Controlling shockwave dynamics using architecture in periodic porous materials

Control of materials function via control of structure and defects, or the concept of “materials by design,” holds promise for novel materials tailored to meet the requirements of an intended application.^1–3 A variety of advanced manufacturing techniques have been recently developed to tailor material structure during fabrication, including spray and electron beam deposition, laser energy focusing, and micro- or nanomachining to name a few. Many of these techniques couple to specific material properties (such as melting point), and are therefore limited in their applicability to broad classes of materials, and in their ability to achieve controlled structure at micron to sub-micron length scales. Hierarchical assembly is an attractive means of achieving unprecedented material properties via control of structure across decades in length scale. Numerous examples exist in both natures, and more recently, by an ability to deposit and control porosity and parent material structures through additive manufacturing (AM). Specifically, polymer foams have been explored for applications^4,5 in the aerospace and defense industries that include structural support, vibration dampening, and shockwave mitigation. Although the overall porosity or relative density can be controlled in stochastic foams to some degree through synthesis and foaming methods, a lack of structural control at the micro-to-mesoscale makes it challenging to control deformation mechanisms at the relevant length scales (nm-to-μm) which ultimately dictate continuum-level properties. Through AM, polymer-based foams have been realized which exhibit unprecedented stiffness-to-weight ratios, tailorable load–deflection responses, and novel “metamaterial” properties such as negative Poisson ratios (“auxetics”) under uniaxial quasi-static compression through hierarchical assembly and manipulation of the underlying physical deformation mechanisms.^6–13 Furthermore, concepts for designing materials with spatial gradations in structure were developed for use in thermal barrier materials in the 1980s.^14,15 Since then, functionally graded materials have become a cornerstone of modern materials research with applications in defense, energy, aerospace, and medical sectors.

Additive manufacturing by digital 3-dimensional (3-D) printing allows for layer-by-layer fabrication of multi-dimensional assemblies with precise control of structural features.¹⁶ By assembling materials in this fashion, organization of strut and node topologies may be used to control the mesoscale deformation mechanisms activated under load. The recent proliferation of additive manufacturing initiatives has largely been driven by the advent of 3-D printing technologies that have greatly broadened the scope of printable materials at dramatically reduced costs. While there are numerous examples illustrating how the quasi-static mechanical responses of polymer foams have been tailored by additive manufacturing, there is limited understanding of the response of these materials under shockwave compression.^17,18 Furthermore, there have been few examples of in situ measurements of high rate yield behavior, wave dynamics, or wave front homogeneity (localization) within shock-loaded porous polymer foams. The majority of polymer foam shockwave information has come from bulk measurements of shockwave transit through the material. Here, we illustrate for the first time how shockwave dynamics can be modulated and controlled at micron-length scales in AM periodic porous polymer structures using in situ, time-resolved x-ray phase contrast imaging at the Advanced Photon Source. Further, we demonstrate how functionally graded structures can be used to modify shockwave dynamics over (<400 μm) lengths. Our work builds on the recent observations that during dynamic compression experiments of AM engineered lattice materials, an elastic deflection of the structure is observed ahead of the compaction of the lattice versus no elastic deformation in a stochastic structured material.¹⁸ This previous work and the results shown here are the first steps towards controlling dynamic material behavior at the mesoscale, which opens up the possibility of designing and engineering material properties to precisely meet the demands of the intended application.

3-D printed polymer architectures were prepared in simple cubic (SC) and face-centered tetragonal (FCT) layer symmetries from a polydimethylsiloxane adhesive elastomer using a direct ink write method (Fig. 1(a)). Samples comprised 11 printed layers with a filament center-to-center spacing of ∼440 μm (strut diameters of ∼220 μm). The elastomeric architectures were previously developed by Duoss et al., and their measured and simulated quasi-static compressive responses were reported previously.¹⁹ In the SC-like structure, the struts or filaments are parallel to one another in the xy plane, the subsequent layer orthogonal to the first, and every other layer in the z-direction aligned. In the FCT structure, every other layer is offset by half of the filament center-to-center spacing, creating a staggered layer symmetry. Under quasi-static compression, the load–deflection responses were found to be dominated by the layer symmetry and strut overlap, with the SC structure exhibiting a higher initial compressive strength, until the structure becomes unstable and buckles, resulting in a stress plateau prior to further stiffening at high strains that commensurate with the densification regime. In addition to SC and FCT architectures, a functionally graded elastomer was prepared with 4 layers of SC structure and 4 layers of FCT repeat units, oriented for shockwave propagation from the SC repeat units into the FCT units.

