arXiv subjects

Zhiren Zhu

Publications and source records attributed to Zhiren Zhu.

5 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↗

arXiv2025

Field evaluation of a wearable instrumented headband designed for measuring head kinematics

Purpose: To study the relationship between soccer heading and the risk of mild traumatic brain injury (mTBI), we previously developed an instrumented headband and data processing scheme to measure the angular head kinematics of soccer headers. Laboratory evaluation of the headband on an anthropomorphic test device showed good agreement with a reference sensor for soccer ball impacts to the front of the head. In this study, we evaluate the headband in measuring the full head kinematics of soccer headers in the field. Methods: The headband was evaluated under typical soccer heading scenarios (throw-ins, goal-kicks, and corner-kicks) on a human subject. The measured time history and peak kinematics from the headband were compared with those from an instrumented mouthpiece, which is a widely accepted method for measuring head kinematics in the field. Results: The time history agreement (CORA scores) between the headband and the mouthpiece ranged from 'fair' to 'excellent', with the highest agreement for angular velocities (0.79 \pm 0.08) and translational accelerations (0.73 \pm 0.05) and lowest for angular accelerations (0.67 \pm 0.06). A Bland-Altman analysis of the peak kinematics from the headband and mouthpiece found the mean bias to be 40.9% (of the maximum mouthpiece reading) for the angular velocity, 16.6% for the translational acceleration, and-14.1% for the angular acceleration. Conclusion: The field evaluation of the instrumented headband showed reasonable agreement with the mouthpiece for some kinematic measures and impact conditions. Future work should focus on improving the headband performance across all kinematic measures.

eess.SP↗

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 Gâteaux 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

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↗