High-throughput quantification of quasistatic, dynamic and spall strength of materials across 10 orders of strain rates.

The response of metals and their microstructures under extreme dynamic conditions can be markedly different from that under quasistatic conditions. Traditionally, high strain rates and shock stresses are achieved using cumbersome and expensive methods such as the Kolsky bar or large spall experiments. These methods are low throughput and do not facilitate high-fidelity microstructure-property linkages. In this work, we combine two powerful small-scale testing methods, custom nanoindentation, and laser-driven microflyer (LDMF) shock, to measure the dynamic and spall strength of metals. The nanoindentation system is configured to test samples from quasistatic to dynamic strain-rate regimes. The LDMF shock system can test samples through impact loading, triggering spall failure. The model material used for testing is magnesium alloys, which are lightweight, possess high-specific strengths, and have historically been challenging to design and strengthen due to their mechanical anisotropy. We adopt two distinct microstructures, solutionized (no precipitates) and peak-aged (with precipitates) to demonstrate interesting upticks in strain-rate sensitivity and evolution of dynamic strength. At high shock-loading rates, we unravel an interesting paradigm where the spall strength vs. strain rate of these materials converges, but the failure mechanisms are markedly different. Peak aging, considered to be a standard method to strengthen metallic alloys, causes catastrophic failure, faring much worse than solutionized alloys. Our high-throughput testing framework not only quantifies strength but also teases out unexplored failure mechanisms at extreme strain rates, providing valuable insights for the rapid design and improvement of materials for extreme environments.

Effect of Human Head Shape on the Risk of Traumatic Brain Injury: A Gaussian Process Regression-based Machine Learning Approach.

INTRODUCTION: Computational head injury models are promising tools for understanding and predicting traumatic brain injuries. However, most available head injury models are "average" models that employ a single set of head geometry (e.g., 50th-percentile U.S. male) without considering variability in these parameters across the human population. A significant variability of head shapes exists in U.S. Army soldiers, evident from the Anthropometric Survey of U.S. Army Personnel (ANSUR II). The objective of this study is to elucidate the effects of head shape on the predicted risk of traumatic brain injury from computational head injury models. MATERIALS AND METHODS: Magnetic resonance imaging scans of 25 human subjects are collected. These images are registered to the standard MNI152 brain atlas, and the resulting transformation matrix components (called head shape parameters) are used to quantify head shapes of the subjects. A generative machine learning model is used to generate 25 additional head shape parameter datasets to augment our database. Head injury models are developed for these head shapes, and a rapid injurious head rotation event is simulated to obtain several brain injury predictor variables (BIPVs): Peak cumulative maximum principal strain (CMPS), average CMPS, and the volume fraction of brain exceeding an injurious CMPS threshold. A Gaussian process regression model is trained between head shape parameters and BIPVs, which is then used to study the relative sensitivity of the various BIPVs on individual head shape parameters. We distinguish head shape parameters into 2 types: Scaling components ${T_{xx}}$, ${T_{yy}}$, and ${T_{zz}}$ that capture the breadth, length, and height of the head, respectively, and shearing components (${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$) that capture the relative skewness of the head shape. RESULTS: An overall positive correlation is evident between scaling components and BIPVs. Notably, a very high, positive correlation is seen between the BIPVs and the head volume. As an example, a 57% increase in peak CMPS was noted between the smallest and the largest investigated head volume parameters. The variation in shearing components ${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$ on average does not cause notable changes in the BIPVs. From the Gaussian process regression model, all 3 BIPVs showed an increasing trend with each of the 3 scaling components, but the BIPVs are found to be most sensitive to the height dimension of the head. From the Sobol sensitivity analysis, the ${T_{zz}}$ scaling parameter contributes nearly 60% to the total variance in peak and average CMPS; ${T_{yy}}$ contributes approximately 20%, whereas ${T_{xx}}$ contributes less than 5%. The remaining contribution is from the 6 shearing components. Unlike peak and average CMPS, the VF-CMPS BIPV is associated with relatively evenly distributed Sobol indices across the 3 scaling parameters. Furthermore, the contribution of shearing components on the total variance in this case is negligible. CONCLUSIONS: Head shape has a considerable influence on the injury predictions of computational head injury models. Available "average" head injury models based on a 50th-percentile U.S. male are likely associated with considerable uncertainty. In general, larger head sizes correspond to greater BIPV magnitudes, which point to potentially a greater injury risk under rapid neck rotation for people with larger heads.

