Experimental Shock Research Articles

Angiotensin 1–7 in an experimental septic shock model

BackgroundAlterations in the renin–angiotensin system have been implicated in the pathophysiology of septic shock. In particular, angiotensin 1–7 (Ang-(1–7)), an anti-inflammatory heptapeptide, has been hypothesized to have beneficial effects. The aim of the present study was to test the effects of Ang-(1–7) infusion on the development and severity of septic shock.MethodsThis randomized, open-label, controlled study was performed in 14 anesthetized and mechanically ventilated sheep. Immediately after sepsis induction by bacterial peritonitis, animals received either Ang-(1–7) (n = 7) or placebo (n = 7) intravenously. Fluid resuscitation, antimicrobial therapy, and peritoneal lavage were initiated 4 h after sepsis induction. Norepinephrine administration was titrated to maintain mean arterial pressure (MAP) between 65 and 75 mmHg.ResultsThere were no differences in baseline characteristics between groups. Septic shock was prevented in 6 of the 7 animals in the Ang-(1–7) group at the end of the 24-h period. Fluid balance and MAP were similar in the two groups; however, MAP was achieved with a mean norepinephrine dose of 0.4 μg/kg/min in the Ang-(1–7) group compared to 4.3 μg/kg/min in the control group. Heart rate and cardiac output index were lower in the Ang (1–7) than in the control group, as were plasma interleukin-6 levels, and creatinine levels. Platelet count and PaO2/FiO2 ratio were higher in the Ang-(1–7) group. Mean arterial lactate at the end of the experiment was 1.6 mmol/L in the Ang-(1–7) group compared to 7.4 mmol/L in the control group.ConclusionsIn this experimental septic shock model, early Ang-(1–7) infusion prevented the development of septic shock, reduced norepinephrine requirements, limited interleukine-6 increase and prevented renal dysfunction.

Studies on the Kinetics of the CH + H2 Reaction and Implications for the Reverse Reaction, 3CH2 + H.

The reaction of CH radicals with H2 has been studied by the use of laser flash photolysis, probing CH decays under pseudo-first-order conditions using laser-induced fluorescence (LIF) over the temperature range 298-748 K at pressures of ∼5-100 Torr. Careful data analysis was required to separate the CH LIF signal at ∼428 nm from broad background fluorescence, and this interference increased with temperature. We believe that this interference may have been the source of anomalous pressure behavior reported previously in the literature (Brownsword, R. A.; J. Chem. Phys. 1997, 106, 7662-7677). The rate coefficient k1 shows complex behavior: at low pressures, the main route for the CH3* formed from the insertion of CH into H2 is the formation of 3CH2 + H, and as the pressure is increased, CH3* is increasingly stabilized to CH3. The kinetic data on CH + H2 have been combined with experimental shock tube data on methyl decomposition and literature thermochemistry within a master equation program to precisely determine the rate coefficient of the reverse reaction, 3CH2 + H → CH + H2. The resulting parametrization is kCH2+H(T) = (1.69 ± 0.11) × 10-10 × (T/298 K)(0.05±0.010) cm3 molecule-1 s-1, where the errors are 1σ.

Ti-6Al-4V to over 1.2 TPa: Shock Hugoniot experiments, ab initio calculations, and a broad-range multiphase equation of state

Titanium alloys are used in a large array of applications. In this work we focus our attention on the most used alloy, Ti-6Al-4V (Ti64), which has excellent mechanical and biocompatibility properties with applications in aerospace, defense, biomedical, and other fields. Here we present high-fidelity experimental shock compression data measured on Sandia's Z machine. We extend the principal shock Hugoniot for Ti64 to more than threefold compression, up to over 1.2 TPa. We use the data to validate our ab initio molecular dynamics simulations and to develop a highly reliable, multiphase equation of state (EOS) for Ti64, spanning a broad range of temperature and pressures. The first-principles simulations show very good agreement with Z data and with previous three-stage gas gun data from Sandia's STAR facility. The resulting principal Hugoniot and the broad-range EOS and phase diagram up to 10 TPa and ${10}^{5}$ K are suitable for use in shock experiments and in hydrodynamic simulations. The high-precision experimental results and high-fidelity simulations demonstrate that the Hugoniot of the Ti64 alloy is stiffer than that of pure Ti and reveal that Ti64 melts on the Hugoniot at a significantly lower pressure and temperature than previously modeled.

