We present simulations and experiments of time integrated radiographic imaging of a moving 1D shock wave front and a quantitative method for determining the statistical error in locating the shock front as a function of integration time and noise in the radiograph. We discuss the trade-off between increasing motion blur, which leads to decreased shock front location certainty, and increasing signal-to-noise, which leads to improved image quality with increasing integration time. We find an optimum integration time between a short integration time, where noise limits the error, and a long integration time, where motion blurring limits the error. This methodology can be used to tune experimental configurations to obtain the highest quality radiograph for a given experimental configuration.

Micro-architected structures are increasingly valued for their light weight and tunable mechanical properties; this class of material includes sheet structures like the Schöen gyroid and beam lattices like the octet. For design purposes, it is critical to understand how to tune the relative density (RD) to obtain desired mechanical properties. This study investigates the mechanical response of Ti-6Al-4V gyroid structures, spanning a broad range of RDs (0.03–0.90), unit cell sizes (1–4 cm), and sheet thicknesses (0.2–7.8 mm). Results demonstrate that the classical Gibson-Ashby power law scaling between RD and modulus and yield stress does not adequately capture the response over a wide range of RDs, nor does it extrapolate correctly to the fully dense solid. Analytical models, in concert with experimental results and high-fidelity finite element calculations, show that the deviation from Gibson-Ashby reflects a transition from structure-dominated to material-dominated behavior. Distinctions are drawn between scaling relationships and property-porosity models, and an analytical model is proposed to better capture the evolution of mechanical properties with RD. These observations are mirrored in other architected topologies, like the octet, and highlight the importance of understanding the relationship between mechanical properties and geometry for design purposes.

Predicting the extreme hydrodynamic response of porous and architected lattice materials is a fundamental challenge in high energy density physics, where shock-induced pore collapse, baroclinic vorticity, and anomalous kinetic and thermodynamic states must be resolved across multiple scales. Traditional high-fidelity hydrocodes are computationally prohibitive for large-scale design exploration in applications like planetary defense and inertial confinement fusion. We present a multi-field spatio-temporal model (MSTM) designed to overcome the limitations of standard machine learning surrogates, which often fail to capture the sharp gradients and non-linear field couplings characteristic of shock propagation. By training on high-fidelity, multiscale multiphysics data, MSTM simultaneously evolves seven coupled thermodynamic and kinetic fields, including pressure, temperature, density, and velocity, across complex material architectures. Our framework demonstrates strong predictive performance on held-out cases within the studied simulation setting, including anomalous responses such as counterintuitive post-shock density reductions and localized hotspot formation, with mean root-mean-square errors as low as 1.4%. The model's multi-field formulation maintains low mass-conservation error and improved interface agreement over long autoregressive rollouts, outperforming single-field models by 94% in structural fidelity. This framework enables a 1000 & times; reduction in time to solution, providing a practical pathway for rapid analysis and optimization of energy dissipation and momentum transfer in meso-structured media.

Additively manufactured lattice metamaterials offer design versatility in strength and energy absorption and provide an additional degree of freedom through the selection of the lattice topology. Under quasistatic loading, the unit cell structure can strongly affect the stiffness, yield, and post-yield behavior, but whether and to what degree the effect of lattice topology persists into dynamic loading scenarios, up to the compaction shock regime, has not been established. LLNL's ALE3D hydrocode was used to perform a computational investigation of dynamic loading in multiple lattice types, including the gyroid, octet, Schwarz D, and rhombic dodecahedron, under impact velocities from 0.25 to 2.25 km/s. Shock Hugoniots for each lattice topology are generated and compared, suggesting that above a critical velocity, distinctions between architectures may not persevere and compacted lattices behave similarly. To investigate the transition between topology-dependent quasistatic compression and the topology-independent regime above the critical velocity, a onedimensional elastic-linear hardening plasticity-densified solid (E-LHP-DS) shock model for lattice materials was developed that relies upon confined compression to link the quasistatic and shock mechanics. Unlike similar works, the model does not assume rigid behavior prior to yield or locking behavior at densification, allowing a richer exploration of lattice mechanics. With only six parameters, the analytical model simultaneously fit quasistatic confined compression simulations for relative densities 0.1 <= rho <= 0.9 and predicted dynamic compaction behavior to traverse several distinct shock modes, each defined by a critical impact speed (equivalently, critical stresses). Comparing the numerical results to the one-dimensional E-LHP-DS shock model predictions suggests that the topology-independence under strong shocks is linked to the onset of densification, which can be predicted based on quasistatic confined compression results.