Shock compression experiments^20,21 were designed so that a direct comparison could be made between traditional shockwave diagnostics (wave arrival times and optical velocimetry) and in situ X-ray phase contrast imaging (PCI). The print integrity of the micro-lattice samples (∼2 mm × 35 mm × 35 mm) was measured using x-ray computed tomography,²² Fig. 1(b) and in more detail Fig. 1S (supplementary material). The foams were trimmed into individual targets (∼2 mm × 5 mm × 8.25 mm) and epoxied (Angstrom Bond) to a PMMA window (3 mm × 5 mm × 8.25 mm) with a 0.8 μm Al mirror deposited on the foam/PMMA interface. A 0.5 mm thick Cu impact plate was affixed to the opposing surface of the micro-lattice sample to act as a drive plate, Fig. 2(a), and the assembly was secured in the target holder. Similar targets were fabricated for simple cubic, face-centered tetragonal and graded architectures. Three photonic Doppler velocimetry (PDV) collimated probes (AC Photonics) were used to measure the incoming projectile velocity (u₀, PDV 1 in Fig. 2(a)), shock breakout into the foam at the Cu drive plate/foam interface (PDV 2, Fig. 2(a)), and the wave profile at shock breakout at the foam/PMMA interface (PDV 3, Fig. 2(a)). Finally, a piezoelectric impact pin (Dynasen, Inc.) was used to synchronize the impact event, the incident X-ray beam, and the detectors.

Shock waves were generated in the AM architectures (Fig. 1(c)) by impact using the IMPact system for the ULtrafast Synchrotron Experiments (IMPULSE) at the Advanced Photon Source (Argonne, IL). X-ray phase imaging was used to obtain time-resolved images of the shock wave as it propagated through the AM samples with 2–3 μm spatial resolution.^23–25 80-ps width X-ray bunches (E = 25 ± 0.9 keV, λ = 0.05 nm) spaced 153.4 ns apart were transmitted through the samples and detected using a LuAg:Ce (Lu₃Al₅O₁₂:Ce) scintillator optically coupled to four independent image intensified charge coupled device (ICCD) detectors (Princeton Instruments) to provide 4–8 X-ray images per experiment.

Multi-frame X-ray Phase Contrast Imaging (PCI) was used to observe the shock wave coupling with the AM foam architectures using the 24-bunch mode of the synchrotron.²³ Plate impact experiments were performed on SC, FCT, and graded architectures each nearly-matched in impact velocity u₀ ∼ 0.7 km/s (Table I). Additional experiments were performed at u₀ ∼0.3 and 0.5 km/s, but are not reported here in detail. Fig. 2 shows 4 sequential frames from SC (top) and FCT (bottom) structures. The times reported below the images are relative to the pin trigger time for each experiment, which are arbitrary. Fig. 2S (supplementary material) shows the cross-timed PDV data and the relative ICCD detector frames with their respective rate for the simple cubic architecture.

In the SC architecture, the initial shockwave couples to the periodic strut structure at the Cu base plate with non-planar stress localization between the struts resulting in the ejection of the elastomer from the free surface of the filaments (supplementary material Movie 1S). The ejecta promptly (<100 ns) consolidates into an articulated jet that propagates at a velocity greater than the free surface velocity U_jet > 2u_p ≈ u_fs due to non-uniaxial strain, and focusing of the shock-driven flow between the struts. Jet formation was observed at several impact velocities spanning u₀ = 0.3–0.7 km/s. A single frame from an experiment at u₀ = 0.313 km/s is shown in Fig. 2 (top right) at an earlier stage of jet consolidation, and shows the articulation of jet formation similar to the double “humped” structure into the focused jet observed at t = 4.967 μs in the higher velocity experiment. Within ∼200 ns and ∼200 μm, the large strains affect jet break-up and material disintegration as seen both in loss of jet integrity, as well as lower contrast due to loss of material. The jet velocity U_jet = 2.484 ± 0.035 mm/μs is more than 2 times faster than the bulk compaction wave speed U_s,pl = 1.172 ± 0.060 mm/μs.

By contrast, in the FCT architecture jetting is thwarted by an inability to consolidate and propagate between struts due to the staggering of the layer symmetry in the x-direction, and the result is a modulation of the shockwave into a shaped sinusoidal wave front (supplementary material Movie 2S). This is most clearly observed in Fig. 2 (bottom right), for a lower velocity experiment with u₀ = 0.309 km/s. This is the first direct measurement of shock wave modulation via the microstructural control afforded by additive manufacturing techniques in elastomer foams.

