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NASA NTRS2005

Instrumentation and Control Needs for Reliable Operation of Lunar Base Surface Nuclear Power Systems

As one of the near-term goals of the President's Vision for Space Exploration, establishment of a multi-person lunar base will require high-endurance power systems which are independent of the sun, and can operate without replenishment for several years. These requirements may be obtained using nuclear power systems specifically designed for use on the lunar surface. While it is envisioned that such a system will generally be supervised by humans, some of the evolutions required maybe semi or fully autonomous. The entire base complement for near-term missions may be less than 10 individuals, most or all of which may not be qualified nuclear plant operators and may be off-base for extended periods thus, the need for power system autonomous operation. Startup, shutdown, and load following operations will require the application of advanced control and health management strategies with an emphasis on robust, supervisory, coordinated control of, for example, the nuclear heat source, energy conversion plant (e.g., Brayton Energy Conversion units), and power management system. Autonomous operation implies that, in addition to being capable of automatic response to disturbance input or load changes, the system is also capable of assessing the status of the integrated plant, determining the risk associated with the possible actions, and making a decision as to the action that optimizes system performance while minimizing risk to the mission. Adapting the control to deviations from design conditions and degradation due to component failures will be essential to ensure base inhabitant safety and mission success. Intelligent decisions will have to be made to choose the right set of sensors to provide the data needed to do condition monitoring and fault detection and isolation because of liftoff weight and space limitations, it will not be possible to have an extensive set of instruments as used for earth-based systems. Advanced instrumentation and control technologies will be needed to enable this critical functionality of autonomous operation. It will be imperative to consider instrumentation and control requirements in parallel to system configuration development so as to identify control-related, as well as integrated system-related, problem areas early to avoid potentially expensive work-arounds . This paper presents an overview of the enabling technologies necessary for the development of reliable, autonomous lunar base nuclear power systems with an emphasis on system architectures and off-the-shelf algorithms rather than hardware. Autonomy needs are presented in the context of a hypothetical lunar base nuclear power system. The scenarios and applications presented are hypothetical in nature, based on information from open-literature sources, and only intended to provoke thought and provide motivation for the use of autonomous, intelligent control and diagnostics.

Turso, James↗
NASA NTRS2008

Instrumentation System Diagnoses a Thermocouple

An improved self-validating thermocouple (SVT) instrumentation system not only acquires readings from a thermocouple but is also capable of detecting deterioration and a variety of discrete faults in the thermocouple and its lead wires. Prime examples of detectable discrete faults and deterioration include open- and short-circuit conditions and debonding of the thermocouple junction from the object, the temperature of which one seeks to measure. Debonding is the most common cause of errors in thermocouple measurements, but most prior SVT instrumentation systems have not been capable of detecting debonding. The improved SVT instrumentation system includes power circuitry, a cold-junction compensator, signal-conditioning circuitry, pulse-width-modulation (PWM) thermocouple-excitation circuitry, an analog-to-digital converter (ADC), a digital data processor, and a universal serial bus (USB) interface. The system can operate in any of the following three modes: temperature measurement, thermocouple validation, and bonding/debonding detection. The software running in the processor includes components that implement statistical algorithms to evaluate the state of the thermocouple and the instrumentation system. When the power is first turned on, the user can elect to start a diagnosis/ monitoring sequence, in which the PWM is used to estimate the characteristic times corresponding to the correct configuration. The user also has the option of using previous diagnostic values, which are stored in an electrically erasable, programmable read-only memory so that they are available every time the power is turned on.

Perotti, Jose↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASA's Space Launch System

The development of the Space Launch System (SLS) launch vehicle requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The characteristics of these systems must be matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large complex systems engineering challenge being addressed in part by focusing on the specific subsystems handling of off-nominal mission and fault tolerance. Using traditional model based system and software engineering design principles from the Unified Modeling Language (UML), the Mission and Fault Management (M&FM) algorithms are crafted and vetted in specialized Integrated Development Teams composed of multiple development disciplines. NASA also has formed an M&FM team for addressing fault management early in the development lifecycle. This team has developed a dedicated Vehicle Management End-to-End Testbed (VMET) that integrates specific M&FM algorithms, specialized nominal and off-nominal test cases, and vendor-supplied physics-based launch vehicle subsystem models. The flexibility of VMET enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the algorithms utilizing actual subsystem models. The intent is to validate the algorithms and substantiate them with performance baselines for each of the vehicle subsystems in an independent platform exterior to flight software test processes. In any software development process there is inherent risk in the interpretation and implementation of concepts into software through requirements and test processes. Risk reduction is addressed by working with other organizations such as S&MA, Structures and Environments, GNC, Orion, the Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission and Loss of Crew probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and detection and responses that can be tested in VMET and confirm that responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - ARINC 653 partitioned OS, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM. The plan for VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by Flight Software. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure the effectiveness of M&FM algorithms performance in the FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗
NASA NTRS2008