Analysis of Shock Deceleration Effects in the NASA Electric Arc Shock Tube

Complex processes related to nonequilibrium thermochemistry and radiation are a fundamental aspect of atmospheric entry flowfields. Shock tubes provide a means of generating test gas conditions analogous to those found on the stagnation line of flight shock layers, which allows extraction of thermochemical rates and radiative intensities. Currently, the NASA Electric Arc Shock Tube (EAST) is the best source of such data. Although simple in principle, nuances of these experimental facilities can affect the observed results. Notably, electron densities and radiance levels in excess of equilibrium predictions have been observed at EAST for many years. The deceleration of the shock as it passes along the tube has been posited as a source of these discrepancies. In this work, a recently developed numerical methodology (LASTA) is applied to these results from the literature. Using the experimental shock speed profile as an input, trends in postshock electron density are computed. Radiance throughout the shock layer is also predicted by coupling the simulation to the NASA NEQAIR code. It is shown that the predictions of LASTA provide a good match to the magnitudes and trends of the experimental differences, confirming shock speed deceleration as their cause.

Hemorrhagic Shock: Blood Marker Sequencing and Pulmonary Gas Exchange

The early identification of internal hemorrhage in critically ill patients may be difficult. Besides circulatory parameters, hemoglobin and lactate concentration, metabolic acidosis and hyperglycemia serve as laboratory markers for bleeding. In this experiment, we examined pulmonary gas exchange in a porcine model of hemorrhagic shock. Moreover, we sought to investigate if a chronological order of appearance regarding hemoglobin, lactatemia, standard base excess/deficit (SBED) and hyperglycemia exists in early severe hemorrhage. In this prospective, laboratory study, twelve anesthetized pigs were randomly allocated to exsanguination or a control group. Animals in the exsanguination group (n = 6) endured a 65% blood loss over 20 min. No intravenous fluids were administered. Measurements were taken before, immediately after, and at 60 min after the completed exsanguination. Measurements included pulmonary and systemic hemodynamic variables, hemoglobin concentration, lactate, base excess (SBED), glucose concentration, arterial blood gases, and a multiple inert gas assessment of pulmonary function. At baseline, variables were comparable. Immediately after exsanguination, lactate and blood glucose were increased (p = 0.001). The arterial partial pressure of oxygen was increased at 60 min after exsanguination (p = 0.04) owing to a decrease in intrapulmonary right-to-left shunt and less ventilation-perfusion inequality. SBED was different to the control only at 60 min post bleeding (p < 0.001). Hemoglobin concentration did not change at any time (p = 0.97 and p = 0.14). In experimental shock, markers of blood loss became positive in chronological order: lactate and blood glucose concentrations were raised immediately after blood loss, while changes in SBED lagged behind and became significant one hour later. Pulmonary gas exchange is improved in shock.

Shock compression of poly(methyl methacrylate) PMMA in the 1000 GPa regime: Z machine experiments

Hydrocarbon polymers are used in a wide variety of practical applications. In the field of dynamic compression at extreme pressures, these polymers are used at several high energy density (HED) experimental facilities. One of the most common polymers is poly(methyl methacrylate) or PMMA, also called Plexiglass® or Lucite®. Here, we present high-fidelity, hundreds of GPa range experimental shock compression data measured on Sandia’s Z machine. We extend the principal shock Hugoniot for PMMA to more than threefold compression up to 650 GPa and re-shock Hugoniot states up to 1020 GPa in an off-Hugoniot regime, where experimental data are even sparser. These data can be used to put additional constraints on tabular equation of state (EOS) models. The present results provide clear evidence for the need to re-examine the existing tabular EOS models for PMMA above ∼120 GPa as well as perhaps revisit EOSs of similar hydrocarbon polymers commonly used in HED experiments investigating dynamic compression, hydrodynamics, or inertial confinement fusion.

