain-rates (10³ s⁻¹–10⁶ s⁻¹) is challenging due to their compliance, slow wave speeds, and non-linear viscoelasticity. However, knowledge of their material is important in many biological and engineering applications from minimizing tissue damage in ultrasound and laser surgeries to diagnosing and mitigating impact injuries. Recently, a minimally invasive, local 3D micro-rheology technique based on inertial microcavitation rheometry (IMR) has been developed to determine the general viscoelastic material properties of soft matter as compliant as a few kilopascals. For example, material behavior of polyacrylamide undergoing large, finite deformations (|E _rr| > 0.05) at strain-rates of up to 10⁶ s⁻¹ has been measured and fitted using nonlinear Kelvin-Voigt model, which extends the traditional quasi-static neo-Hookean description of polyacrylamide to include a dynamic material viscosity in the order of 10⁻¹ Pa·s.

In the classical case study of polyacrylamide, the nonlinear neo-Hookean Kelvin-Voigt model fitting results shows that the shear moduli obtained during cavitation are stiffer than their quasi-static counterparts. This strain stiffening effects needs additional consideration and treatment. Here we address the issue of strain stiffening by replacing the traditional neo-Hookean spring in the nonlinear Kelvin-Voigt model with a higher order constitutive relation inspired by the Fung model.