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At least 397 records · Page 22

Thermal control on the lunar surface

For a mission to the Moon which lasts more than a few days, thermal control is a challenging problem because of the Moon's wide temperature swings and long day and night periods. During the lunar day it is difficult to reject heat temperatures low enough to be comfortable for either humans or electronic components, while excessive heat loss can damage unprotected equipment at night. Fluid systems can readily be designed to operate at either the hot or cold temperature extreme but it is more difficult to accomodate both extermes within the same system. Special consideration should be given to sensitive systems, such as optics and humans, and systems that generate large amounts of waste heat, such as lunar bases or manufacturing facilities. Passive thermal control systems such as covers, shades and optical coatings can be used to mitigate the temperature swings experienced by components. For more precise thermal control active systems such as heaters or heat pumps are required although they require more power than passive systems.

Walker, Sherry T.↗

Electrolytes for Use in High Energy Lithium-Ion Batteries with Wide Operating Temperature Range

Objectives of this work are: (1) Develop advanced Li -ion electrolytes that enable cell operation over a wide temperature range (i.e., -30 to +60C). (2) Improve the high temperature stability and lifetime characteristics of wide operating temperature electrolytes. (3) Improve the high voltage stability of these candidate electrolytes systems to enable operation up to 5V with high specific energy cathode materials. (4) Define the performance limitations at low and high temperature extremes, as well as, life limiting processes. (5) Demonstrate the performance of advanced electrolytes in large capacity prototype cells.

voltage stability↗

Heat capacities of liquid metals above 1500 K

Heat capacity data are presented for liquid transition metals for temperatures close to the melting point and for 3000, 4000, and 5000 K. The data have been obtained by summarizing the results of levitation, exploding-wire, and drop-calorimetry measurements reported in the literature and by providing analytical estimates where experimental data are not available. The data given here are useful in assigning heat loads and predicting structure survival during extreme temperature excursions caused by nuclear, laser, or particle irradiations.

Margrave, J. L.↗

Habitable planets with high obliquities

Earth's obliquity would vary chaotically from 0 degrees to 85 degrees were it not for the presence of the Moon (J. Laskar, F. Joutel, and P. Robutel, 1993, Nature 361, 615-617). The Moon itself is thought to be an accident of accretion, formed by a glancing blow from a Mars-sized planetesimal. Hence, planets with similar moons and stable obliquities may be extremely rare. This has lead Laskar and colleagues to suggest that the number of Earth-like planets with high obliquities and temperate, life-supporting climates may be small. To test this proposition, we have used an energy-balance climate model to simulate Earth's climate at obliquities up to 90 degrees. We show that Earth's climate would become regionally severe in such circumstances, with large seasonal cycles and accompanying temperature extremes on middle- and high-latitude continents which might be damaging to many forms of life. The response of other, hypothetical, Earth-like planets to large obliquity fluctuations depends on their land-sea distribution and on their position within the habitable zone (HZ) around their star. Planets with several modest-sized continents or equatorial supercontinents are more climatically stable than those with polar supercontinents. Planets farther out in the HZ are less affected by high obliquities because their atmospheres should accumulate CO2 in response to the carbonate-silicate cycle. Dense, CO2-rich atmospheres transport heat very effectively and therefore limit the magnitude of both seasonal cycles and latitudinal temperature gradients. We conclude that a significant fraction of extrasolar Earth-like planets may still be habitable, even if they are subject to large obliquity fluctuations.

NASA Discipline Exobiology↗

Power over fiber development for HEP detectors

Power-over-Fiber (PoF) technology has been used extensively in settings where high voltages require isolation from ground and electromagnetic isolation is critical. In cryogenic environments, PoF offers a reliable power transmission technology, leveraging optical fibers to transfer power with minimal system degradation. PoF technology excels in maintaining low noise levels and isolation when delivering power to sensitive electronic systems operating in extreme temperature ranges and high voltage environments. Here, in a novel application of PoF for a HEP detector, power is provided to photon detector modules located on a surface at ~300 kV with respect to ground in the planned DUNE experiment. This summary paper of the PoF talk at the 16th PISA Meeting on Advanced Detectors highlights the R&D effort of PoF in extreme conditions and underscores its capacity to revolutionize power delivery and management in critical applications offering a dependable solution with low noise, optimal efficiency, and superior isolation. The DUNE (Abi et al., 2020) experiment will soon deploy large liquid argon (LAr) time projection chambers (TPC) to detect neutrino interactions and other particle physics phenomena. In addition to the particle tracking provided by the TPC, photon detectors, powered by a first ever PoF system, in the cryostat will leverage the high scintillation light yield of LAr to provide crucial timing and additional calorimetric information.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Improved Hermetic Feedthrough Seals For Optical Fibers

