  Characterization of soft materials is challenging due to their high
compliance and the strain-rate dependence of their mechanical properties. The
inertial microcavitation-based high strain-rate rheometry (IMR) method [Estrada
et al., J. Mech. Phys. Solids, 2018, 112, 291-317] combines laser-induced
cavitation measurements with a model for the bubble dynamics to measure local
properties of polyacrylamide hydrogel under high strain-rates from $10^3$ to
$10^8$ s$^{-1}$. While promising, laser-induced cavitation involves plasma
formation and optical breakdown during nucleation, a process that could alter
local material properties before measurements are obtained. In the present
study, we extend the IMR method to another means to generate cavitation, namely
high-amplitude focused ultrasound, and apply the resulting
acoustic-cavitation-based IMR to characterize the mechanical properties of
agarose hydrogels. Material properties including viscosity, elastic constants,
and a stress-free bubble radius are inferred from bubble radius histories in
$0.3\%$ and $1\%$ agarose gels. An ensemble-based data assimilation is used to
further help interpret the obtained estimates. The resulting parameter
distributions are consistent with available measurements of agarose gel
properties and with expected trends related to gel concentration and high
strain-rate loading. Our findings demonstrate the utility of applying IMR and
data assimilation methods with single-bubble acoustic cavitation data for
measurement of viscoelastic properties.