Owing to their ability to provide tunable mechanical responses, lattice materials are frequently studied to elucidate their response to static and dynamic loads. However, these roles are typically in opposition: static loads must be supported sufficiently far away from the onset of buckling or yielding, whereas dynamic loads are typically ameliorated by crushing of the lattice, which provides excellent energy-absorption due to the large plastic deformation accompanying densification. In contrast, this work considers the octet truss as an exemplar topology, in a structural role where it must simultaneously support static loads while enduring high-amplitude impulsive loads. This study focuses on the ability to withstand impulsive loads without yielding, an essential prerequisite to enduring dual loading. Computational studies using the ALE3D hydrocode were performed to examine the response of the octet truss under a short temporal width impulse shape associated with laser-driven shocks. A key finding was that covering the lattice with a solid face sheet and treating this face sheet thickness as a design variable allows the Taylor-like pulse to be attenuated prior to entering the weaker lattice, at the cost of added mass up front. Experimental validation was accomplished by laser-driven shock testing, using octet trusses printed out of Ti-5Al-5V-5Mo-3Cr. The results show that for a given quantity of mass, the attenuation is maximized when as much mass as possible is moved into the face sheet, leaving a more slender lattice structure. The effect of placing mass in the face sheet rather than lattice beams dominates the effect of relative density, to the point where a low-mass structure with most of the mass concentrated in the face sheet can outperform a high-mass structure with most of the mass in the lattice. By further understanding the propagation of short pulse width waves within under-dense structures, this study expand the domain of applicability of such structures, including lattice materials, to challenging dual-loading regimes spanning decades of strain rates.

Here we present simulations and experiments of time integrated radiographic imaging of a moving 1D interface. We discuss the trade-off between motion blurring of the interface and signal to noise with increasing integration time.

The ability to predict how shock waves traverse porous and architected materials is a key challenge in planetary defense and in the pursuit of inertial fusion energy. Yet capturing pore collapse, anomalous Hugoniot responses, and localized heating—phenomena that strongly influence asteroid deflection or fusion ignition—has remained a major challenge despite recent advances in single-field and reduced representations. We introduce a multi-field spatio-temporal model (MSTM) that unifies seven coupled fields—pressure, density, temperature, energy, material distribution, and two velocity components—into a single autoregressive surrogate. Trained on high-fidelity hydrocode data, MSTM captures nonlinear shock-driven dynamics across porous and architected configurations, achieving mean errors of 1.4% and 3.2% respectively, all while delivering over three orders of magnitude in speedup. MSTM reduces mean-squared error and structural dissimilarity by 94% relative torelative to single-field spatio-temporal models. This advance transforms problems once considered intractable into tractable design studies, establishing a practical framework for optimizing meso-structured materials in planetary impact mitigation and inertial fusion energy.

Time-integrated radiography using MeV Bremsstrahlung X-ray sources is the norm for imaging during system-level testing of components and structures under dynamic condition. One source of error in the analysis of the time-integrated radiography data sets stems from motion blur which smears out sharp interfaces to a greater degree with longer exposure times, which become necessary to provide sufficient signal-to-noise with low X-ray penetration of objects of interest. To quantify motion blur, a 1D shock wave through PMMA was investigated experimentally at The Dynamic Compression Sector at The Advanced Photon Source (DCS@APS) with tapered broadband and 25.46 +/- 1.06 keV narrowband X-rays. Four cameras with different exposure times were used for each experiment to compare the effect that exposure time has on motion blur. In addition, our methodology to accurately simulate motion blur in terms of transmission and shape is presented and compared to our experimental results and quantified. There is a high level of agreement between the experimental and simulation results across the range of data sets investigated in this study with a percent difference range of 0.29-1.31% for the four shots. The methodology of this work serves as a steppingstone towards a physically validated model that could be used in conjunction with experimental results to deconvolve physical parameters, densities, and interfaces of interest in a way that would not be possible with experimental results alone.

Phase transformations and the accompanying changes in room temperature mechanical properties and mechanisms of deformation in an Ni-25Mo-8Cr (wt%) alloy are reported as a function of aging temperature and time. Two-fold increase in strength is achieved as the short range to long range transformation proceeds in the temperature range of 550°–750°C, though ductility remains significantly high even in well-aged samples. Major contribution to strength comes from the precipitation of long range ordered domains of Ni2Mo in a short range ordered matrix. The mode of deformation in solution treated samples is crystallographic glide. However, in aged samples the deformation mode changes from crystallographic glide to micro-twinning, as a function of strain and ordering. These results will be discussed in the context of the tremendous strain hardening achieved in this alloy and other macro-mechanical properties.