Improved inorganic sealing materials withstand widely ranging temperatures. Hermetic feedthrough seals for optical fibers withstand temperatures from as low as minus 325 degrees F (about minus 198 degrees C) to as high as 392 degrees F (about 200 degrees C) while maintaining helium leak rate of below 10 to the negative 11th power cm(3)/s. Demonstrated to perform exceptionally through salt spray, sinusoidal and random vibrations (20 to 2000 Hz), mechanical shock (40 g's) thermal shock at extreme temperatures, humidity, and radiation (neutron fluence, gamma, and ion) testing.

Fan, Robert Jui-Lin↗

Overview of Nasa's Watts on the Moon Challenge Phase 1

As NASA works to extend human exploration of the solar system, unprecedented capacity for electrical and thermal energy will be needed to support sustained human presence and the beginning of industrial activity on the Moon. Solar energy is abundant on the lunar surface but extended night hours (up to 350 consecutive hours) and extreme temperature change from daylight to nighttime operation creates complexity for solar power use. Analogous issues arise on Earth, where demand for additional renewable energy generation, including solar, is rising, but better power management, distribution, and energy storage solutions are needed to address intermittency and resiliency, among other issues. To accelerate the development of technologies for power distribution and energy storage that can operate in extreme lunar conditions, NASA’s Centennial Challenges Program launched the Watts on the Moon Challenge in September 2020. Submissions for Phase 1 of the challenge were due in March 2021 and winners were announced in May 2021. This paper provides an overview of the challenge, key technical requirements, outcomes from Phase 1, and an update on Phase 2 of the challenge, which is currently ongoing.

Denise P. Morris↗

Oxygen Production from Lunar Regolith using Ionic Liquids

The objective of this work and future follow-on work is to develop a safe, efficient, and recyclable method for oxygen and/or metals extraction from lunar regolith, in support of establishing a manned lunar outpost. The approach is to solubilize the oxides that comprise lunar regolith in media consisting of ionic liquids (ILs) and/or their mixtures at temperatures at or below 300 C. Once in solution, electrolysis can either be performed in-situ to generate oxygen at the anode and hydrogen and/or metals (silicon, iron, aluminum, titanium, etc.) at the cathode. Alternatively, the water that is generated during the solubilization process can be distilled out and condensed into a separate IL and then electrolysized to produce hydrogen and oxygen. In the case of lunar regolith, this method could theoretically produce 44g oxygen per 100g of regolith. The oxygen can be used for human life support and/or as an oxidizer for rocket fuels, and the metals can be used as raw materials for construction and/or device fabrication. Moreover, the hydrogen produced can be used to re-generate the acidic medium, which can then be used to process additional regolith, thereby making the materials recyclable and limiting upmass requirements. An important advantage of IL acid systems is that they are much "greener" and safer than conventional materials used for regolith processing such as sulfuric or hydrochloric acids. They have very low vapor pressures, which means that they contain virtually no toxic and/or flammable volatile content, they are relatively non-corrosive, and they can exhibit good stability in harsh environments (extreme temperatures, hard vacuum, etc.). Furthermore, regolith processing can be achieved at lower temperatures than other processes such as molten oxide electrolysis or hydrogen reduction, thereby reducing initial power requirements. Six ILs have been synthesized and tested for their capability to dissolve lunar simulant, and for electrochemical and thermal stability. The results showed that ILs can be very efficient electrolytes; in particular IL/phosphoric-acid mixtures appear extremely promising for solubilizing lunar simulant. Results from preliminary experiments for distillation of water produced from the oxygen within the metal oxides of the simulant and the hydrogen from the acid indicates that over 75% of the oxygen from the simulant can be harvested as water at a temperature of 150 C. A method for collection of oxygen from electrolysis of the water derived from solubilizing simulant was developed by using a liquid nitrogen trap to liquefy and collect the oxygen. Although precise quantification of the liquid oxygen trapped is difficult to obtain, the amount of hydrogen and oxygen collected from electrolysis of water in this system was greater than 98%. This set-up also included a portable mass spectrometer for the identification of gases released from electrolysis cells. Regeneration of ILs through re-protonation was also demonstrated. Four sequential re-generations of an IL following solubilization of simulant showed no significant differences in amounts of simulant dissolved. Follow-on work for this project should include more studies of IL/phosphoric acid systems. Also, much more work is necessary for defining methods for electrolysis and purification of metals from regolith solubilized in ILs, and for developing a system to use the produced hydrogen to regenerate the spent IL. Finally, design and development of flight breadboard and prototype hardware is required.

