Alexander McGhee

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• Bremer-Sai, E., Yang, J., McGhee, A., & Franck, C. (2024). Ballistic and Blast-Relevant, High-Rate Material Properties of Physically and Chemically Crosslinked Hydrogels. Experimental Mechanics, 64(4). doi:10.1007/s11340-024-01043-3
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  Background: 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. Objective: Building on our prior works using Inertial Microcavitation Rheometry (IMR), here we present a comprehensive list of the high-strain rate (> 103 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. Methods: We analyze existing experimental gelatin IMR datasets and compare the results with prior data on polyacrylamide. Results: 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. Conclusions: 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.
• Yang, J., McGhee, A., Radtke, G., Rodriguez, M., & Franck, C. (2024). Estimating viscoelastic, soft material properties using a modified Rayleigh cavitation bubble collapse time. Physics of Fluids, 36(1). doi:10.1063/5.0179368
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  Accurate determination of high strain rate (>103 1/s) constitutive properties of soft materials remains a formidable challenge. Albeit recent advancements among experimental techniques, in particular inertial microcavitation rheometry (IMR), the intrinsic requirement to visualize the bubble cavitation dynamics has limited its application to nominally transparent materials. Here, in an effort to address this challenge and to expand the experimental capability of IMR to optically opaque materials, we investigated whether one could use the acoustic signature of the time interval between the bubble's maximum radius and first collapse time point, characterized as the bubble collapse time, to infer the viscoelastic material properties without being able to image the bubble directly in the tissue. By introducing a modified Rayleigh collapse time for soft materials, which is strongly dependent on the stiffness of the material at hand, we show that, in principle, one can obtain an order of magnitude or better estimate of the viscoelastic material properties of the soft material under investigation. Using a newly developed energy-based theoretical framework, we show that for materials stiffer than 10 kPa the bubble collapse time during a single bubble cavitation event can provide quantitative and meaningful information about the constitutive properties of the material at hand. For very soft materials (i.e., shear modulus less than 10 kPa), our theory shows that unless the collapse time measurement has very high precision and low uncertainties, the material property estimates based on the bubble collapse time only will not be accurate and require visual resolution of the full cavitation kinematics.
• McGhee, A., Yang, J., Bremer, E., Xu, Z., Cramer, H., Estrada, J., Henann, D., & Franck, C. (2023). High-Speed, Full-Field Deformation Measurements Near Inertial Microcavitation Bubbles Inside Viscoelastic Hydrogels. Experimental Mechanics, 63(1). doi:10.1007/s11340-022-00893-z
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  Background: Inertial microcavitation is a well-known phenomenon that generates large stresses and deformations at extremely high loading rates in various soft materials, ranging from commercial polymer coatings to biological tissues. Recent advances in soft material characterization have taken advantage of inertial cavitation as a means towards a high-rate, minimally invasive soft material rheology approach. Yet, most of these studies rely on idealizations to infer the full deformation fields around the bubble based only on the experimentally measured temporal evolution of the bubble radius (akin to relying on crosshead strain data in a traditional materials test). Objective: Here, we develop an experimental method to quantitatively measure full-field deformation and associated strains due to laser-induced inertial cavitation (LIC) in gelatin hydrogels, where the surrounding material is subjected to ultra-high strain rates (10 3∼ 10 6 s- 1). Methods: Our method combines two broad experimental techniques: the embedded speckle plane patterning (ESP) method and spatiotemporally adaptive quadtree mesh digital image correlation (STAQ-DIC). Results: We illustrate the powerful capability of our approach by testing three concentrations of gelatin hydrogels 6%, 10%, and 14% as benchmark cases and quantitatively capture their kinematics during LIC. Conclusions: These full-field, quantitative investigations are of significant interest in many cavitation-related applications including high strain-rate material characterization, guided advanced laser & ultrasound therapies, tissue engineering, and advanced manufacturing.
