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1. Ballistic and Blast-Relevant, High-Rate Material Properties of Physically and Chemically Crosslinked Hydrogels

   https://doi.org/10.1007/s11340-024-01043-3  

   Bremer-Sai, E C ; Yang, J ; McGhee, A ; Franck, C ( April 2024 , Experimental Mechanics)

   Hydrogels are one of the most ubiquitous polymeric materials. Among them gelatin, agarose and polyacrylamide-based formulations have been effectively utilized in a variety of biomedical and defense-related applications including ultrasound-based therapies and soft tissue injury investigations stemming from ballistic and blast exposures. Interestingly, while in most cases accurate prediction of the mechanical response of these surrogate gels requires knowledge of the underlying finite deformation, high-strain rate material properties, it is these properties that have remained scarce in the literature.

   Building on our prior works using Inertial Microcavitation Rheometry (IMR), here we present a comprehensive list of the high-strain rate (> 10$$^3$$${}^3$1/s) mechanical properties of these three popular classes of hydrogel materials characterized via laser-based IMR, further showing that the choice in finite-deformation, rate-dependent constitutive model can be informed directly by the type of crosslinking mechanism and resultant network structure of the hydrogel, thus providing a chemophysical basis of the the choice of phenomenological constitutive model.

   We analyze existing experimental gelatin IMR datasets and compare the results with prior data on polyacrylamide.

   We show that a Neo-Hookean Kelvin-Voigt (NHKV) model can suitably simulate the high-rate material response of dynamic, physically crosslinked hydrogels like gelatin, while the introduction of a strain-stiffening parameter through the use of the quadratic Kelvin-Voigt (qKV) model was necessary to appropriately model chemically crosslinked hydrogels such as polyacrylamide due to the nature of the static,covalent bonds that comprise their structure.

   In this brief we show that knowledge of the type of underlying polymer structure, including its bond mobility, can directly inform the appropriate finite deformation, time-dependent viscoelastic material model for commonly employed tissue surrogate hydrogels undergoing high strain rate loading within the ballistic and blast regimes.

    

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2. Laser cavitation rheology for measurement of elastic moduli and failure strain within hydrogels

   https://doi.org/10.1038/s41598-020-68621-y  

   Luo, Justin_C ; Ching, Herman ; Wilson, Bryce_G ; Mohraz, Ali ; Botvinick, Elliot_L ; Venugopalan, Vasan ( August 2020 , Scientific Reports)

   We introduce laser cavitation rheology (LCR) as a minimally-invasive optical method to characterize mechanical properties within the interior of biological and synthetic aqueous soft materials at high strain-rates. We utilized time-resolved photography to measure cavitation bubble dynamics generated by the delivery of focused 500 ps duration laser radiation at λ = 532 nm within fibrin hydrogels at pulse energies ofE_p = 12, 18 µJ and within polyethylene glycol (600) diacrylate (PEG (600) DA) hydrogels atE_p = 2, 5, 12 µJ. Elastic moduli and failure strains of fibrin and PEG (600) DA hydrogels were calculated from these measurements by determining parameter values which provide the best fit of the measured data to a theoretical model of cavitation bubble dynamics in a Neo-Hookean viscoelastic medium subject to material failure. We demonstrate the use of this method to retrieve the local, interior elastic modulus of these hydrogels and both the radial and circumferential failure strains.

    

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3. Gaussian Process to Identify Hydrogel Constitutive Model

   Wang J., Li T. ( December 2021 , Challenges in Mechanics of Time Dependent Materials, Mechanics of Biological Systems and Materials & Micro-and Nanomechanics, Volume 2.)

   Unlike traditional structural materials, soft solids can often sustain very large deformation before failure, and many exhibit nonlinear viscoelastic behavior. Modeling nonlinear viscoelasticity is a challenging problem for a number of reasons. In particular, a large number of material parameters are needed to capture material response and validation of models can be hindered by limited amounts of experimental data available. We have developed a Gaussian Process (GP) approach to determine the material parameters of a constitutive model describing the mechanical behavior of a soft, viscoelastic PVA hydrogel. A large number of stress histories generated by the constitutive model constitute the training sets. The low-rank representations of stress histories by Singular Value Decomposition (SVD) are taken to be random variables which can be modeled via Gaussian Processes with respect to the material parameters of the constitutive model. We obtain optimal material parameters by minimizing an objective function over the input set. We find that there are many good sets of parameters. Further the process reveals relationships between the model parameters. Results so far show that GP has great potential in fitting constitutive models. 

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4. Investigation of the Primary Mechanisms of Cavitation-Induced Damages

   Zhao, Ben ; Cao, Shunxiang ; Wang, Kevin ; Coutier-Delgosha, Olivier ( July 2018 , Cav2018)

   Erosion of solid surfaces due to cavitation has been studied for decades. However, it has been a long debate that which mechanism, namely shockwaves, microjets towards the surface, or both, during the cavitation bubble collapse is the primary factor responsible for that erosion. In this project we investigate the small-scale mechanisms of material erosion induced by the collapse of a single cavitation bubble close to a wall. More specifically, our experimental setup includes modification of the initial nucleus size, the maximum bubble radius, the stand-off distance to the wall, the material softness, and the initial flow temperature. We record the evolution of the bubble using high speed cameras as well as the local impacts on the materials. With the help of specifically designed cold-wires, we also measure the temperature in the liquid and in the bubble. Two different methods are used to generate the bubble: (i) an acoustic shockwave of variable intensity, (ii) a YAG laser, which may introduce a high temperature at the start. We also combine the two methods in which the laser initially creates a nucleus, then the shockwave triggers the expansion of the bubble. The objectives of the project are included in this paper, while some first results will be presented at the CAV2018 conference. 

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5. Shock-induced bubble collapse near solid materials: effect of acoustic impedance

   https://doi.org/10.1017/jfm.2020.810  

   Cao, S. ; Wang, G. ; Coutier-Delgosha, O. ; Wang, K. ( January 2021 , Journal of Fluid Mechanics)

   null (Ed.)

   The fluid dynamics of a bubble collapsing near an elastic or viscoelastic material is coupled with the mechanical response of the material. We apply a multiphase fluid–solid coupled computational model to simulate the collapse of an air bubble in water induced by an ultrasound shock wave, near different types of materials including metals (e.g. aluminium), polymers (e.g. polyurea), minerals (e.g. gypsum), glass and foams. We characterize the two-way fluid–material interaction by examining the fluid pressure and velocity fields, the time history of bubble shape and volume and the maximum tensile and shear stresses produced in the material. We show that the ratio of the longitudinal acoustic impedance of the material compared to that of the ambient fluid, $Z/Z_0$ , plays a significant role. When $Z/Z_0<1$ , the material reflects the compressive front of the incident shock into a tensile wave. The reflected tensile wave impinges on the bubble and decelerates its collapse. As a result, the collapse produces a liquid jet, but not necessarily a shock wave. When $Z/Z_0>1$ , the reflected wave is compressive and accelerates the bubble's collapse, leading to the emission of a shock wave whose amplitude increases linearly with $\log (Z/Z_0)$ , and can be much higher than the amplitude of the incident shock. The reflection of this emitted shock wave impinges on the bubble during its rebound. It reduces the speed of the bubble's rebound and the velocity of the liquid jet. Furthermore, we show that, for a set of materials with $Z/Z_0\in [0.04, 10.8]$ , the effect of acoustic impedance on the bubble's collapse time and minimum volume can be captured using phenomenological models constructed based on the solution of Rayleigh–Plesset equation. 

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