Paley, Mark Steven↗

Intensive and extensive margins of the peak load: Measuring adaptation with mixed frequency panel data

In this work we investigate the response of daily electricity peak load to daily maximum temperatures across states in Europe and India. We propose a method that decomposes short- from medium/long-run effects, retains the high frequency nature of the load-weather covariation and treats economic growth as a modulating factor. By simultaneously exploiting variation in unexpected daily weather anomalies and decade-long climatic changes in each location we decompose transitory - intensive margin - adjustments from permanent - extensive margin - adjustments. We find that the shocks over the long-run differ substantially from the short-run dynamics. Furthermore, we find evidence that per capita income modulates the adjustments over the short- and long-run. We project that in response to climate change around 2050 the peak load may increase by up to 20%-30% in Southern Europe and in several states in India, depending on the degree of warming and the evolution of socio-economic conditions. Even with a limited scope to two world regions, we identify that the structure of the economy and differences in future income growth matter in shaping the adaptation to climate change. Our decomposition allows to identify how future weather anomalies can further amplify the relative increase associated to the shift in the climate norm. Assuming that the interannual variability of maximum temperatures follows the distribution observed in the past, we find a doubling of the impacts of climate change during the summer in Europe. Uncertainty around the distribution of future weather anomalies may lead to further unexpected peak load amplifications. Our results have important policy implications for power systems’ generation capacity, transmission and storage, as we show that the challenges to accommodate the peak load in days with extreme temperatures may substantially increase already around mid-century.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

High Temperature Emissivity Measurement System (HiTEMS)

The High Temperature Emissivity Measurement System (HiTEMS) is a ground test capability at NASA Marshall Space Flight Center enabling near normal and varied incident angle spectral and total emittance measurements. This data is gathered at vacuum levels as low as approximately 10-7 Torr within a temperature range of 600°C to approximately 2,600°C, providing essential material property data to assist with improved thermal control estimates for spacecraft hardware. Recent work focusing on the measurement of smooth and bead blasted tungsten samples in support of the Propulsion Research and Tech Branch at NASA MSFC provides a thorough examination into HiTEMS capabilities and insight into the variabilities related to sample roughness at extreme temperatures.

Meghan Carrico↗

A comparison of global estimates of marine primary production from ocean color

The third primary production algorithm round robin (PPARR3) compares output from 24 models that estimate depth-integrated primary production from satellite measurements of ocean color, as well as seven general circulation models (GCMs) coupled with ecosystem or biogeochemical models. Here we compare the global primary production fields corresponding to eight months of 1998 and 1999 as estimated from common input fields of photosynthetically-available radiation (PAR), sea-surface temperature (SST), mixed-layer depth, and chlorophyll concentration. We also quantify the sensitivity of the ocean-color-based models to perturbations in their input variables. The pair-wise correlation between ocean-color models was used to cluster them into groups or related output, which reflect the regions and environmental conditions under which they respond differently. The groups do not follow model complexity with regards to wavelength or depth dependence, though they are related to the manner in which temperature is used to parameterize photosynthesis. Global average PP varies by a factor of two between models. The models diverged the most for the Southern Ocean, SST under 10 C, and chlorophyll concentration exceeding 1mg Chlm-3. Based on the conditions under which the model results diverge most, we conclude that current ocean-color-based models are challenged by high-nutrient low-chlorophyll conditions, and extreme temperatures or chlorophyll concentrations. The GCM-based models predict comparable primary production to those based on ocean color: they estimate higher values in the Southern Ocean, at low SST, and in the equatorial band, while they estimate lower values in eutrophic regions (probably because the area of high chlorophyll concentrations is smaller in the GCMs). Further progress in primary production modeling requires improved understanding of the effect of temperature on photosynthesis and better parameterization of the maximum photosynthetic rate.