NASA Tech Briefs, November 2008

Topics covered include: Digital Phase Meter for a Laser Heterodyne Interferometer; Vision System Measures Motions of Robot and External Objects; Advanced Precipitation Radar Antenna to Measure Rainfall From Space; Wide-Band Radar for Measuring Thickness of Sea Ice; Vertical Isolation for Photodiodes in CMOS Imagers; Wide-Band Microwave Receivers Using Photonic Processing; L-Band Transmit/Receive Module for Phase-Stable Array Antennas; Microwave Power Combiner/Switch Utilizing a Faraday Rotator; Compact Low-Loss Planar Magic-T; Using Pipelined XNOR Logic to Reduce SEU Risks in State Machines; Quasi-Optical Transmission Line for 94-GHz Radar; Next Generation Flight Controller Trainer System; Converting from DDOR SASF to APF; Converting from CVF to AAF; Documenting AUTOGEN and APGEN Model Files; Sequence History Update Tool; Extraction and Analysis of Display Data; MRO DKF Post-Processing Tool; Rig Diagnostic Tools; MRO Sequence Checking Tool; Science Activity Planner for the MER Mission; UAVSAR Flight-Planning System; Templates for Deposition of Microscopic Pointed Structures; Adjustable Membrane Mirrors Incorporating G-Elastomers; Hall-Effect Thruster Utilizing Bismuth as Propellant; High-Temperature Crystal-Growth Cartridge Tubes Made by VPS; Quench Crucibles Reinforced with Metal; Deep-Sea Hydrothermal-Vent Sampler; Mars Rocket Propulsion System; Two-Stage Passive Vibration Isolator; Improved Thermal Design of a Compression Mold; Enhanced Pseudo-Waypoint Guidance for Spacecraft Maneuvers; Altimetry Using GPS-Reflection/Occultation Interferometry; Thermally Driven Josephson Effect; Perturbation Effects on a Supercritical C7H16/N2 Mixing Layer; Gold Nanoparticle Labels Amplify Ellipsometric Signals; Phase Matching of Diverse Modes in a WGM Resonator; WGM Resonators for Terahertz-to-Optical Frequency Conversion; Determining Concentration of Nanoparticles from Ellipsometry; Microwave-to-Optical Conversion in WGM Resonators; Four-Pass Coupler for Laser-Diode-Pumped Solid-State Laser; Low-Resolution Raman-Spectroscopy Combustion Thermometry; Temperature Sensors Based on WGM Optical Resonators; Varying the Divergence of Multiple Parallel Laser Beams; Efficient Algorithm for Rectangular Spiral Search; Algorithm-Based Fault Tolerance Integrated with Replication; Targeting and Localization for Mars Rover Operations; Terrain-Adaptive Navigation Architecture; Self-Adjusting Hash Tables for Embedded Flight Applications; Schema for Spacecraft-Command Dictionary; Combined GMSK Communications and PN Ranging; System-Level Integration of Mass Memory; Network-Attached Solid-State Recorder Architecture; Method of Cross-Linking Aerogels Using a One-Pot Reaction Scheme; An Efficient Reachability Analysis Algorithm.

Source record↗
NASA NTRS2013

Vibration Based Sun Gear Damage Detection

Seeded fault experiments were conducted on the planetary stage of an OH-58C helicopter transmission. Two vibration based methods are discussed that isolate the dynamics of the sun gear from that of the planet gears, bearings, input spiral bevel stage, and other components in and around the gearbox. Three damaged sun gears: two spalled and one cracked, serve as the focus of this current work. A non-sequential vibration separation algorithm was developed and the resulting signals analyzed. The second method uses only the time synchronously averaged data but takes advantage of the signal/source mapping required for vibration separation. Both algorithms were successful in identifying the spall damage. Sun gear damage was confirmed by the presence of sun mesh groups. The sun tooth crack condition was inconclusive.

diagnostics↗
NASA NTRSDate not supplied

Repurposing Drilling Control Diagnostics for Subsurface Edge Detection and Boundary Advisement During Planetary Drilling