• Summey, L., Zhang, J., Landauer, A., Sergay, J., Yang, J., Daul, A., Tao, J., Park, J., McGhee, A., & Franck, C. (2023). Open Source, In-Situ, Intermediate Strain-Rate Tensile Impact Device for Soft Materials and Cell Culture Systems. Experimental Mechanics, 63(9). doi:10.1007/s11340-023-00999-y
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  Background: Intermediate-strain-rate mechanical testing of soft and biological materials is important when designing, measuring, predicting, or manipulating an object or system’s response to common impact scenarios. Open source micro-mechanical test instruments that provide high spatial and temporal resolution volumetric strain field measurements, non-destructive testing and gripping of soft materials with low elastic moduli, programmable strain rates spanning from 10 - 6 s - 1 to 10 2 s - 1 , and biocompatibility for living cell cultures and tissues in one instrument are lacking in the current literature. Methods: We introduce a micro-tensile testing device developed to meet all these criteria while being straightforwardly accessible to the end user. This device sits atop an inverted microscope stage, granting the researcher access to 3D spatial resolutions as low as 100 nm and frame rates only limited by the camera speed and availability of recordable photons. The micro-tensile specimen is attached to the test device by a specially designed fixture. This enables a material to be cast into the mold assembly and tested without being manually manipulated before or after testing. The tensile deformation is controlled by two voice-coil linear actuators synchronized to pull a specimen in opposing directions. A field of view focused centrally on the specimen experiences a highly-controllable uniform tensile strain with minimal rigid body motion. Results: We validate the resulting in-plane strain fields on a 2D poly-dimethylsiloxane (PDMS) substrate and a heterogeneous polyurethane foam using Digital Image Correlation (DIC) and volumetrically on 3D polyacrylamide (PA) hydrogels using Digital Volume Correlation (DVC). High-Rate Volumetric Particle Tracking Microscopy (HR-VPTM) is used to quantify and validate the 3D volumetric strain fields at impact-relevant rates. The device can apply up to 200% engineering strain with peak strain rate up to approximately 240 s - 1 to a 7 mm long dogbone specimen. Proof-of-concept biocompatibility was tested on 2D and 3D in vitro neural cell cultures, demonstrating the versatility and applicability for both soft materials and living biomaterials. Conclusion: We demonstrate and validate a versatile micro-tensile impact device for soft materials and in vitro cellular biomechanics investigations. The achievable strain rates for such a design are some of the highest we have found reported to date and enable experiments that replicate the full range of observable large material deformations seen during real-world blunt impacts.
• Yang, J., Rubino, V., Ma, Z., Tao, J., Yin, Y., McGhee, A., Pan, W., & Franck, C. (2022). SpatioTemporally Adaptive Quadtree Mesh (STAQ) Digital Image Correlation for Resolving Large Deformations Around Complex Geometries and Discontinuities. Experimental Mechanics, 62(7). doi:10.1007/s11340-022-00872-4
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  Background: Digital image correlation (DIC) is a powerful experimental tool for measuring full-field material deformations. Inherent limitations of typical DIC algorithms can cause a multitude of errors when analyzing the displacement field of samples containing complex geometries or discontinuities. Most adaptations rely on either splitting or augmenting the local DIC subsets that pass through the discontinuity path. However, these methods are challenging to generalize and automate, often requiring significant user intervention. Objective: To address these shortcomings, we present a new, user-friendly automatic experimental approach for resolving the deformation fields around complex geometries and displacement discontinuities, which we call the spatiotemporally adaptive quadtree mesh (STAQ) DIC method. Methods: In this method, the adaptive quadtree mesh is automatically generated from a mask file of the DIC image itself to handle the inherent complex geometry. Subsets that span either geometric or displacement discontinuities are automatically split to improve their DIC accuracy. A binary image mask is also used to inform an interpolation scheme for displacement and strain calculations. Furthermore, we also propose a data-driven reduced order modeling (ROM) approach to further reduce the computational costs by skipping unnecessary image frames thus achieving temporal adaptability for efficiently processing large image sequences. Results: We demonstrate that our STAQ method has high accuracy in solving complex geometric and discontinuous deformation fields in an automated fashion. We find that the proposed data-driven ROM method can provide up to 60% in computational cost savings while maintaining the same level of accuracy compared to a fully processed image set. Conclusions: STAQ DIC is a computationally efficient method for accurately solving geometrically complex and discontinuous deformation fields. Using the data-driven ROM method as part of STAQ can further reduce computational costs for processing large image sequences. An open-source Matlab implementation is freely available.