Shockwave experiments were designed to obtain direct measurement of shock and particle velocities via PCI, as well as by traditional velocimetric techniques. Table I summarizes measured and calculated shock states for three experiments using two foam architectures. Using the PCI images, the in-material particle velocity, u_p,pl, of the compaction wave was measured by the motion of the Cu baseplate/foam interface. An edge-finding algorithm was used to locate the position of the interface in the images. The positions of the foam filaments allow for the determination of the compaction shockwave velocity, U_s,_pl, from the decrease in x-ray transmission associated with densification behind the compacted wavefront.²⁶ The compaction wave parameters obtained by analysis of the PCI images are given in Table I. Using traditional techniques, the arrival of the input and transmitted shockwave in the foams was measured by two cross-timed photonic Doppler velocimetry probes at the Cu baseplate and foam/PMMA windowed interface. In the PDV spectrograms, evidence of a low pressure elastic precursor was observed that could not be detected in the PCI images (Fig. 3S (supplementary material)). Standard multiple wave analysis²⁷ was performed to determine the particle velocity, shock wave velocity, and longitudinal stress for the elastic and plastic states. The shock amplitude of the elastic precursor was found to be negligible (P≪ 0.1 GPa), and commensurate with the quasi-static compressive yield strengths of the SC and FCT structures.¹⁹ The bulk shock states, Table I, are nearly identical for SC and FCT structures, which is expected given the same parent material and relative initial densities. Yet PCI reveals how the wave dynamics at the micron length scale are dramatically modulated by structure.

To gain insight into the compression of the AM foams and localization phenomena in detail, the shock compression experiments were modeled using the commercial Finite Element Method (FEM) simulation code ABAQUS.²⁹ This code incorporated the material response described by a Mie–Grüneisen linear U_s-u_p equation of state (EOS) and a Maxwell viscoelastic model. No failure model was used at this time. Relevant material parameters (the material used here is proprietary) were obtained from the work of Winter et al.³⁰ and work performed at the Los Alamos National Laboratory³¹ on silica-filled polymer (Sylgard 184™), which we assume approximates the AM foams studied here (See Table 1S). The two structures (SC and FCT) were discretized into tetrahedron elements with the diameter of the struts approximately 200 μm, and the element number for the entire sample typically between 1 and 2 million elements.

The numerical results for an impact speed of u₀ = 0.7 km/s are shown in Figs. 3 and 4 with more detail shown in Figs. 5S (SC) and 6S (FCT) (supplementary material). In Fig. 3, the material density is plotted using the colormap where density is increasing from blue to red. The calculated particle velocity was u_p = 0.7 km/s and the shock velocity was U_s = 1.3 km/s, in close agreement with the experiment. The analysis shows that for the SC structure, high deformation occurs in the regions between the struts leading to simulated “jetting” similar to that observed in the experiments. Initiated as two distinct protrusions (Fig. 3(a)), as the polymer is forced between the struts in the adjacent higher layers, a single jet is formed as the two come into contact (Fig. 3(b)). The sharpness of the jet is a strong function of the shear viscoelastic behavior of the polymer. That is, the jetting is associated with the shear response at high strain rate. The softer the material, the more pronounced the jetting. In the FCT structure, jetting was not observed, as the deformation of the struts was blocked by the layer symmetry. In this case a sinusoidal region was observed behind the shock front. As shown in the figures it is distinguished by having a lower than expected density (Fig. 3(c)), similar to that observed in the experiments.

In addition to the numerical analysis, areal density was extracted from the PCI images with distinct wave characteristics. Both the x-ray attenuation as well as gradients in the x-ray phase of the sample contribute to contrast in the PCI image formation as the x-rays propagate beyond the object to the detector plane.^32–34 For an object composed of a single material, both the attenuation and phase are related to the line-integrated areal density ρT (g/cm²), where ρ and T are the mass density and projected thickness. The areal density can be reconstructed from a single PCI image by solving the transport of intensity (TIE) equation,³⁵ detailed in the supplementary material. Corresponding contour plots of areal density are shown in Fig. 3 and in more detail in Fig. 7S (supplementary material). The reconstructed areal density is accurate to 1st order only since the TIE is a geometric optics approximation to the complete scalar diffraction theory.