Validation of a computational biomechanical mouse brain model for rotational head acceleration.

Recent mouse brain injury experiments examine diffuse axonal injury resulting from accelerative head rotations. Evaluating brain deformation during these events would provide valuable information on tissue level thresholds for brain injury, but there are many challenges to imaging the brain's mechanical response during dynamic loading events, such as a blunt head impact. To address this shortcoming, we present an experimentally validated computational biomechanics model of the mouse brain that predicts tissue deformation, given the motion of the mouse head during laboratory experiments. First, we developed a finite element model of the mouse brain that computes tissue strains, given the same head rotations as previously conducted in situ hemicephalic mouse brain experiments. Second, we calibrated the model using a single brain segment, and then validated the model based on the spatial and temporal strain responses of other regions. The result is a computational tool that will provide researchers with the ability to predict brain tissue strains that occur during mouse laboratory experiments, and to link the experiments to the resulting neuropathology, such as diffuse axonal injury.

Dynamic strain fields of the mouse brain during rotation.

Mouse models are used to better understand brain injury mechanisms in humans, yet there is a limited understanding of biomechanical relevance, beginning with how the murine brain deforms when the head undergoes rapid rotation from blunt impact. This problem makes it difficult to translate some aspects of diffuse axonal injury from mouse to human. To address this gap, we present the two-dimensional strain field of the mouse brain undergoing dynamic rotation in the sagittal plane. Using a high-speed camera with digital image correlation measurements of the exposed mid-sagittal brain surface, we found that pure rotations (no direct impact to the skull) of 100-200 rad/s are capable of producing complex strain fields that evolve over time with respect to rotational acceleration and deceleration. At the highest rotational velocity tested, the largest tensile strains (≥ 21% elongation) in selected regions of the mouse brain approach strain thresholds previously associated with axonal injury in prior work. These findings provide a benchmark to validate the mechanical response in biomechanical computational models predicting diffuse axonal injury, but much work remains in correlating tissue deformation patterns from computational models with underlying neuropathology.

First contact: Fine structure of the impact flash and ejecta during hypervelocity impact.

Hypervelocity impacts are a significant threat in low-earth orbit and in hypersonic flight applications. The earliest observable phenomena and mechanisms activated under these extreme conditions are typically obscured by a very bright flash, called the impact flash, that contains the signatures of the critical mechanisms, the impacting materials, and the impact environment. However, these signatures have been very difficult to observe because of the small length and time scales involved coupled with the high intensities associated with the flash. Here we perform experiments investigating the structure and characteristics of the impact flash generated by 3 km s-1 spherical projectile impacts on structural metals using temporally co-registered high-resolution diagnostics. Reciprocal impact configurations, in which the projectile and target material are swapped, are used to demonstrate the coupling of early-stage mechanisms in the flash and later-stage ejection mechanisms responsible for the development of the impact crater.

Data-driven Uncertainty Quantification in Computational Human Head Models.

Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e., model geometry, material properties, and boundary conditions) are often associated with significant uncertainty and variability. As a result, uncertainty quantification (UQ), which involves quantification of the effect of this uncertainty and variability on the simulated response, becomes critical to ensure reliability of model predictions. Modern biofidelic head model simulations are associated with very high computational cost and high-dimensional inputs and outputs, which limits the applicability of traditional UQ methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input-output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of the strain fields highlights significant spatial variation in model uncertainty, and reveals key differences in uncertainty among commonly used strain-based brain injury predictor variables.

Twin boundary migration mechanisms in quasi-statically compressed and plate-impacted Mg single crystals.

Twinning is a prominent deformation mode that accommodates plasticity in many materials. This study elucidates the role of deformation rate on the atomic-scale mechanisms that govern twin boundary migration. Examination of Mg single crystals deformed under quasi-static compression was compared with crystals deformed via plate impact. Evidence of two mechanisms was uncovered. Atomic-level observations using high-resolution transmission electron microscopy revealed that twin boundaries in the -axis quasi-statically compressed single crystals are relatively smooth. At these modest stresses and rates, the twin boundaries were found to migrate predominantly via shear (i.e., disconnection nucleation and propagation). By contrast, in the plate-impacted crystals, which are subjected to higher stresses and rates, twin boundary migration was facilitated by local atomic shuffling and rearrangement, resulting in rumpled twin boundaries. This rate dependency also leads to marked variations in twin variant, size, and number density in Mg. Analogous effects are anticipated in other hexagonal closed-packed crystals.