Parameters of the oscillatory process of the sleeper base in the area of the rail joint when using elastic spacers

The article presents the results of field tests of under-rail pads in order to assess the effect of stiffness and the number of standard and experimental pads-shock absorbers on the amplitude-frequency characteristic of vibrations that occur in the ballast layer in the rail joint zone when the rolling stock is moving. To achieve this goal, we measured the vertical vibration accelerations arising during the passage of trains in the area of the rail joint with a different number of standard under-rail shock absorbers TsP-204-M-ARS (standard) and Getzner Sylodyn NF shock absorber pads with increased elasticity (experimental). On the basis of the obtained values, the amplitude-frequency characteristic of the oscillatory process was determined by means of the Fourier transform. The main (carrier) frequencies, at which the maximum amplitudes of vibration accelerations are recorded, are determined, first of all, not by the material of the damper pad, but by the magnitude of the force effect. The use of experimental shock absorber pads allows to reduce and redistribute the vibration energy transmitted to the ballast layer.

A wide-range semiclassical self-consistent average atom model

The discovery of material properties at extremes, which are essential for high energy density physics development, requires the most advanced experimental facilities, theories, and computations. Nowadays, it is possible to model properties of matter in such conditions using the state-of-the-art density functional theory (DFT) or path-integral Monte Carlo approaches with remarkable precision. However, fundamental and computational limitations of these methods impede their practical usage, while wide-range thermodynamic and transport models of plasma are required. As a consequence, an average atom (AA) framework is still relevant today and has been attracting more and more attention lately. The self-consistent field and electron density in an atomic cell is usually obtained using the Thomas–Fermi (TF), Hartree–Fock, Kohn–Sham approaches, or their extensions. In this study, we present the AA model, where semiclassical wave functions are used for bound states, while free electrons are approximated by the TF model with a thermodynamically consistent energy boundary. The model is compared in various regions of temperatures and pressures with the reference data: the Saha model for rarefied plasma, DFT for warm dense matter, and experimental shock Hugoniot data. It is demonstrated that a single AA model may provide a reasonable agreement with the established techniques at low computational cost and with stable convergence of the self-consistent field.

Synthesis and evaluation of a new class of MIF-inhibitors in activated macrophage cells and in experimental septic shock in mice

Macrophage migration inhibitory factor (MIF) is a proinflammatory cytokine with enzymatic activities. Anti-inflammatory effects of MIF enzyme inhibitors indicate a link between its cytokine- and catalytic activities. Herein the synthesis, docking, and bioactivity of substituted benzylidene-1-indanone and -1-tetralone derivatives as MIF-tautomerase inhibitors is reported. Many of these substituted benzylidene-1-tetralones and -indan-1-ones were potent MIF-tautomerase inhibitors (IC50 < 10 μmol/L), and the most potent inhibitors were the 1-indanone derivatives 16 and 20. Some of these compounds acted as selective enolase or ketonase inhibitors. In addition, compounds 16, 20, 26, 37 and 61 efficiently inhibited NO, TNFα and IL-6 production in lipopolysaccharide-induced macrophages. Compound 20, 37 and 61 also inhibited ROS generation, and compound 26 and 37 abolished activation of NF-κB. Compound 37 significantly augmented hypothermia induced by high dose of lipopolysaccharide in mice. The possible mechanisms of action were explored using molecular modelling and docking, as well as molecular dynamics simulations.