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. Here, we focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

The science and engineering communities have significant interest in experimental platforms to evaluate and improve models for dynamic material deformation. While well-developed platforms exist, there are still gaps to fill for strain and strain rate conditions accessed during impact and other high-rate loading scenarios. To fill one such gap for strength measurements, a platform was recently developed that accesses high strain rate (≥105/s) and large strain (≥50%) conditions by measuring the transient closure of a cylindrical hole using in situ x-ray imaging. In the work reported here, further refinement of the platform is performed to reduce the potential effects of porosity and anelasticity on the measurement. This helps us to isolate the strength effects that are the focus of the experiment. The updated experimental configuration employs a two-layer flyer design and elongated target to reduce the magnitude of the tensile excursions associated with rarefaction wave interactions. This allows for a more direct assessment of strength models commonly used for dynamic simulations of metals. We apply the new technique to well-characterized tantalum material, allowing for a robust connection to other experimental techniques. Deformation localization can be a concern in large strain experiments, and to help inform future use of the experimental platform, we use simulations with a sub-zone treatment of shear banding to explore potential localization behavior. Overall, we develop and utilize an experimental configuration with improved isolation of strength effects that can be applied to an expanded range of materials.

Solid particles can be fragmented by a fast-moving fluid if their velocity difference is great enough, such as during the atmospheric entry of meteoroids or the shock compression of engineered particulate composites. The extent of particle deformation and breakup in such systems is poorly understood because the necessary extreme conditions make observation difficult and data scarce. To meet this need, experiments combining ultrafast synchrotron-based radiography with plate impact loading were performed at the dynamic compression sector at the advanced photon source. Metal microspheres of several densities and strengths (Au, Ta, and W) were placed inside a polymer matrix. A planar shock wave was then produced in the polymer by the impact of a gun-launched flyer plate. X-ray images of the resulting flow were collected at ∼150 ns intervals. These images document the progression of particle deformation across a range of flow conditions and particle materials. They show that the extent of deformation is sensitive to the ratio of drag stress to particle strength. The deforming particle's shape is determined by the initial shock–particle interaction, fluid stagnation pressure, and vorticity, each acting on its own timescale. A set of scaling relationships is presented to capture these observations and enable comparison with prior hydrodynamic data. The result is a framework for predicting the conditions under which strong particles are severely deformed by a shock-driven flow.

For understanding material performance under dynamic loading, there is significant interest in the strain rate dependence of material response and in the degree to which high-rate response depends on initial material state. Experimental tests at high strain rates (>103/s) often use measurement of shape change to infer flow strength behavior. Given stress and strain heterogeneities, inferences about flow strength behavior from those observations are facilitated by comparisons with advanced simulations. A new plate impact-based experimental test is described, consisting of in situ X-ray imaging to observe the closure of a cylindrical hole during the passage of a pressure pulse of controlled amplitude and duration. With the goal of providing unique data regarding plastic response at high strain rates, the closure of the hole is measured through time using multi-frame imaging. A first set of experiments on copper examines the role of starting microstructure on material flow behavior. The experimental observations are compared with predictions from direct numerical simulations using the Preston-Tonks-Wallace (PTW) and the Mechanical Threshold Stress (MTS) flow strength models. The quantitative utility of the overall approach is demonstrated in that the results provide information about MTS model parameters associated with high-rate hardening behavior, with the parameters having been unconstrained by quasi-static experimental data.

Metal lattice structures are optimized for high specific strength properties and are now customizable using additive manufacturing methods. However, many of these methods, like selective laser melting, can introduce defects such as porosity, parasitic material, and disconnected struts into the structure, which can negatively affect mechanical behavior. While there are many computational models used to predict the mechanical response of lattice-structured materials, most use an idealized structure and are often not robust enough to account for defects. In this study, metal lattice structures are characterized for defects and mechanically tested in compression. The defect types and distributions are characterized using x-ray micro-tomography and the tomography analyses is used in two different model predictions. First, in an equivalent continuum model, where the defects are used to predict the variability in mechanical properties, and second, in a finite element analysis, where the predicted stress-strain response for both realistic and idealized structures are compared. Investigating this further, a finite element analysis of an octet lattice quantifies the reduction in strength associated with disconnected struts and captures a dependence on the strut's orientation relative to the loading direction. Overall, incorporating defect information gleaned from tomography data improves predictions of mechanical properties by capturing a more realistic deformation response for lattice-structured material.