MR Imaging of Human Brain Mechanics In Vivo: New Measurements to Facilitate the Development of Computational Models of Brain Injury.

Computational models of the brain and its biomechanical response to skull accelerations are important tools for understanding and predicting traumatic brain injuries (TBIs). However, most models have been developed using experimental data collected on animal models and cadaveric specimens, both of which differ from the living human brain. Here we describe efforts to noninvasively measure the biomechanical response of the human brain with MRI-at non-injurious strain levels-and generate data that can be used to develop, calibrate, and evaluate computational brain biomechanics models. Specifically, this paper reports on a project supported by the National Institute of Neurological Disorders and Stroke to comprehensively image brain anatomy and geometry, mechanical properties, and brain deformations that arise from impulsive and harmonic skull loadings. The outcome of this work will be a publicly available dataset ( http://www.nitrc.org/projects/bbir ) that includes measurements on both males and females across an age range from adolescence to older adulthood. This article describes the rationale and approach for this study, the data available, and how these data may be used to develop new computational models and augment existing approaches; it will serve as a reference to researchers interested in using these data.

Integrating material properties from magnetic resonance elastography into subject-specific computational models for the human brain.

Advances in brain imaging and computational methods have facilitated the creation of subject-specific computational brain models that aid researchers in investigating brain trauma using simulated impacts. The emergence of magnetic resonance elastography (MRE) as a non-invasive mechanical neuroimaging tool has enabled in vivo estimation of material properties at low-strain, harmonic loading. An open question in the field has been how this data can be integrated into computational models. The goals of this study were to use a novel MRI dataset acquired in human volunteers to generate models with subject-specific anatomy and material properties, and then to compare simulated brain deformations to subject-specific brain deformation data under non-injurious loading. Models of five subjects were simulated with linear viscoelastic (LVE) material properties estimated directly from MRE data. Model predictions were compared to experimental brain deformation acquired in the same subjects using tagged MRI. Outcomes from the models matched the spatial distribution and magnitude of the measured peak strain components as well as the 95th percentile in-plane peak strains within 0.005 mm/mm and maximum principal strain within 0.012 mm/mm. Sensitivity to material heterogeneity was also investigated. Simulated brain deformations from a model with homogenous brain properties and a model with brain properties discretized with up to ten regions were very similar (a mean absolute difference less than 0.0015 mm/mm in peak strains). Incorporating material properties directly from MRE into a biofidelic subject-specific model is an important step toward future investigations of higher-order model features and simulations under more severe loading conditions.

The Influence of Shear Anisotropy in mTBI: A White Matter Constitutive Model.

We examine the influence of shear anisotropy of brain tissue on the potential for mild traumatic brain injury. First we develop a new constitutive description for the white matter in the brain that can capture the anisotropic behavior of the white matter in both tension and shear. The material parameters for the models are determined using a set of three experiments already published in the literature. The calibrated and parameterized model is then implemented in a computational (finite element) model of the head. This computational model is two-dimensional and is used to simulate a previously published injury-causing event in the National Hockey League, using axonal strain as criterion to assess the level of diffuse axonal injury. It is demonstrated that the inclusion of shear anisotropy affects both the nature and the extent of predicted injury. Further, the locations of the predicted injury are more consistent with observations in the literature.

Determination of size distributions of non-spherical pores or particles from single x-ray phase contrast images.

Although x-ray tomography is commonly used to characterize the three-dimensional structure of materials, sometimes this is impractical due either to limited time for data collection (such as in rapidly-evolving systems) or the need to limit the radiation exposure of the sample. In such situations, it is desirable to extract as much information as possible from a more limited data set. In this paper, we describe how to extract the size distribution of non-spherical pores (or, equivalently, particles) from single x-ray phase contrast imaging (XPCI). Because the pores overlap in projection, interpreting the images and extracting quantitative information about the size distribution is non-trivial. In this paper we extend a previously-developed Fourier-based framework for interpreting the speckle pattern of XPCI images from materials with spherical pores to the more challenging case of non-spherical pores. We develop an analytical expression for the XPCI image from a distribution of randomly-oriented ellipsoidal pores, and show that we can use this expression to extract quantitative information about the size distribution from single images. We discuss three approaches to evaluating this expression, corresponding to different assumptions about the nature of the size distribution, and validate our results with simulated XPCI images and experimental data from Berea sandstone.

A 3D Computational Head Model Under Dynamic Head Rotation and Head Extension Validated Using Live Human Brain Data, Including the Falx and the Tentorium.

