Particle-Assisted Laser-Induced Inertial Cavitation for High Strain-Rate Soft Material Characterization

Abstract

Background

While there are few reliable techniques for characterizing highly compliant and viscoelastic materials under large deformations, laser-induced Inertial Microcavitaton Rheometry (IMR) was recently developed to fill this void and to characterize soft materials at high to ultra-high strain rates ($O(10^{3}) \sim O(10^{8})$ s$^{-1}$). Yet, one of the current limitations in IMR has been the dependence of the cavitation nucleation physics on the intrinsic material properties often generating extreme deformation levels and thus complicating material characterization procedures.

Objective

The objective of this study was to develop an experimental approach for modulating laser-induced cavitation (LIC) bubble amplitudes and their resulting maximum material deformations. Lowering the material stretch ratios during inertial cavitation will provide an experimental platform of broad applicability to a large class of polymeric materials and environmental conditions.

Methods

Experimental methods include using three types of micron-sized nucleation seed particles and varying laser energies in polyacrylamide hydrogels of known concentration. Using a Quadratic law Kelvin-Voigt material model, we implemented ensemble-based data assimilation (DA) techniques to robustly quantify the nonlinear constitutive material parameters, up through the first, second, and third bubble collapse cycles. Fitted values were then used to simulate bubble dynamics to compute critical bubble collapse Mach numbers, and to assess time-varying uncertainties of the full cavitation dynamics with respect to the current state-of-the art theoretical model featured in the IMR model.

Results

While varying laser energy modulated bubble amplitude, seed particles successfully expanded (more than doubled) the finite deformation regime (i.e., maximum material stretch, $\lambda _{max} \approx$ 4 - 9). Comparing experimental data to IMR simulations, we found that fitting beyond the first bubble collapse, as well as increasing laser energy, increased the bubble radius fit error, and larger $\lambda _{max}$ values exhibited increasingly violent bubble behavior (marked by increasing collapse Mach numbers greater than 0.08). Additionally, time-varying analysis showed the greatest model uncertainty during initial bubble collapse, where bubbles nucleated at lower laser energies and resulting $\lambda _{max}$ had less uncertainty at collapse compared to higher laser energy and $\lambda _{max}$ cases.

Conclusions

This study indicates IMR’s current theoretical framework might be lacking important additional cavitation and/or material physics. However, expanding the finite deformation regime of soft materials to attain lower stretch regimes enables broader applicability to a larger class of soft polymeric materials and will enable future, systematic development and incorporation of more complex physics and constitutive models including damage and failure mechanisms into the theoretical framework of IMR.