1265: EFFECTS OF ENTERAL PROTEASE INHIBITION ON COAGULATION PROTEOLYSIS AFTER TRAUMA-HEMORRHAGIC SHOCK

Introduction: Coagulopathy and uncontrolled proteolysis are frequent sequelae of circulatory shock, and are associated with poor outcomes. We have previously demonstrated that enteral protease inhibition improves hemodynamics and survival in experimental shock. However, the mechanisms of inappropriate systemic protease activity in shock are not well understood. Our aim was to identify the effects of enteral protease inhibition on plasma proteolysis by examination of the plasma peptidome in experimental trauma-hemorrhagic shock (T-HS). Methods: Anesthetized Wistar rats were subjected to experimental T-HS with laparotomy. An oral catheter was inserted into the proximal duodenum and either gabexate mesilate+Golytely (GM) (10mg/kg) (n=8) or Golytely as a vehicle (n=8) was enterally infused starting 30min into the hypotension period. Blood was removed to achieve a mean blood pressure (MAP) of 35-40mmHg for 90min before reperfusion with lactated Ringer’s to obtain a target MAP of ≥65mmHg. Blood was taken for mass spectrometry peptidomics analysis at baseline and 120min after reperfusion. Results: Plasma proteolysis was increased 8.8±0.9 fold in the Shock-control group, and was reduced to 2.0±0.2 times baseline values in GM-treated animals (p< 0.0001). Despite representing only 0.3% of all proteins found in the peptidome, fibrinogen fragments comprised 11.3% of all peptides recovered after T-HS in our model, and were often non-canonically cleaved. Enteral GM decreased proteolysis of other proteins involved in coagulation, including: C4 (increased 1092±131% from baseline in Shock-control vs 154±22% in GM-treated animals, p< 0.0001); Kininogen-1 (relative intensity 90.5±20.4 in Shock-control vs. 19.8±1.4 in GM-treated group, p< 0.0001); Protein C (118% in Shock-control vs. GM-treated animals, p=0.0012). In addition, fragments from inter-alpha-trypsin inhibitor were exclusively found in the Shock-control group, suggesting breakdown of anti-proteases in the blood after shock. Conclusions: Enteral protease inhibition with gabexate mesilate significantly reduced plasma proteolysis after experimental T/HS as measured by peptidomics, especially of proteins involved with coagulation. This approach opens new insights for the understanding and treatment of Trauma-hemorrhagic shock, particularly related to coagulopathies.

The structure of 3-D collisional magnetized bow shocks in pulsed-power-driven plasma flows

We investigate three-dimensional (3-D) bow shocks in a highly collisional magnetized aluminium plasma, generated during the ablation phase of an exploding wire array on the MAGPIE facility (1.4 MA, 240 ns). Ablation of plasma from the wire array generates radially diverging, supersonic ( $M_S \sim 7$ ), super-Alfvénic ( $M_A &gt; 1$ ) magnetized flows with frozen-in magnetic flux ( $R_M \gg 1$ ). These flows collide with an inductive probe placed in the flow, which serves both as the obstacle that generates the magnetized bow shock, and as a diagnostic of the advected magnetic field. Laser interferometry along two orthogonal lines of sight is used to measure the line-integrated electron density. A detached bow shock forms ahead of the probe, with a larger opening angle in the plane parallel to the magnetic field than in the plane normal to it. Since the resistive diffusion length of the plasma is comparable to the probe size, the magnetic field decouples from the ion fluid at the shock front and generates a hydrodynamic shock, whose structure is determined by the sonic Mach number, rather than the magnetosonic Mach number of the flow. The 3-D simulations performed using the resistive magnetohydrodynamic (MHD) code Gorgon confirm this picture, but under-predict the anisotropy observed in the shape of the experimental bow shock, suggesting that non-MHD mechanisms may be important for modifying the shock structure.

High-temperature vibrational relaxation and decomposition of shock-heated nitric oxide. I. Argon dilution from 2200 to 8700 K