Informed decision-making during lunar drilling and sampling missions will require data monitoring tools and specialized ground data systems. Accurate and updated situational awareness, with ongoing data monitoring, is critical for timely responses by to incoming science data. Traverse plans and scheduled activities may need to be flexibly changed in order to react to unexpected data or situations. Unlike (for example) Mars missions, the relative lightspeed closeness of the Moon allows for near-real-time ground processing of incoming mission and instrument data. An Apollo-class lunar regolith drill will in a sense “travel” a meter or two vertically at a given subsurface characterization site. As the drill penetrates into lunar regolith, it is likely to encounter a range of material densities, orientations, fracture toughness, and (perhaps) ice percentages. Lunar drill telemetry can provide science teams with a valuable first look into the subsurface structure, the regolith bulk properties, and constituents at each drilled site. Real-time AI-based recognition and reaction to downhole situations has been developed for automated deeper drilling on Mars and beyond. We can leverage the same knowledge bases and pattern-matching as areal-time interpreter of the subsurface, a situational awareness tool during drilling operations. We recently (Sept. 2019) demonstrated this AI drilling monitoring and analysis capability, in control of in-situ drilling and sampling operations, mounted on a KREX-2 rover in Chile’s Atacama Desert. Terrestrial automated drilling log analyses in oil exploration have used similar machine learning techniques in classifying and identifying features in drilling logs –but these typically are designed assuming a drilling fluid influencing downhole measurements and data (permeability, resistivity). Drilling models and existing AI software designed to detect and respond to drilling faults and hard materials can be repurposed, for near-real-time (ground-based) interpretation of drilling telemetry –a potentially valuable advisory tool for strata boundaries and changes in drilling parameters. On the Moon, this approach could be used to study the structure and to some extent the composition of lunar regolith vs. borehole depth, based on recognizable variations in fracture hardness, drilling energy and penetration rates while actively drilling. Since the early 2000s, a series of increasingly-capable real-time drilling telemetry interpretation and characterization software tools have been developed. These subsurface models and software tools have monitored the real-time drilling data received, and automatically identified changes in drill behavior (e.g., encountering a harder target layer, bit inclusions, drill choking due to infall downhole, and others) correlating these with subsurface structures and features. We discuss the mappings between drill borehole parameters, faults or events detected, and modeled changes in rock layer boundaries, in examples drawn from field testing at analog sites in an Arctic impact crater, Rio Tinto, and Chile’s Atacama Desert. These demonstrate how subsurface structural boundaries led to fault detections and responses by the software.

drilling advisor↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASA's Space Launch System

The engineering development of the new Space Launch System (SLS) launch vehicle requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The characteristics of these spacecraft systems must be matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex system engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in specialized Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model based algorithms and their development lifecycle from inception through Flight Software certification are an important focus of this development effort to further insure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. NASA formed a dedicated M&FM team for addressing fault management early in the development lifecycle for the SLS initiative. As part of the development of the M&FM capabilities, this team has developed a dedicated testbed that integrates specific M&FM algorithms, specialized nominal and off-nominal test cases, and vendor-supplied physics-based launch vehicle subsystem models. Additionally, the team has developed processes for implementing and validating these algorithms for concept validation and risk reduction for the SLS program. The flexibility of the Vehicle Management End-to-end Testbed (VMET) enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS. The intent of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software development infrastructure and its related testing entities. In any software development process there is inherent risk in the interpretation and implementation of concepts into software through requirements and test cases into flight software compounded with potential human errors throughout the development lifecycle. Risk reduction is addressed by the M&FM analysis group working with other organizations such as S&MA, Structures and Environments, GNC, Orion, the Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission and Loss of Crew probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses that can be tested in VMET to ensure that failures can be detected, and confirm that responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - ARINC 653 partitioned OS, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by Flight Software. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure the effectiveness of M&FM algorithms performance in the FSW development and test processes.

Trevino, Luis↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASAs Space Launch System

The engineering development of the National Aeronautics and Space Administration's (NASA) new Space Launch System (SLS) requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The nominal and off-nominal characteristics of SLS's elements and subsystems must be understood and matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex systems engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model-based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model-based algorithms and their development lifecycle from inception through FSW certification are an important focus of SLS's development effort to further ensure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. To test and validate these M&FM algorithms a dedicated test-bed was developed for full Vehicle Management End-to-End Testing (VMET). For addressing fault management (FM) early in the development lifecycle for the SLS program, NASA formed the M&FM team as part of the Integrated Systems Health Management and Automation Branch under the Spacecraft Vehicle Systems Department at the Marshall Space Flight Center (MSFC). To support the development of the FM algorithms, the VMET developed by the M&FM team provides the ability to integrate the algorithms, perform test cases, and integrate vendor-supplied physics-based launch vehicle (LV) subsystem models. Additionally, the team has developed processes for implementing and validating the M&FM algorithms for concept validation and risk reduction. The flexibility of the VMET capabilities enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS, GNC, and others. One of the principal functions of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software test and validation processes. In any software development process there is inherent risk in the interpretation and implementation of concepts from requirements and test cases into flight software compounded with potential human errors throughout the development and regression testing lifecycle. Risk reduction is addressed by the M&FM group but in particular by the Analysis Team working with other organizations such as S&MA, Structures and Environments, GNC, Orion, Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission (LOM) and Loss of Crew (LOC) probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses to be tested in VMET to ensure reliable failure detection, and confirm responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - the ARINC 6535-partitioned Operating System, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by FSW. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure their effectiveness and performance in the exterior FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗
NASA NTRS1999