In Fig. 4 the strain distribution is shown for both structures SC and FCT taken at the same simulation time after impact. One can note that large tensile strains exist in localized regions (⁠$εzz≈2.0)$⁠, thus simulating the “jetting” in the SC structure (Fig. 4(a)). This behavior was not observed in the FCT structure (Fig. 4(b)). In the numerical simulations, behind the shock front, a spatial non-uniform pressure distribution was observed with an average value $P≈0.5 GPa$ in the struts. Within the jets, the local tensile stress reached values of $σzz≈0.3 GPa$⁠, with an average density of $ρ≈0.75 g/cm3$⁠.

From the PCI experiments and simulations of the SC and FCT structures, AM structures offer a promising means of tuning the shock-driven flow at the mesoscale. Graded materials exhibit unique properties and/or functionality not achievable in traditional stochastic structures and can provide a mechanism of tailoring shock properties for response such as detonation reactive flow, reactivity, or spatial control of shock-driven flow; e.g., shockwave metamaterials.³⁶ To demonstrate these principles at micron length scales, a graded SC-FCT structure was prepared and shocked at a similar shock input condition to the SC and FCT architectures. Fig. 5 shows the PCI images and wave dynamics in the graded structure consisting of 4 layers of SC structure and 4 layers of FCT structure repeated through the part (supplementary material Movie 3S). PCI shows jets initially forming as seen previously in the SC structure, but as the bulk wave propagates between structures, the jets are suppressed and the compaction wave morphology shapes into the characteristic sinusoidal wave of the FCT architecture. As seen previously, at time 5.054 μs the two protrusions of the filament ejecting into the subsequent layer is re-established as the structure changes back to SC. This is the first report to our knowledge of graded control of shockwave dynamics at the micron scale.

Modifying the shockwave properties within a material through induced microstructure provides a means to the design and fabrication of superior protective materials implemented in personal armor, impact zones in cars, or protective shielding in aviator or space vehicle applications, where the shock may be dispersed or dissipated depending on the design. It is also envisioned that this approach may be applied to explosive design through microstructured architectures to exploit detonation wave acceleration or tailored shock sensitivity.³⁷ Recent advances in 3-D additive manufacturing techniques matched in length scale with the spatial resolution of dynamic x-ray phase contrast imaging has provided both unprecedented insights into and control of shockwave dynamics and compaction phenomena in elastomeric foams.

Micro-lattice Elastomer Fabrication: A Dow Corning SE1700 clear adhesive was purchased from Ellsworth Adhesives. The two-part polydimethylsiloxane adhesive was mixed with 10:1 part A:B by weight ratio. Typically, we mixed 10 grams of SE 1700 part A and 1 gram of part B with a spatula for 3 min. The material was then loaded in a 5 cc syringe barrel (Nordson) and collected at the extruder tip by manually pressing the piston until material began to extrude. The barrel was then sealed with an endcap and centrifuged at 5400 rpm for 5 min. Excess air was removed in a similar way after centrifugation. The endcap was exchanged for a micronozzle (200 μm ID, Nordson) and the syringe was mounted to the z-stage of a three-axis linear positioning system (Aerotech). The simple cubic (SC) and face-centered tetragonal (FCT) architectures were prepared on glass substrates mounted to the xy stages of the positioning system. A positive displacement fluid dispensing system (EFD UltimusV, Nordson) was attached to the syringe barrel and supplied at a given pressure (32.5 psi) to match the programmed print speed (5 mm/s) for a 200 μm ID dispensing tip. After aligning the tip to the glass substrate, a numerical control program was executed in the A3200 CNC Operator Interface Control software (Aerotech) with simultaneous automation of the dispensing system. Each build consisted of 11 layers with a filament center-to-center spacing of ∼440 μm for both SC and FCT architectures with a total build area of 35 mm × 35 mm. After printing the glass substrate along with the part were transferred to an oven at 150 °C for 24 h. Each part was then detached from the substrate after sufficient cooling at room temperature. Three targets were built from each micro-lattice (SC and FCT) part. The micro-lattice (∼2 mm × 35 mm × 35 mm) was cut into individual targets (∼2 mm × 5 mm × 8.25 mm) and glued (Angstrom Bond) to a PMMA window (3 mm × 5 mm × 8.25 mm) with an 8 kÅ Al film deposited on the surface. Next a 0.5 mm thick Cu impact plate was glued to the opposing surface of the micro-lattice and the assembly was placed in the target holder and glued. Finally, a piezoelectric impact pin (Dynasen, Inc.) was incorporated in order to synchronize the impact event, the incident X-ray beam, and the detectors. Identical targets were fabricated for simple cubic, face-centered tetragonal and graded architectures.