• Yang, J., Yin, Y., Landauer, A., Buyukozturk, S., Zhang, J., Summey, L., McGhee, A., Fu, M., Dabiri, J., & Franck, C. (2022). SerialTrack: ScalE and rotation invariant augmented Lagrangian particle tracking. SoftwareX, 19. doi:10.1016/j.softx.2022.101204
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  We present a new particle tracking algorithm for accurately resolving large deformation and rotational motion fields, which takes advantage of both local and global particle tracking algorithms. We call this method ScalE and Rotation Invariant Augmented Lagrangian Particle Tracking (SerialTrack). This method builds an iterative scale and rotation invariant topology-based feature vector for each particle within a multi-scale tracking algorithm. The global kinematic compatibility condition is applied as a global augmented Lagrangian constraint to enhance tracking accuracy. An open source software package implementing this numerical approach to track both 2D and 3D, incremental and cumulative deformation fields is provided.
• McGhee, A., McGhee, E., Famiglietti, J., & Schulze, K. (2021). Dynamic Subsurface Deformation and Strain of Soft Hydrogel Interfaces Using an Embedded Speckle Pattern With 2D Digital Image Correlation. Experimental Mechanics, 61(6). doi:10.1007/s11340-021-00713-w
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  Background: Subsurface mechanisms can greatly affect the mechanical behavior of biological materials, but observation of these mechanisms has remained elusive primarily due to unfavorable optical characteristics. Researchers attempt to overcome these limitations by performing experiments in biological mimics like hydrogels, but measurements are generally restricted due to the spatio-temporal limitations of current methods. Objective: Utilization of contemporary 3D printing techniques into soft, transparent, aqueous yield-stress materials have opened new avenues of approach to overcoming these roadblocks. By incorporating digital image correlation with such 3D printing techniques, a method is shown here that can acquire full-field deformation of a hydrogel subsurface in real-time. Methods: Briefly, the method replaces the solvent of a transparent and low polymer concentration yield-stress material with an aqueous hydrogel precursor solution, then a DIC speckle plane is 3D printed into it. This complex is then polymerized using photoinitiation thereby locking the speckle plane in place. Results: Full-field deformation measurements are made in real-time as the embedded speckle plane (ESP) responds with the bulk to the applied load. Example results of deformation and strain fields associated with indentation, relaxation, and sliding contact experiments are shown. Conclusions: This method has successfully observed the subsurface mechanical response in the bulk of a hydrogel and has the potential to answer fundamental questions regarding biological material mechanical behaviors.
• DeVries, M., Subhash, G., Mcghee, A., Ifju, P., Jones, T., Zheng, J., & Halls, V. (2018). Quasi-static and dynamic response of 3D-printed alumina. Journal of the European Ceramic Society, 38(9). doi:10.1016/j.jeurceramsoc.2018.03.006
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  Mechanical properties and microstructure of 3D-printed alumina processed using pressurized spray deposition have been compared to a commercial sintered alumina. The 3D-printed alumina microstructure was found to be bimodal in nature, with alumina particles agglomerated into large spheres, which resulted in 6.1% porosity. Compared to the sintered alumina, the 3D-printed material exhibited lower quasi-static and dynamic compressive strength, negligible differences in quasi-static and dynamic Vickers hardness, and negligible differences in quasi-static and dynamic fracture toughness. However, while the dynamic fracture surfaces of 3D-printed alumina were smooth and planar, large undulations were observed under quasi-static loading. It is concluded that the pressurized spray deposition 3D-printing technique is a promising method for processing alumina with properties comparable to that produced by traditional techniques, and further improvements may be gained by eliminating porosity.