Yamanaka, Yasuhiro↗

Module-Level Thermal Interface Material Degradation in HALT

Abstract In this study, thermal interface material (TIM) degradation is driven through highly accelerated life test (HALT) using temperature cycling with a prescribed vibrational acceleration for two commercially available materials having thermal conductivities of 6.0 and 8.5 W/m K. HALT specimens were prepared by applying TIM through a 4-mil stencil over AlSiC baseplates in the shape of those used in Wolfspeed CAS325M12HM2 power electronics modules. Baseplates were mounted onto aluminum carrier blocks with embedded thermocouples to characterize the thermal resistance across the baseplate and TIM layer. Thermal dissipation into the top of the baseplates was provided by a custom heating block, which mimics the size and placement of the die junctions in CAS325 modules, applying power loads of 200, 300, and 400 W. After initial characterization, samples were transferred to the HALT chamber with one set of samples exposed to temperature cycling only (TCO) and the other temperature cycling and vibration (TCV). Both sample sets were cycled between temperature extremes of −40 °C and 180 °C with vibrations applied at a peak acceleration of 3.21 Grms. After hundreds of cycles, samples were reevaluated to assess changes in thermal resistance to provide an accelerated measure of TIM degradation. This allows for reliability prediction of useful lifetime (illustrated in a solar inverter case study herein), as well as to provide a basis for developing an accelerated testing method to related temperature cycling to faster methods of degradation. Such techniques provide a means to develop maintenance schedules for power modules for ensuring sufficient thermal performance over the operating lifetime.

Engineering↗

Response of Surface Shortwave Cloud Radiative Effect to Greenhouse Gases and Aerosols and Its Impact on Summer Maximum Temperature

Shortwave cloud radiative effects (SWCREs), defined as the difference of the shortwave radiative flux between all-sky and clear-sky conditions at the surface, have been reported to play an important role in influencing the Earth's energy budget and temperature extremes. In this study, we employed a set of global climate models to examine the SWCRE responses to CO2, black carbon (BC) aerosols, and sulfate aerosols in boreal summer over the Northern Hemisphere. We found that CO2 causes positive SWCRE changes over most of the NH, and BC causes similar positive responses over North America, Europe, and eastern China but negative SWCRE over India and tropical Africa. When normalized by effective radiative forcing, the SWCRE from BC is roughly 3–5 times larger than that from CO2. SWCRE change is mainly due to cloud cover changes resulting from changes in relative humidity (RH) and, to a lesser extent, changes in cloud liquid water, circulation, dynamics, and stability. The SWCRE response to sulfate aerosols, however, is negligible compared to that for CO2 and BC because part of the radiation scattered by clouds under all-sky conditions will also be scattered by aerosols under clear-sky conditions. Using a multilinear regression model, it is found that mean daily maximum temperature (Tmax) increases by 0.15 and 0.13 K per watt per square meter (W m−2) increase in local SWCRE under the CO2 and BC experiment, respectively. When domain-averaged, the contribution of SWCRE change to summer mean Tmax changes was 10 %–30 % under CO2 forcing and 30 %–50 % under BC forcing, varying by region, which can have important implications for extreme climatic events and socioeconomic activities.

surface shortwave cloud radiative effect↗

Cascaded Sapphire Fiber Bragg Gratings Inscribed by Femtosecond Laser for Molten Steel Studies

This research reports a distributed fiber optic high-temperature sensing system tailored for applications in the steel industry and various other sectors. Recent advancements in optical sensor technology have led to the exploration of sapphire crystal fibers as a solution for sensing in harsh environments. Utilizing a femtosecond (fs) laser, cascaded fiber Bragg gratings (FBGs) were meticulously fabricated within a multimode sapphire optical fiber. These FBGs endowed the system with distributed sensing capabilities and underwent rigorous testing under extreme temperatures, reaching up to 1800 °C. Here, the study delves into the investigation of the FBG reflection spectrum, facilitated by the development of a sophisticated multimode demodulation system, which contributed to the attainment of precise temperature measurements with a performance accuracy of 99.9%. Demonstrating exceptional thermal stability, the sapphire FBGs endured temperatures of 1600 °C for a sustained duration of 22 h. Furthermore, this article explores the application of distributed temperature sensing employing multiple sapphire FBGs, showcasing their utility in temperature measurements related to molten steel studies.