We report on the continued development of thermodynamics-based analysis of shock waves propagation with the objective of extracting information related to materials strength at high strain rates and pressures. Building on previous results reported for peak stresses of 10 GPa and 25 GPa, we present a series of three-step gas-gun shock experiments designed to explore the pressure and strain rate dependence of plastic flow in polycrystalline tantalum. These experiments at nominal peak stresses of 50 GPa and 75 GPa show the irreversible deformation before pullback to be almost entirely confined to the shock loading, with negligible plastic relaxation on the post-shock plateau. We also add a reverse-ballistics shot at 25 GPa, which was designed to reveal the pullback response with negligible interference from free-surface effects. General thermodynamic considerations allow us to place bounds on the plastic behavior even for parts of the curve that change far too rapidly for the velocimetric time resolution of (conservatively) ~ 5 ns. To analyze the data, we found it necessary to substantially improve the interpolation/extrapolation scheme in order to improve its robustness, flexibility and range of applicability. We describe the new scheme based on splines, as well as an extension of free-surface corrections to the post-shock rarefaction waves. Reanalysis with the new scheme produces results essentially within the error bars previously reported, showing that the known systematic errors associated with free-surface effects are relatively inconsequential for determining thermodynamic paths.

Large-scale molecular dynamics (MD) simulations were carried out to investigate the shock-induced evolution of microstructure in Fe-based systems comprising single-crystal and layered Cu/Fe alloys with a distribution of interfaces. The shock compression of pure single-crystal Fe oriented along [110] above a threshold pressure results in a BCC (α) → HCP (ɛ) phase transformation behavior that generates a distribution of ε phase variants in the phase transformed region of the microstructure behind the shock front. The propagation of the release wave through a phase transformed ε phase causes a reverse ɛ → α phase transformation and renders a distribution of twins for the [110] oriented Fe that serve as void nucleation sites during spall failure. The simulations reveal that the α → ɛ → α transformation-induced twinning for shock loading along the [110] direction is due to a dominant ɛ phase variant formed during compression that rotates on the arrival of the release wave followed by a reverse phase transformation to twins in the α phase. The modifications in the evolution of the ɛ phase variants and twins in Fe behavior are also studied for Cu–Fe layered microstructures due to the shock wave interactions with the Cu/Fe interfaces using a newly constructed Cu–Fe alloy potential. The MD simulations suggest that interfaces affect the observed variants during shock compression and, hence, distributions of twins during shock release that affects the void nucleation stresses in the Fe phase of Cu/Fe microstructures.

The flow stress in a metal is dependent on a variety of factors such as strain, strain rate, microstructure, and temperature. Experiments (i.e. quasi-static tensile testing or Kolsky bar testing) with well characterized stress states have been used to determine the relation between flow stress and these many factors. However, for higher strain rates (>105/s) there is a dearth of high-fidelity data at high plastic strains. Here, we present results of a recent in-situ gas-gun experimental technique that can probe strength effects at strain rates of >105/s. By measuring the diameter of a long cylindrical hole using x-ray imaging in conjunction with back surface velocimetry while the sample is subjected to controlled dynamic loading, the factors affecting flow stress can be inferred. Materials with higher dynamic flow stresses tend to exhibit less diameter reduction than materials with lower flow stresses all else being equal. Typically, the hole size is measured through imaging, but if the hole is blocked, it becomes necessary to infer the amount of closure from another diagnostic like velocimetry. We present preliminary analysis and results on the velocimetry traces from a suite of hole closure experiments that indicates hole size information may be embedded in velocimetry traces.

Architected lattices are gaining prominence for structural applications as additive manufacturing technologies mature. Emergent behavior, such as material jetting and wave propagation, arising from the open architecture has been observed under dynamic loading conditions. The origin of the observed jetting and how it might come about across a broad spectrum of lattice types, material compositions, length scales, and dynamic loading conditions is still an open question. The jetting behavior due to lattice structures was studied through a series of dynamic compression plate impact experiments with in situ x-ray imaging. The role of the impact conditions, the lattice spacing, the lattice architecture, and the lattice base material is explored in the context of promoting or suppressing jet formation. A transition from lattice-led to impactor-led jetting is observed above a certain impact threshold. Complementary direct numerical simulations were also performed to compare with the experiments, to study the underlying stress state giving rise to jetting, and to provide insight into conditions not accessed experimentally. We present a geometric argument on the competitive process leading to lattice and/or impactor jetting which incorporates base material properties, the periodicity of the lattice, and basic tunable length scales of the lattice. Using two-dimensional calculations, we further look at how tuning of a single parameter of the studied systems changes the observed jetting transition.