This work investigates the high-temperature vibrational relaxation and decomposition of nitric oxide (NO) diluted in argon (Ar) to target NO–Ar and NO–NO interactions and to augment the subsequent inference of rates for NO diluted in nitrogen (N2). [J. W. Streicher et al., “High-temperature vibrational relaxation and decomposition of shock-heated nitric oxide. II. Nitrogen dilution from 1900 to 8200 K,” Phys. Fluids (submitted)]. In both Part I and Part II, two continuous-wave ultraviolet laser diagnostics were used to probe quantum-state-specific time-histories of NO behind reflected shocks in high-temperature shock-tube experiments, enabling inferences of multiple vibrational relaxation times and reaction rate constants for NO decomposition reactions. These diagnostics both probed absorbance (α) in the ground vibrational state of NO but in multiple rotational states utilizing light at 224.8150 and 226.1025 nm. The absorbance was subsequently used to infer quantum-state-specific time-histories for translational/rotational temperature (Ttr) via the absorbance ratio and number density of NO (nNO) via α, Ttr, and the absorbance cross sections (σ). The experiments for Ar dilution probed mixtures of 2% NO/Ar, 1% NO/Ar, and 0.4% NO/Ar for initial post-reflected-shock conditions from 2200–8700 K and 0.12–0.97 atm. Further analysis of the absorbance, temperature, and number density time-histories yielded two vibrational relaxation times (τVTNO−Ar and τVTNO−NO) and four rate coefficients for multiple NO decomposition reactions (kdNO−Ar, kdNO−NO, kfN2O, and kzNO−O)—each of which is extended to higher temperatures than any previous study and with reduced scatter and uncertainty. Generally, these rate data are consistent with data from the literature, although τVTNO−Ar and τVTNO−NO are observed to differ strongly from both the Millikan and White correlation and Park two-temperature model.

Resveratrol therapy improves liver function via estrogen-receptors after hemorrhagic shock in rats.

BackgroundResveratrol may improve organ dysfunction after experimental hemorrhagic or septic shock, and some of these effects appear to be mediated by estrogen receptors. However, the influence of resveratrol on liver function and hepatic microcirculation after hemorrhagic shock is unknown, and a presumed mediation via estrogen receptors has not been investigated in this context.MethodsMale Sprague-Dawley rats (200-300g, n = 14/group) underwent hemorrhagic shock for 90 min (MAP 35±5 mmHg) and were resuscitated with shed blood and Ringer’s solution. Animals were treated intravenously with vehicle (1% EtOH), resveratrol (0.2 mg/kg), the unselective estrogen receptor antagonist ICI 182,780 (0.05 mg/kg) or resveratrol + ICI 182,780 prior to retransfusion. Sham-operated animals did not undergo hemorrhage but were treated likewise. After 2 hours of reperfusion, liver function was assessed either by plasma disappearance rate of indocyanine green (PDRICG) or evaluation of hepatic perfusion and hepatic integrity by intravital microscopy, serum enzyme as well as cytokine levels.ResultsCompared to vehicle controls, administration of resveratrol significantly improved PDRICG, hepatic perfusion index and hepatic integrity after hemorrhagic shock. The co-administration of ICI 182,780 completely abolished the protective effect only with regard to liver function.ConclusionsThis study shows that resveratrol may improve liver function and hepatocellular integrity after hemorrhagic shock in rats; estrogen receptors mediate these effects at least partially.

Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility.

A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. The measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.

Single crystal elasticity and equation of state of tantalum up to 54 GPa

We measured single crystal elasticity of Ta under high pressures up to 54 GPa at room temperature using inelastic x-ray scattering at room temperature. Simultaneously, we measured the density of Ta using x-ray diffraction. Combining the bulk modulus and density, we obtain an equation of state of Ta as a primary scale. The Vinet equation was fitted to the pressure–volume data and we found consistency with previous work including experimental static and shock compressions and theoretical calculation. We proposed a parameter set for the Vinet equation [K0 = 191.1(3) GPa, K′0 = 4.006(2)] which is consistent with the pressure based on extrapolated velocities within 2% up to ∼80 GPa. Furthermore, we found the present scale to be consistent with a recent ruby scale (Ruby2020) up to ∼50 GPa.