We employ an advanced 3D computational model of the head with high anatomical fidelity, together with measured tissue properties, to assess the consequences of dynamic loading to the head in two distinct modes: head rotation and head extension. We use a subject-specific computational head model, using the material point method, built from T1 magnetic resonance images, and considering the anisotropic properties of the white matter which can predict strains in the brain under large rotational accelerations. The material model now includes the shear anisotropy of the white matter. We validate the model under head rotation and head extension motions using live human data, and advance a prior version of the model to include biofidelic falx and tentorium. We then examine the consequences of incorporating the falx and tentorium in terms of the predictions from the computational head model.

A mechanism for injury through cerebral arteriole inflation.

An increase in arterial pressure within the cerebral vasculature appears to coincide with ischemia and dysfunction of the neurovascular unit in some cases of traumatic brain injury. In this study, we examine a new mechanism of brain tissue damage that results from excessive cerebral arteriole pressurization. We begin by considering the morphological and material properties of normotensive and hypertensive arterioles and present a computational model that captures the interaction of neighboring pressurized arterioles and the surrounding brain tissue. Assuming an axonal strain-induced injury criterion, we find that the injury depends on vessel spacing, proximity to an unconfined free surface, and the relative difference in stiffness between the arterioles and the surrounding tissue. We find that a steeper heterogeneity (stiffer vessels surrounded by softer brain tissue) causes larger axial strains to develop at some distance from the arteriole wall, within the brain parenchyma. For a more gradual heterogeneity (softer vessels), we observe more larger strain fields close to the arteriole walls. Both deformation patterns are comparable to damage seen in previous pathology studies on postmortem TBI patients. Finally, we use an analytical model to approximate the interplay between internal pressure, arteriole thickness, and the variation in mechanical properties of arterioles.

Effect of bulk modulus on deformation of the brain under rotational accelerations.

Traumatic brain injury such as that developed as a consequence of blast is a complex injury with a broad range of symptoms and disabilities. Computational models of brain biomechanics hold promise for illuminating the mechanics of traumatic brain injury (TBI) and for developing preventive devices. However, reliable material parameters are needed for models to be predictive. Unfortunately, the properties of human brain tissue are difficult to measure, and the bulk modulus of brain tissue in particular is not well-characterized. Thus, a wide range of bulk modulus values are used in computational models of brain biomechanics, spanning up to three orders of magnitude in the differences between values. However, the sensitivity of these variations on computational predictions is not known. In this work, we study the sensitivity of a 3D computational human head model to various bulk modulus values. A subject-specific human head model was constructed from T1-weighted MRI images at 2 mm3 voxel resolution. Diffusion tensor imaging provided data on spatial distribution and orientation of axonal fiber-bundles for modeling white-matter anisotropy. Non-injurious, full-field brain deformations in a human volunteer were used to assess the simulated predictions. The comparison suggests that a bulk modulus value on the order of GPa gives the best agreement with experimentally measured in vivo deformation in the human brain. Further, simulations of injurious loading suggest that bulk modulus values on the order of GPa provide the closest match with the clinical findings in terms of predicated injured regions and extent of injury.

Unraveling the Anomalous Grain Size Dependence of Cavitation.

Experimental studies have identified an anomalous grain size dependence associated with the critical tensile pressure that a metal may sustain before catastrophic failure by cavitation processes. Here we derive the first quantitative theory (and its associated closed-form solution) capable of explaining this phenomena. The theory agrees well with experimental measurements and atomistic calculations over a very wide range of conditions. Utilizing this theory, we are able to map out three distinct regimes in which the critical tensile pressure for cavitation failure (i) increases with decreasing grain size in accordance with conventional wisdom, (ii) nonintuitively decreases with decreasing grain size, and (iii) is independent of grain size. The theory also predicts microscopic signatures of the cavitation process which agree with available data.

Acoustic Emission of Deformation Twinning in Magnesium.