• McGhee, A., Bennett, A., Ifju, P., Sawyer, G., & Angelini, T. (2018). Full-Field Deformation Measurements in Liquid-like-Solid Granular Microgel Using Digital Image Correlation. Experimental Mechanics, 58(1). doi:10.1007/s11340-017-0337-4
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  This paper presents the experimental characterization of the in-plane deformation field at any depth within a granular support medium (GSM) called Carbomer 940 using digital image correlation (DIC) and particle image velocimetry (PIV). A method was developed to produce a 2D plane of randomly shaped speckles within the GSM for DIC. Four different needle diameters and four different speeds were used as test specimens representative of those utilized for 3D printing of soft matter in the GSM. The results can be used to determine dimensional tolerances and assessing interactions between multiple injection needles and acceptable spacing. The displacements in the direction of needle motion (u) and transverse (v) were obtained. Subsequently, the magnitudes were determined as a function of distance from the needle path and time history. Results show that near the needle there is a region of yielded/fluidized material and away from the needle path the material acts like a viscoelastic solid. Permanent deformation decreases with increased distance from the path and recovery is enhanced by reversing back through the path.
• McGhee, E., Pitenis, A., Schulze, K., McGhee, A., O'Bryan, C., Bhattacharjee, T., Angelini, T., Sawyer, W., & Urueña, J. (2018). In Situ Measurements of Contact Dynamics in Speed-dependent Hydrogel Friction. Biotribology, 13. doi:10.1016/j.biotri.2017.12.002
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  The friction behavior of soft, aqueous, biotribological contacts depends on contact geometry, speed, and pressure. Previous efforts to measure the surface profile of soft sliding contacts have been stymied by the matching index of refraction of aqueous materials submerged in water. Here, hydrogel surface deformations were imaged using confocal microscopy to experimentally investigate the contact geometry as a function of sliding speed. In situ fluorescence confocal microscopy measurements of the contact deformation during unidirectional friction experiments revealed the existence of a front/back asymmetry that increased with increasing sliding speed. A polyacrylamide hydrogel disk (96.5% water) was polymerized with fluorescent dyes and used as a rotating countersample below a polished glass hemispherical pin (1 mm radius of curvature). All experiments were performed submerged in a dilute (0.7 wt%) suspension of 1 μm red fluorescent microspheres in ultrapure water. Imaging of the contact was performed using a confocal microscope in situ with unidirectional sliding at 0.1, 1, 10, and 100 mm/s. The friction coefficient increased monotonically with increasing speed from μ ~ 0.04 at 0.1 mm/s to μ ~ 0.20 at 100 mm/s. All imaging was performed relative to the stationary glass probe under steady-state conditions. The contact line measured by connecting the leading and exiting contact points was nearly perpendicular to the loading direction at 0.1 mm/s sliding speed, but distorted as sliding speed increased. Consistent with the theories of viscoelastic contributions to polymer friction, the tangent of the contact-line angle correlated with friction.
• Bennett, A., Harris, K., Schulze, K., McGhee, A., Pitenis, A., Angelini, T., Sawyer, W., Müser, M., & Urueña, J. (2017). Contact Measurements of Randomly Rough Surfaces. Tribology Letters, 65(4). doi:10.1007/s11249-017-0918-5
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  This manuscript presents an experimental effort to directly measure contact areas and the details behind these scaled experiments on a randomly rough model surface used in the “Contact Mechanics Challenge” (2017). For these experiments, the randomly rough surface model was scaled up by a factor of 1000× to give a 100 mm square sample that was 3D printed from opaque polymethylmethacrylate (PMMA). This sample was loaded against various optically smooth and transparent samples of PDMS that were approximately 15 mm thick and had a range in elastic modulus from 14 kPa to 2.1 MPa. During loading, a digital camera recorded contact locations by imaging the scattering of light that occurs off of the PMMA rough surface when it was in contact with the PDMS substrate. This method of illuminating contact areas is called frustrated total internal reflection and is performed by creating a condition of total internal reflection within the unperturbed PDMS samples. Contact or deformation of the surface results in light being diffusely transmitted from the PDMS and detected by the camera. For these experiments, a range of reduced pressure (nominal pressure/elastic modulus) from below 0.001 to over 1.0 was examined, and the resulting relative contact area (real area of contact/apparent area of contact) was found to increase from below 0.1% to over 60% at the highest pressures. The experimental uncertainties associated with experiments are discussed, and the results are compared to the numerical results from the simulation solution to the “Contact Mechanics Challenge.” The simulation results and experimental results of the relative contact areas as a function of reduced pressure are in agreement (within experimental uncertainties).