Inferring the temperature profile of the radiative shock in the COAX experiment with shock radiography, Dante, and spectral temperature diagnostics

Predicting and modeling the behavior of experiments with radiation waves propagating through low-density foams require a detailed quantification of the numerous uncertainties present. In regimes where a prominent radiative shock is produced, key dynamical features include the shock position, temperature, and curvature and the spatial distribution and temperature of the corresponding supersonic radiation wave. The COAX experimental platform is designed to constrain numerical models of such a radiative shock propagating through a low-density foam by employing radiography for spatial and shock information, Dante for characterizing the x-ray flux from the indirectly driven target, and a novel spectral diagnostic designed to probe the temperature profile of the wave. In this work, we model COAX with parameterized 2D simulations and a Hohlraum-laser modeling package to study uncertainties in diagnosing the experiment. The inferred temperature profile of the COAX radiation transport experiments has been shown to differ from simulations more than expected from drive uncertainties that have been constrained by simultaneous soft x-ray flux and radiography measurements.

Vulnerable atheromatous plaque stabilization using extracorporeal shock wave- mediated sonoporation therapy- assisted HDL and atorvastatin combination therapy

Background and Aims : Large mature or immature lipid core (atheroma) within a thin- fibrous cap, is called vulnerable atheromatous plaque. The management of vulnerable atheromatous plaque reduces the risk of ischemic disease and its related deaths. In this study, we developed an experimental electrohydraulic shock wave generator (0–20 kv) and investigated its effectiveness on vulnerable atheromatous plaque stabilization in the golden Syrian hamster common carotid artery.

Treatment of advanced atherosclerosis with calcified fibroatheroma plaque using B- mode ultrasound- guided high- dose atorvastatin- loaded microbubbles- mediated shock wave therapy

Background and Aims : Atherosclerosis is the leading cause of cerebrovascular and cardiovascular diseases. The management of advanced atherosclerosis with calcification reduces the risk of stroke and myocardial infarction and their related deaths. In this study, we developed an experimental intravascular shock wave therapy system, and investigated its effectiveness on intraplaque calcium content reduction and advanced atherosclerotic plaque regression, wherein diagnostic B- mode ultrasound is combined with therapy system, with a goal of increased safety.

Shock-driven dispersal of a corrugated finite-thickness particle layer

A research area emerging in the multiphase flow community is the study of shock-driven multiphase instability (SDMI), a gas–particle analog of the traditional fluid-fluid Richtmyer–Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian–Lagrangian approach. One objective of this study is to compare the simulated particle curtains to a comparable set of shock tube experiments performed to analyze traditional RMI of a gas curtain. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while also matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. Varying particle diameters are tested in the simulations to explore the impact of particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of the multiphase Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that the comparison depends on the diameter of the particles (thus, dependent on the Stokes number of the flow). A second objective of this study is to analyze the effect of the initial particle volume fraction on the evolution of the curtain and the behavior of the instability. This is done through analyzing the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.

Modelling the anomalous shock response of titanium diboride

In planar shock compression experiments, polycrystalline titanium diboride ( TiB 2 ) often exhibits double-yield phenomena, atypical among non-transforming ceramics, in particle velocity histories. A finite-strain phase-field theory, with order parameters accounting for fracture and dilatation, followed by limited plastic slip and compaction, is specialized to study the uniaxial shock response of TiB 2 . The model accurately depicts longitudinal stress up to 120 GPa on the Hugoniot from multiple published sources, as well as shear stress inferred elsewhere from experimental shock data. A novel phase-field analysis enables one-, two- or three-wave structures depending on impact stress. These results are observed in experimental data and have not been successfully captured by prior numerical models. Results support the conjecture that (i) fracture and dilatation, followed by (ii) plastic deformation and compaction, and then (iii) fragmentation to a comminuted, viscous granular medium is a plausible sequence of physical mechanisms as shock stress increases. The first break in the velocity profile always corresponds to micro-cracking in the model, which correlates with the first yield point on the Hugoniot. In the three-wave regime, two plastic waves correlate with two yield points, where the first plastic wave after the precursor is due to fracture and the second dominated by plasticity. When impact is severe enough such that the second plastic wave overtakes the first, a single plastic waveform with multiple kinks emerges in particle velocity histories, consistent with some experimental data. These kinks are well explained by pressure-dependent viscosity in crack kinetics and by small-magnitude plastic deformation, and corresponding stress perturbations need not precisely correspond to particular cusps on the stress–volume Hugoniot.