The Acoustic Emission of deformation twinning in Magnesium is investigated in this article. Single crystal testing with combined full field deformation measurements, as well as polycrystalline testing inside the scanning electron microscope with simultaneous monitoring of texture evolution and twin nucleation were compared to testing at the laboratory scale with respect to recordings of Acoustic Emission activity. Single crystal testing revealed the formation of layered twin boundaries in areas of strain localization which was accompanied by distinct changes in the acoustic data. Testing inside the microscope directly showed twin nucleation, proliferation and growth as well as associated crystallographic reorientations. A post processing approach of the Acoustic Emission activity revealed the existence of a class of signals that appears in a strain range in which twinning is profuse, as validated by the in situ and ex situ microscopy observations. Features extracted from such activity were cross-correlated both with the available mechanical and microscopy data, as well as with the Acoustic Emission activity recorded at the laboratory scale for similarly prepared specimens. The overall approach demonstrates that the method of Acoustic Emission could provide real time volumetric information related to the activation of deformation twinning in Magnesium alloys, in spite of the complexity of the propagation phenomena, the possible activation of several deformation modes and the challenges posed by the sensing approach itself when applied in this type of materials evaluation approach.

Changes in Neurofilament and Microtubule Distribution following Focal Axon Compression.

Although a number of cytoskeletal derangements have been described in the setting of traumatic axonal injury (TAI), little is known of early structural changes that may serve to initiate a cascade of further axonal degeneration. Recent work by the authors has examined conformational changes in cytoskeletal constituents of neuronal axons undergoing traumatic axonal injury (TAI) following focal compression through confocal imaging data taken in vitro and in situ. The present study uses electron microscopy to understand and quantify in vitro alterations in the ultrastructural composition of microtubules and neurofilaments within neuronal axons of rats following focal compression. Standard transmission electron microscopy processing methods are used to identify microtubules, while neurofilament identification is performed using antibody labeling through gold nanoparticles. The number, density, and spacing of microtubules and neurofilaments are quantified for specimens in sham Control and Crushed groups with fixation at <1 min following load. Our results indicate that the axon caliber dependency known to exist for microtubule and neurofilament metrics extends to axons undergoing TAI, with the exception of neurofilament spacing, which appears to remain constant across all Crushed axon diameters. Confidence interval comparisons between Control and Crushed cytoskeletal measures suggests early changes in the neurofilament spatial distributions within axons undergoing TAI may precede microtubule changes in response to applied loads. This may serve as a trigger for further secondary damage to the axon, representing a key insight into the temporal aspects of cytoskeletal degeneration at the component level, and suggests the rapid removal of neurofilament sidearms as one possible mechanism.

Time-resolved x-ray diffraction techniques for bulk polycrystalline materials under dynamic loading.

We have developed two techniques for time-resolved x-ray diffraction from bulk polycrystalline materials during dynamic loading. In the first technique, we synchronize a fast detector with loading of samples at strain rates of ~10(3)-10(4) s(-1) in a compression Kolsky bar (split Hopkinson pressure bar) apparatus to obtain in situ diffraction patterns with exposures as short as 70 ns. This approach employs moderate x-ray energies (10-20 keV) and is well suited to weakly absorbing materials such as magnesium alloys. The second technique is useful for more strongly absorbing materials, and uses high-energy x-rays (86 keV) and a fast shutter synchronized with the Kolsky bar to produce short (~40 µs) pulses timed with the arrival of the strain pulse at the specimen, recording the diffraction pattern on a large-format amorphous silicon detector. For both techniques we present sample data demonstrating the ability of these techniques to characterize elastic strains and polycrystalline texture as a function of time during high-rate deformation.

In vitro and in situ visualization of cytoskeletal deformation under load: traumatic axonal injury.

It is difficult to obtain insight into the mechanisms occurring within live cells during mechanical loading, because this complex environment is dynamic and evolving. This is a particular challenge from a subcellular mechanics perspective, where temporal and spatial information on the evolving cytoskeletal structures is required under loading. Using fluorescently labeled proteins, we visualize 3-dimensional live subcellular cytoskeletal populations under mechanical loading using a high-resolution confocal microscope. The mechanical forces are determined using a computational (finite element) model that is validated by integrating instrumentation into the testing platform. Transfected microtubules and neurofilaments of E17 rat neuronal axons are imaged before, during, and after loading. Comparisons between unloaded and loaded live cells demonstrate both spatial and temporal changes for cytoskeletal populations within the imaged volume. NF signal decreases by 24%, yet the microtubule signal exhibits no significant change 20-35 s after loading. Transmission electron microscopy assesses cytoskeletal structure spatial distribution for undeformed and deformed axons. While cytoskeletal degeneration occurs at prolonged time intervals following loads, our data provides insights into real time cytoskeletal evolution occurring in situ. Our findings suggest that, for axons undergoing traumatic injury in response to applied mechanical loads, changes at the substructural level of neurofilaments may precede microtubule rupture and degeneration.