arXiv subjects

Jonathan B. Estrada

Publications and source records attributed to Jonathan B. Estrada.

9 recordsLinked to original sources

arXiv2026

Migration of inflated cavities in graded hyperelastic solids

The inflation of a pre-existing, fluid-filled cavity is a timeless topic in the finite-deformation analysis of soft materials. However, classical solutions for cavity inflation rely on radially symmetric material properties, leaving unresolved the effects of non-radial stiffness heterogeneity that are commonly present in biological tissues and engineered soft materials. In this work, we investigate the quasi-static inflation of a pressurized cavity in a hyperelastic solid with shear modulus varying monotonically along a reference Cartesian direction. Finite-element simulations reveal that, beyond an initial small-inflation regime, the most pronounced symmetry-breaking response is the migration of the cavity toward the more compliant end of the material, while nonspherical distortion remains comparatively weak. To analytically quantify this migration-dominated response, we develop a Rayleigh--Ritz reduced-order framework to determine the strain-energy-minimizing migration amplitude for prescribed gradation parameters and inflation level. Without using fitted parameters, the Rayleigh--Ritz framework recovers key features of the cavity migration that are intimately linked to the mechanical gradation parameters. The identification of centroid migration as a salient geometric signal, together with the reduced-order prediction of its evolution, suggests a roadmap for inverse characterization of graded materials through cavity-inflation experiments.

cond-mat.soft↗

arXiv2026

Limits of constant-parameter constitutive models for hydrogels under inertial cavitation

Mechanical characterization of soft materials at high strain rates is challenging due to their high compliance, nonlinear viscoelastic behavior, and potentially history-dependent responses. Inertial microcavitation rheometry (IMR) addresses this challenge by coupling laser-induced cavitation (LIC) experiments with numerical simulations of bubble dynamics models to infer constitutive models and material parameters. Both IMR and its variants infer parameters that depend on the chosen fitting window, which suggests that a constant-parameter constitutive model is insufficient to describe the full cavitation event. We use this window dependence to identify when the constant-parameter assumption fails, rather than to report a single effective parameter set. The constitutive parameters are estimated over moving, overlapping windows using a modified iterative ensemble Kalman smoother with multiple data assimilation (MIEnKS-MDA). Within the neo-Hookean Kelvin--Voigt (NHKV) constitutive model, we obtain time-resolved estimates of the constitutive response in polyacrylamide (PAAm) hydrogels with different crosslinker concentrations. The inferred shear modulus and viscosity generally decrease and then plateau during cavitation, while exhibiting relatively weak temperature sensitivity. For gelatin gels, by contrast, the inferred property evolution shows a pronounced temperature dependence, with distinct trends at low and high temperatures. Moreover, both the apparent shear modulus and viscosity exhibit significant variations during the first two bubble collapses. These results show that time-resolved parameter estimation within the prescribed NHKV constitutive structure can diagnose where the constant-parameter model assumption falls short during cavitation, thereby guiding the development of improved physics-based models of complex bubble--material interactions.

cond-mat.soft↗

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

Variation-matching sensitivity-based virtual fields for hyperelastic material model calibration

Accurate identification of nonlinear material parameters from three-dimensional full-field deformation data remains a challenge in experimental mechanics. The virtual fields method (VFM) provides a powerful, computationally efficient approach for material model calibration, however, its success depends critically on the choice of virtual fields and the informativeness of available kinematic data. In this work, we advance the state-of-the-art discrete formulation of the sensitivity-based virtual fields (SBVF) method by systematically developing and comparing alternative variational and analytical SBVFs within a strain-invariant-based modeling framework. A central contribution of this work is the implementation and assessment of variation-based SBVFs (vSBVFs), formulated using directional G\^ateaux derivatives, as well as virtual fields derived from analytical differentiation (aSBVFs) which provide explicit, model-tailored virtual displacement fields for parameter identification. Using simulated noisy volumetric datasets, we demonstrate that vSBVFs and aSBVFs enable procedural, automated construction of optimal virtual fields for each material parameter, substantially enhancing the robustness and efficiency of calibration without the need for manual field selection or high temporal resolution in the data acquisition. We quantify data richness -- the effective diversity of sampled kinematic states -- showing that increased data richness via sample geometry and loading protocols leads to improved parameter identifiability. These findings establish a pathway for automated, noise-robust material model calibration suitable for future deployment with experimental full-field imaging of soft, complex materials, and provide a foundation for optimizing shape topology and extending to viscoelastic and anisotropic behaviors.

cond-mat.soft↗

arXiv2025

Accelerating Bayesian Optimal Experimental Design via Local Radial Basis Functions: Application to Soft Material Characterization

We develop a computational approach that significantly improves the efficiency of Bayesian optimal experimental design (BOED) using local radial basis functions (RBFs). The presented RBF--BOED method uses the intrinsic ability of RBFs to handle scattered parameter points, a property that aligns naturally with the probabilistic sampling inherent in Bayesian methods. By constructing accurate deterministic surrogates from local neighborhood information, the method enables high-order approximations with reduced computational overhead. As a result, computing the expected information gain (EIG) requires evaluating only a small uniformly sampled subset of prior parameter values, greatly reducing the number of expensive forward-model simulations needed. For demonstration, we apply RBF--BOED to optimize a laser-induced cavitation (LIC) experimental setup, where forward simulations follow from inertial microcavitation rheometry (IMR) and characterize the viscoelastic properties of hydrogels. Two experimental design scenarios, single- and multi-constitutive-model problems, are explored. Results show that EIG estimates can be obtained at just 8% of the full computational cost in a five-model problem within a two-dimensional design space. This advance offers a scalable path toward optimal experimental design in soft and biological materials.

physics.comp-ph↗

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↗

arXiv2024

Bayesian optimal design accelerates discovery of material properties from bubble dynamics

An optimal sequential experimental design approach is developed to computationally characterize soft material properties at the high strain rates associated with bubble cavitation. The approach involves optimal design and model inference. The optimal design strategy maximizes the expected information gain in a Bayesian statistical setting to design experiments that provide the most informative cavitation data about unknown soft material properties. We infer constitutive models by characterizing the associated viscoelastic properties from measurements via a hybrid ensemble-based 4D-Var method (En4D-Var). The inertial microcavitation-based high strain-rate rheometry (IMR) method ([1]) simulates the bubble dynamics under laser-induced cavitation. We use experimental measurements to create synthetic data representing the viscoelastic behavior of stiff and soft polyacrylamide hydrogels under realistic uncertainties. The synthetic data are seeded with larger errors than state-of-the-art measurements yet match known material properties, reaching 1% relative error within 10 sequential designs (experiments). We discern between two seemingly equally plausible constitutive models, Neo-Hookean Kelvin--Voigt and quadratic Kelvin--Voigt, with a probability of correctness larger than 99% in the same number of experiments. This strategy discovers soft material properties, including discriminating between constitutive models and discerning their parameters, using only a few experiments.

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↗