The laser-induced cavitation (LIC) data presented in Figs.
1 and
2, and Table
1 for both soft and stiff polyacrylamide gels was adapted from Yang et al. [
14]. The raw bubble LIC data, i.e., bubble radius vs. time traces, for gelatin gels were obtained from McGhee et al. [
15] and analyzed in this brief via Eqs. (
1)-(
3) to determine the best constitutive material model and best-fit viscoelastic material properties (reported in Table
1). Finally, all LIC data on agarose gels reported in Table
1 was extracted from Yang et al. [
16].
The theoretical framework of IMR has been detailed in our prior work [
13‐
17], and is followed closely in this study to determine the viscoelastic material properties of gelatin gels. Briefly, within the IMR analysis framework, the cavitation bubble is modeled from its maximum radius to first collapse, where thermodynamic equilibrium is assumed and the 1D Keller-Miksis equation is used to describe the spherically symmetric motion of the bubble, which is provided in Eq. (
1) [
14,
16,
18,
19].
$$\begin{aligned} \begin{aligned} \left( 1-\frac{\dot{R}}{c}\right) R \ddot{R} + \frac{3}{2}\left( 1-\frac{\dot{R}}{3c}\right) \dot{R}^2&= \frac{1}{\rho } \left( 1+\frac{\dot{R}}{c}+\frac{R}{c} \frac{d}{dt}\right) \\ {}&\times \left( p_b - \frac{2 \gamma }{R} + S - p_{\infty }\right) \end{aligned} \end{aligned}$$
(1)
R,
\(\dot{R}\), and
\(\ddot{R}\) are the bubble radius and its first and second time derivatives respectively.
c is the longitudinal wave speed,
\(\rho\) is the mass density of the surrounding material,
\(p_b\) is the internal bubble pressure,
\(\gamma\) is the surface tension,
S is the stress integral for the chosen material model, and
\(p_{\infty }\) is the ambient pressure. For brevity, detailed descriptions of the composition of the internal bubble pressure,
\(p_b\), and its equation of state can be found elsewhere [
13‐
17]. From our prior literature two particular constitutive formulations within the Kelvin-Voigt arrangement accurately represent the material stress integral term. The first, highlighted by Eq. (
2), is the Neo-Hookean Kelvin-Voigt model (NHKV) featuring a hyperelastic, Neo-Hookean spring in parallel with a constant viscosity dashpot. The second is a simplification of the generalized Fung model, called the quadratic Kelvin-Voigt (qKV) model, which incorporates strain-stiffening, characterized by the parameter
\(\alpha\) into the hyperelastic spring (Eq. (
3)) [
14].
$$\begin{aligned} \begin{aligned} S_{NHKV}&= 2 \int _R^{\infty } \frac{\sigma _{rr} - \sigma _{\theta \theta }}{r} dr\\ {}&= -\frac{G}{2} \left[ 5 - \left( \frac{R_0}{R}\right) ^4 - 4\left( \frac{R_0}{R}\right) \right] - \frac{4\mu \dot{R}}{R} \end{aligned} \end{aligned}$$
(2)
$$\begin{aligned} \begin{aligned} S_{qKV}&= \frac{(3\alpha -1)G}{2} \left[ 5-\left( \frac{R_0}{R} \right) ^4 - 4\left( \frac{R_0}{R}\right) \right] - \frac{4\mu \dot{R}}{R} \\&+ 2 \alpha G \left[ \frac{27}{40}+\frac{1}{8}\left( \frac{R_0}{R} \right) ^8 + \frac{1}{5} \left( \frac{R_0}{R}\right) ^5 \right. \\&\left. +\left( \frac{R_0}{R}\right) ^2-\frac{2R}{R_0}\right] \end{aligned} \end{aligned}$$
(3)
G is the rate dependent shear modulus (for NHKV),
\(\mu\) is the viscosity,
R is the bubble radius, and
\(R_0\) is the equilibrium bubble radius. The same follows for qKV with a modification that
G is now the rate independent ground state shear modulus, and
\(\alpha\) is a non-dimensional parameter governing the material’s strain-stiffening.