• McGhee, A., Pitenis, A., Bennett, A., Harris, K., Schulze, K., Ifju, P., Angelini, T., Sawyer, W., Müser, M., & Urueña, J. (2017). Contact and Deformation of Randomly Rough Surfaces with Varying Root-Mean-Square Gradient. Tribology Letters, 65(4). doi:10.1007/s11249-017-0942-5
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  The “Contact Mechanics Challenge” posed to the tribology community by Müser and Dapp in 2015 detailed a 100 µm × 100 µm randomly rough surface with a root-mean-square gradient of unity, g ¯ = 1. Many surfaces, both natural and synthetic, can be described as randomly rough, but rarely with a root-mean-square gradient as steep as g ¯ = 1. The selection of such a challenging surface parameter was intentional, but potentially limiting for broad comparisons across existing models and theories which may be limited by small-slope approximations. In this manuscript, the root-mean-square gradients (g ¯) of the “Contact Mechanics Challenge” surface were produced on 1000 × scaled models such that there were three different surfaces for study with g¯=0.2,0.5, and 1. In situ measurements of the real area of contact and contact area distributions were performed using frustrated total internal reflectance along with surface deformation measurements performed using digital image correlation. These optical in situ experiments used the scaled 3D-printed rough surfaces that were loaded into contact with smooth, flat, and elastic samples that were made from unfilled PDMS: (10:1) E* = 2.1 MPa Δγ = 4 mJ/m2; (20:1) E* = 0.75 MPa Δγ = 3 mJ/m2; (30:1) E* = 0.24 MPa Δγ = 2 mJ/m2. All of the loading was performed using a uniaxial load frame under force control. A Green’s function molecular dynamics simulation assuming the small-slope approximation was compared to all experimental data. These measurements reveal that decreasing root-mean-square gradient noticeably increases real area of contact area under conditions of “equal” applied load, but variations in the root-mean-square gradient did not significantly alter the contact patch geometry under conditions of nearly equal real area of contact. Including g ¯ in the reduced pressure (p= P/ (E∗ g ¯)) reduced the root-mean-square error between the simulation (g ¯ = 1) and all experimental data for the relative area of contact as a function of reduced pressure over the entire range of surfaces, materials, and loads tested.

Proceedings Publications

• McGhee, A., & Ifju, P. (2018). Deformation measurement within a volume of translucent yield stress material using digital image correlation. In Society for experimental Mechanics.
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  This paper introduces a method of determining in-plane deformation of a translucent yield stress material (YSM) at any depth using digital image correlation. A 2D plane of uniquely shaped speckles are introduced to a volume of the YSM using a 3D printing technique. A cylindrical object, is dragged through the 2D plane at four different speeds each with four different diameters. The displacements caused by the cylinder were found and analyzed.
• McGhee, A., Nguyen, D., & Ifju, P. (2018). Surface deformation with simultaneous contact area measurement for soft transparent media due to spherical contact. In Society for experimental mechanics.
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  We present a method to measure surface deformations between a steel sphere and a flat PDMS surface. A sphere was chosen as the specimen to ensure the resulting deformation measurement can be compared to known theoretical models. A 36 mm diameter steel sphere was pressed into contact against flat, transparent polydimethylsiloxane (PDMS) sheets with a constant load rate controlled by an Instron testing machine. The modulus of the PDMS samples range from 241 kPa to 2.1 MPa. A digital image correlation technique was used to measure the surface deformation of the PDMS with increasing applied load.