3D micro X-ray tomographic images were collected (Fig. 1S of supplementary material). The images were collected using a Carl Zeiss X-ray Microscopy Inc., Xradia Micro-CT (Pleasanton, CA). The instrument uses a Hamamatsu microfocus X-ray source with a tungsten anode that was operated at 50 kVp, 10 W of power. The source shines a cone beam of X-rays through the sample, which is absorbed based upon the electron density of the material. The X-rays impinges upon a scintillator, is magnified by the 2× microscope objective, and is imaged by the 2 k × 2 k, piezo electrically cooled camera. The camera was binned by 2. The pixel size at the sample was 9.08 μm. 1261 radiographs with an exposure time of 20 s each were collected, as the sample was rotated 184°. The radiographs were then reconstructed (Fig. 1S of supplementary material) using TXM reconstructor (Carl Zeiss X-ray Microscopy Inc.) and then rendered using Avizo 9.0.1 (FEI Visualization Sciences Group, Burlington, MA).

Shock waves were generated in the micro-lattice foams using the IMPact system for Ultrafast Synchrotron Experiments (IMPULSE) located at Sector 32 ID-B at the Advanced Photon Source (Argonne, IL). Further details of the experimental setup and timing along with the X-ray imaging techniques are described previously.^{17,23,24,38,39} Projectiles with copper impactors were accelerated down the gun barrel to impact the foam target located in an evacuated target chamber (<100 mTorr) positioned in the X-ray beam. After impact, a shock wave propagates through the micro-lattice foam. X-ray imaging was used to obtain time-resolved images of the shock wave propagating through each respective micro-lattice (supplementary material Movies 1 S–3 S) with a 2–3 μm spatial resolution for impact velocities approximately at 0.7 mm/μs. During the experiment, X-ray bunches (25 keV) with a 80 ps width and spaced 153.4 ns apart interacted with the foam sample and then illuminated a LuAg scintillator converting to visible light. The visible light was optically coupled to four independent image intensified charge coupled device (ICCD) detectors. Photonic Doppler Velocimetry (PDV) probes were used to measure projectile velocity and the free-surface velocity of the copper impact plate. A 0.8 μm Al reflector was coated on the PMMA window at its interface with the micro-lattice foam. Particle velocity wave profiles were obtained by using the mirrored Cu and the Al reflector to record the Doppler-shifted light from the Cu impact plate and the PMMA/foam interface, respectively (Fig. 2S of supplementary material). Raw PDV data are shown for the simple cubic architecture in Fig. 3S (supplementary material) along with the respective spectrogram.

The shock experiments were modeled using the commercial Finite Element Method (FEM) simulation code ABAQUS (Fig. 4S of supplementary material) and the material density is shown in Figs. 5S (SC) and 6S (FCT) (supplementary material). In Lagrangian form, ABAQUS solves mass, momentum, and energy conservation, respectively, as

where $ρ$ is the mass density, $e$ is the internal energy, $υ$ is the velocity, $D$ is the rate of deformation, $σ$ is the Cauchy stress, $J$ is the determinant of the deformation gradient, and $q$ is the heat flow. The superimposed dots indicate the time derivative (the substantial derivative). For the shock experiments investigated here, heat transport is negligible and thus $q=0.$ The material response is characterized in terms of deviatoric (shear) and the volumetric (pressure) response by $σ=s+p I$⁠, where $s$ is the deviatoric stress, $p$ is the pressure, and $I$ is the identity tensor. The volumetric response was determined using a Mie–Grüneisen Us-Up equation of state (EOS). Material parameters came from the work of Winter et al.³⁰ 

where $Γ$ is the Grüneisen parameter, E is the internal energy, c_s is the intercept of the shock velocity (Us) vs. particle velocity (Up), and S is the slope in the Us-Up equation.

For the deviatoric response a Maxwell viscoelastic model was used, and parameters (Table 1S of supplementary material) for that model came from extensive work done at Los Alamos on the silica-filled polymer, Sylgard 184^™. The actual material is proprietary. The total deviatoric stress is given by

where $μ0$ represents the instantaneous shear modulus, $ė$ the deviatoric strain rate, and $ėv$ the deviatoric viscous strain rate. Equations (1)–(3) were solved incrementally in time with an ABAQUS user-defined constitutive model.

