arXiv subjects

Bachir A. Abeid

Publications and source records attributed to Bachir A. Abeid.

4 recordsLinked to original sources

arXiv2026

Microbubble surface instabilities in a strain stiffening viscoelastic material

Understanding the dynamics of instabilities along fluid-solid interfaces is critical for the efficacy of focused ultrasound therapy tools (e.g., histotripsy) and microcavitation rheometry techniques. Non-uniform pressure fields generated by either ultrasound or a focused laser can cause non-spherical microcavitation bubbles. Previous perturbation amplitude evolution models in viscoelastic materials either assume pure radial deformation or have inconsistent kinematic fields between the fluid and solid contributions. We derive a kinematically-consistent theoretical model for the evolution of surface perturbations. The model captures the non-linear kinematics of a strain-stiffening viscoelastic material surrounding a non-spherical bubble. The model is validated for (i) small, approximately linear radial oscillations and (ii) large inertial oscillations using laser-induced microcavitation experiments in a soft hydrogel. For the former, the bubble is allowed to reach mechanical equilibrium, and then surface perturbations are excited using ultrasound forcing. For the latter, the microbubble forms small bubble surface perturbations at its maximum radius that grow during collapse. The model's dominant surface perturbation mode scales linearly with equilibrium radius and matches experiments. Similarly, the model's perturbation amplitude evolution sufficiently constrains the rheometry problem and is experimentally validated.

physics.flu-dyn↗

arXiv2025

Hierarchical Bayesian constitutive model selection for high-strain-rate soft material characterization

The high-fidelity characterization of soft, tissue-like materials under ultra-high-strain-rate conditions is critical in engineering and medicine. Still, it remains challenging due to limited optical access, sensitivity to initial conditions, and experimental variability. Microcavitation techniques (e.g., laser-induced microcavitation) have emerged as a viable method for determining the mechanical properties of soft materials in the ultra-high-strain-rate regime (higher than 10^3 s^{-1}); however, they are limited by measurement noise and uncertainty in parameter estimation. A hierarchical Bayesian model selection method is employed using the Inertial Microcavitation Rheometry (IMR) technique to address these limitations. With this method, the parameter space of different constitutive models is explored to determine the most credible constitutive model that describes laser-induced microcavitation bubble oscillations in soft, viscoelastic, transparent hydrogels. The target data/evidence is computed using a weighted Gaussian likelihood with a hierarchical noise scale, which enables the quantification of uncertainty in model plausibility. Physically informed priors, including range-invariant, stress-based parameter priors, a model-redundancy prior, and a Bayesian Information Criterion motivated model prior, penalize complex models to enforce Occam's razor. Using a precomputed grid of simulations, the probabilistic model selection process enables an initial guess for the Maximum A Posteriori (MAP) material parameter values. Synthetic tests recover the ground-truth models and expected parameters. Using experimental data for gelatin, fibrin, polyacrylamide, and agarose, MAP simulations of credible models reproduce the data. Moreover, a cross-institutional comparison of 10% gelatin indicates consistent constitutive model selection.

physics.flu-dyn↗

arXiv2025

Parsimonious inertial cavitation rheometry via bubble collapse time

The rapid and accurate characterization of soft, viscoelastic materials at high strain rates is of interest in biological and engineering applications. Examples include assessing the extent of tissue ablation during histotripsy procedures and developing injury criteria for the mitigation of blast injuries. The inertial microcavitation rheometry technique (IMR, Estrada et al., 2018) allows for the characterization of local viscoelastic properties at strain rates up to 1E8 per second. However, IMR now typically relies on bright-field videography of a sufficiently translucent sample at >1 million frames per second and a simulation-dependent fit optimization process that can require hours of post-processing. Here, we present an improved IMR-style technique, called parsimonious inertial microcavitation rheometry (pIMR), that parsimoniously characterizes surrounding viscoelastic materials. The pIMR approach uses experimental advancements to estimate the time to first collapse of the laser-induced cavity within approximately 20 ns and a theoretical energy balance analysis that yields an approximate collapse time based on the material viscoelasticity parameters. The pIMR method closely matches the accuracy of the original IMR procedure while decreasing the computational cost from hours to seconds while potentially reducing reliance on ultra-high-speed videography. This technique can enable nearly real-time characterization of soft, viscoelastic hydrogels and biological materials with a numerical criterion assessing the correct choice of model. We illustrate the efficacy of the technique on batches of tens of experiments for both soft hydrogels and fluids.

cond-mat.soft↗

arXiv2022

Ogden Material Calibration via Magnetic Resonance Cartography, Parameter Sensitivity, and Variational System Identification

Contemporary material characterisation techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterisation problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely-used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability, and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully 3D displacement fields acquired in silicone elastomers with our recently-developed magnetic resonance cartography (MR-u) technique on the order of $>20,000$ points per sample, we leverage PDE-constrained optimisation as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric, and discuss the implications for experimental design.

cond-mat.soft↗