47 OTHER INSTRUMENTATION↗

NASA Tech Briefs, November 2011

The topics include: 1) Flight Test Results from the Rake Airflow Gage Experiment on the F-15B; 2) Telemetry and Science Data Software System; 3) CropEx Web-Based Agricultural Monitoring and Decision Support; 4) High-Performance Data Analysis Tools for Sun-Earth Connection Missions; 5) Experiment in Onboard Synthetic Aperture Radar Data Processing; 6) Microfabrication of a High-Throughput Nanochannel Delivery/Filtration System; 7) Improved Design and Fabrication of Hydrated-Salt Pills; 8) Monolithic Flexure Pre-Stressed Ultrasonic Horns; 9) Cryogenic Quenching Process for Electronic Part Screening; 10) Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions; 11) Wheel-Based Ice Sensors for Road Vehicles; 12) G-DYN Multibody Dynamics Engine; 13) Multibody Simulation Software Testbed for Small-Body Exploration and Sampling; 14) Propulsive Reaction Control System Model; 15) Licklider Transmission Protocol Implementation; 16) Core Recursive Hierarchical Image Segmentation; 17) Two-Stage Centrifugal Fan; 18) Combined Structural and Trajectory Control of Variable-Geometry Planetary Entry Systems; 19) Pressure Regulator With Internal Ejector Circulation Pump, Flow and Pressure Measurement Porting, and Fuel Cell System Integration Options; 20) Temperature-Sensitive Coating Sensor Based on Hematite; 21) Standardization of a Volumetric Displacement Measurement for Two-Body Abrasion Scratch Test Data Analysis; 22) Detection of Carbon Monoxide Using Polymer-Carbon Composite Films; 23) Substituted Quaternary Ammonium Salts Improve Low-Temperature Performance of Double-Layer Capacitors; 24) Sustainably Sourced, Thermally Resistant, Radiation Hard Biopolymer; 25) Integrated Lens Antennas for Multi-Pixel Receivers; 26) 180-GHz Interferometric Imager; 27) Maturation of Structural Health Management Systems for Solid Rocket Motors; 28) Validating Phasing and Geometry of Large Focal Plane Arrays; 29) Transverse Pupil Shifts for Adaptive Optics Non-Common Path Calibration; 30) Qualification of Fiber Optic Cables for Martian Extreme Temperature Environments; 31) Solid-State Spectral Light Source System; 32) Multiple-Event, Single-Photon Counting Imaging Sensor; 33) Surface Modeling to Support Small-Body Spacecraft Exploration and Proximity Operations; and 34) Achieving Exact and Constant Turnaround Ratio in a DDS-Based Coherent Transponder.

Source record↗

Packing the PLSS

NASA Engineers design spacesuits for ultimate protection and functionality in the extreme environment of space. The spacesuit is often referred to as a "personal spacecraft" because it provides the astronaut with everything he or she needs to survive and work in space outside of the vehicle or habitat. The systems within the spacesuit include the pressure garment system (PGS), the Portable Life Support System (PLSS), and the power, avionics, and software (PAS) system. These elements are necessary to protect crewmembers and allow them to work effectively in the pressure and temperature extremes of space environments. Development of the spacesuit system is necessary to support future human extravehicular exploration activities to Lunar, Martian, microgravity, and possibly other space destinations. Although all the systems that makeup the space suit are important, the PLSS is one of the most complex. The PLSS provides the life support needed by the astronaut and consists of the oxygen (O2) subsystem, ventilation subsystem, and thermal control subsystem. Within each subsystem, there are many different components, a few of which are explained as follows. The oxygen tanks hold the oxygen that the crewmember uses to breath and pressurizes the suit. The primary oxygen tank is responsible during normal operations and the secondary oxygen tank kicks on in the case of an emergency. The Rapid Cycle Amine (RCA) canister is used to remove the carbon dioxide (CO2) and extra humidity in the crewmember's ventilation/breathing gas. The fan moves the oxygen around the suit. Suit Water Membrane Evaporator (SWME) is used within the thermal control loop to cool the water that is used to maintain a comfortable temperature for both the crew member and the other equipment inside the suit. Another component is the battery, which supplies the power needed to operate all these and the many other pieces. The battery is one of the biggest and heavies components within the PLSS. These are just a few of the components that encompass the PLSS. Each component has a weight and a certain volume that the NASA Engineers must take into account when building the PLSS, because the weight and volumes affect the crewmembers center of gravity (CG). [See the Notes Section for the link to an Apollo video that demonstrates the issues some of the crewmembers had picking up tools and dealing with center of gravity/tools on the surface of the Moon.] In this activity, students will simulate engineering design techniques that NASA Engineers and Designers are currently implementing to configuring the components within the PLSS. Through testing, students will consider the comfort, mobility, and center of gravity for their test subjects and how that changes after adjusting the placement of their simulated PLSS components.