The areal density was reconstructed for representative frames of PCI images for the SC and FCT architectures and contour plots are shown in Fig. 7S (supplementary material). Dynamic x-ray phase contrast imaging (PCI) relies on spatial gradients in the refractive index of an object to produce image contrast. Spatial variations in the phase led to local curvature in the transmitted x-ray wavefront, causing overlap and interference as the wave propagates. The image formation process for PCI can be simulated using the Fresnel diffraction integral in the paraxial limit, as well as knowledge of the complex index of refraction for the object, the x-ray beam spectrum and divergence, as well as the detector spectral response, resolution, and pixel size.³³ For a single material in the limit for a thin object, both the absorption and phase delay are related to the projected thickness $T(x,y)$ integrated through the object along the propagation direction z. For a complex index of refraction $n=1−δ+iβ$⁠, the intensity is attenuated just past the object according to Beer's law of absorption, $I0e−μT(x,y)$⁠, where I₀ is the uniform intensity of the incident x-rays, and the absorption per unit length is $μ=4πβ/λ$⁠. The phase delay can be written as $φ(x,y)=(2π/λ)δT(x,y)$⁠. Using the transport of intensity equation,⁴⁰ which describes changes to the intensity of a scalar wave as it propagates, Paganin et al.³⁵ solve for the projected thickness $T(x,y)$ using discrete Fourier transforms

where $F{ }, F−1{ }$ are the discrete Fourier transform and inverse transform, $k⊥$ is a vector of the spatial frequencies corresponding to transform coordinates of $x,y$⁠. A fast Fourier transform (FFT) algorithm is implemented using the Interactive Data Language (IDL), and the array $I(x,y)$ corresponding to the measured intensity is padded to decrease the step size $dk⊥$ in order to have sufficient accuracy for large propagation distances z. The areal density is simply $ρ0T(r⊥)$⁠, where ρ₀ = 1.13 g/cm³ is the initial density of Sylgard 184. While the material composition is proprietary, the composition of Sylgard has been estimated as 30.9% wt. C, 7.4% wt. H, 37.8% wt. Si, and 23.9% wt. O, and is used to compute the complex index of refraction.⁴¹ Ideally the incident intensity I₀ is uniform, but is measured to be slowly varying in space $I0(x,y)$⁠, and is fit to a low-order 2-dimensional polynomial. To test the accuracy of retrieving the areal density, DPCI images of synthetic phantom objects of varying size, shape, and thickness were simulated using the x-ray beam parameters and detector resolution found in the experiment. Fresnel propagation in the paraxial limit using the angular spectrum method was used to simulate wave propagation,³³ including absorption, refraction, and diffraction, for the synthetic phantom objects. Varying levels of noise were included in the simulated images, and the retrieval algorithm was found to be robust, as expected, since the TIE propagator effectively filters the intensity image for increasing spatial frequencies as $|k⊥|2$⁠. For the same reason, the TIE is a geometric optics approximation (no diffraction) valid for high Fresnel numbers $NF=1/(k⊥2λz)≫1$⁠, such that sufficiently small objects and sharp features with $(k⊥)−1<3−5λz$ are blurred after retrieval, and are systematically underestimated by up to 25% for features smaller than ∼40-μm. The areal density of synthetic objects and features of 100-μm scale and larger are retrieved with 5% accuracy for noise levels of 2% as found typically in the experiments.

See supplementary material for the x-ray tomographic images of the elastomer architectures studied here with representative PDV data corresponding to the ICCD detector timing and the resulting PDV spectrogram for a single shot. More complete deformation results from finite element simulations and areal density analysis are shown in the supplementary material for SC and FCT structures including the viscoelastic properties used for calculations.

This work was performed by Los Alamos National Laboratory at Argonne National Laboratory's Advanced Photon Source (APS). The authors acknowledge support from the Laboratory Directed Research and Development (LDRD) program at Los Alamos National Laboratory (Project No. 20160103DR) and DOE/NNSA Campaign 2. Branch is supported by an Agnew National Security post-doctoral fellowship. We also thank Lee Gibson, Brian Bartram, Austin Goodbody, and Chuck Owens for assembly and firing of the target assemblies. A. J. Iverson, C. A. Carlson, and M. Teel from National Security Technologies (NSTech) are thanked for their technical support in fielding of the X-ray PCI detector system. A. Deriy and K. Fezzaa (Argonne National Laboratory) are thanked for technical support at the Sector 32 beamline of the APS. LANL is operated by Los Alamos National Security, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC52-06NA25396. Use of the Advanced Photon Source, an Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.