Jennings, Mallory↗

NASA Tech Briefs, June 2011

Topics covered include: Wind and Temperature Spectrometry of the Upper Atmosphere in Low-Earth Orbit; Health Monitor for Multitasking, Safety-Critical, Real-Time Software; Stereo Imaging Miniature Endoscope; Early Oscillation Detection Technique for Hybrid DC/DC Converters; Parallel Wavefront Analysis for a 4D Interferometer; Schottky Heterodyne Receivers With Full Waveguide Bandwidth; Carbon Nanofiber-Based, High-Frequency, High-Q, Miniaturized Mechanical Resonators; Ultracapacitor-Based Uninterrupted Power Supply System; Coaxial Cables for Martian Extreme Temperature Environments; Using Spare Logic Resources To Create Dynamic Test Points; Autonomous Coordination of Science Observations Using Multiple Spacecraft; Autonomous Phase Retrieval Calibration; EOS MLS Level 1B Data Processing Software, Version 3; Cassini Tour Atlas Automated Generation; Software Development Standard Processes (SDSP); Graphite Composite Panel Polishing Fixture; Material Gradients in Oxygen System Components Improve Safety; Ridge Waveguide Structures in Magnesium-Doped Lithium Niobate; Modifying Matrix Materials to Increase Wetting and Adhesion; Lightweight Magnetic Cooler With a Reversible Circulator; The Invasive Species Forecasting System; Method for Cleanly and Precisely Breaking Off a Rock Core Using a Radial Compressive Force; Praying Mantis Bending Core Breakoff and Retention Mechanism; Scoring Dawg Core Breakoff and Retention Mechanism; Rolling-Tooth Core Breakoff and Retention Mechanism; Vibration Isolation and Stabilization System for Spacecraft Exercise Treadmill Devices; Microgravity-Enhanced Stem Cell Selection; Diagnosis and Treatment of Neurological Disorders by Millimeter-Wave Stimulation; Passive Vaporizing Heat Sink; Remote Sensing and Quantization of Analog Sensors; Phase Retrieval for Radio Telescope and Antenna Control; Helium-Cooled Black Shroud for Subscale Cryogenic Testing; Receive Mode Analysis and Design of Microstrip Reflectarrays; and Chance-Constrained Guidance With Non-Convex Constraints.

Source record↗

Planar, longitudinal, compressive waves in solids: Thermodynamics and uniaxial strain restrictions

A new tri-axial pressure-based constitutive expression has been found using Cauchy's stress tensor. This stress state emphasizes pressure and shear stress. The description is a pressure plus an effective shear stress allowing for a constitutive law based on atomic solid-state phase changes in crystalline cells due to pressure plus shear-based dislocation motion commonly associated with plasticity. Pressure has a new role in the material's constitutive response as it is separated from plasticity. The thermo-mechanical system describes third-order Gibbs’ expressions without specific volume restrictions placed upon the material. Isothermally, the ratio of heat to shear work in elastic copper is shown to approach zero at a very low temperature and become larger than one as temperature approaches melting. Wave compression models investigated are elastic and plastic: in fully elastic materials, the planar wave is restricted by Poisson's effect although plastic shear changes this constraint. Plastic deformation, dominated by dissipative shear stresses in uniaxial strain, heats the material while excluding phase changes from hydrostatic pressures. The material properties per se across Hugoniot shocks are described with entropy concepts. Shock waves are exceedingly complex since the constitutive laws are linked at extreme temperatures, pressures, and shear stresses. Isothermal, isentropic, isochoric, and iso-shear conditions are used throughout with Jacobian algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