Simulating the Formation of Lunar Floor-Fracture Craters Using Elastoviscoplastic Relaxation

Lunar floor-fracture craters formed during the height of mare basalt emplacement. Due to a general temporal and spatial relation with the maria, these craters, numbering some 200, may be diagnostic of the thermal structure of the crust during this time. As the name suggests, these craters exhibit brittle failure, generally limited to the central floor region. That, and a shallower depth than fresh lunar craters, has led to two main theories as to their formation: laccolith emplacement under the crater and viscous relaxation. The implications of each model for the state of the Moon's crust during this time are quite different, so the viability of each model must be checked. Laccolith emplacement has been treated elsewhere. However, previous attempts to study the relaxation of the craters have assumed only a uniform, Newtonian viscous response of the near surface to the topographic driving forces, and simply postulated that the fractures resulted from tensile stresses associated with floor uplift. Here, we use a more sophisticated rheological model that includes not only non-Newtonian viscous behavior (i.e., the viscosity is stress-dependent), but also incorporates elastic behavior and a plastic component to the rheology to directly simulate the formation of the floor fractures. The results of our simulations show that while elastoviscoplastic relaxation is potentially viable for larger floor-fracture craters, it is not viable for craters with diameters < or = 60 km, the size of the majority of floor-fracture craters. We employ the finite element method, a numerical technique well suited for boundary-value problems, via the commercially available MARC software package. To test the viability of topographic relaxation, our goal is to prepare the simulations as to maximize the amount of relaxation. We take advantage of the natural axisymmetry of craters, simulating one radial plane. Initial shapes are based on data for fresh craters from Pike. To simplify implementation, a fourth order polynomial is used for the basin, while a third order inverse function is used for the rim. This form closely approximates the long-wavelength behavior of complex craters, while ignoring higher-frequency topography, save the rim. This approximation is appropriate because crater relaxation is strongly controlled by long-wavelength topography. Loading is accomplished assuming a uniform gravity field (1.62 m/s-square) and a uniform density of 2900 kg/cubic m. The initial stress state is set to be hydrostatic, with an additional pressure term to account for any overlying topography. This additional pressure term is tapered exponentially with depth. While the simulations quickly settle on a preferred stress state, and while the final solution is fairly insensitive to the choice of the e-folding depth of the taper, selecting an e-folding depth close to the diameter of the crater sets the initial stress state near the preferred state. We assume a diuranally averaged surface temperature of -20 C, and allow temperature to increase with depth at a rate of 50 K//km. Assuming a thermal conductivity of 2 W/in/K, this gradient translates to a heat flow of 100mW/square m, an extremely high value for the Moon. Temperature, of course, will not increase without bound. To maximize relaxation, we allow our temperature profile to increase linearly until it reaches the solidus (assumed to be 1200C) at a depth of 24.4 km, at which point it is kept constant. The presence of melt will drop the bulk viscosity; however, we have no rheological control for partial melts. Therefore, we make no attempt to simulate this situation. Elastoviscoplastic rheological model. In general, geologic materials can behave in three main ways: elastically, viscously (via solid-state creep), and brittly (plasticity is a continuum approach to simulate this phenomenon). We combine these three deformation mechanisms in an extended Maxwell solid, where the total strain can be broken down into a simple summation of the elastic, creep, and plastic strains. In relaxation phenomena in general, the system takes advantage of any means possible to eliminate deviatoric stresses by relaxing away the topography. Previous analyses have only modeled the viscous response. Comparatively, the elastic response in our model can augment the relaxation, to a point. This effect decreases as the elastic response becomes stiffer; indeed, in the limit of infinite elastic Young's modulus (and with no plasticity), the solution converges on the purely viscous solution. Igneous rocks common to the lunar near-surface have Young's modulii in the range of 10-100 GPa. To maximize relaxation, we use a Young's modulus of 10 GPa. (There is negligible sensitivity to the other elastic modulus, the Poisson's ratio; we use 0.25.) For the viscous response, we use a flow law for steady-state creep in thoroughly dried Columbia diabase, because the high plagioclase (about 70 vol%) and orthopyroxene (about 17 vol%) content is similar to the composition of the lunar highland crust as described by remote sensing and sample studies: noritic anorthosite. This flow law is highly non-Newtonian, i.e., the viscosity is highly stress dependent. That, and the variability with temperature, stands in strong contrast to previous examinations of lunar floor-fracture crater relaxation. To model discrete, brittle faulting, we assume "Byerlee's rule," a standard geodynamical technique. We implement this "rule" with an-angle of internal friction of about 40 deg, and a higher-than-normal cohesion of about 3.2 MPa (to approximate the breaking of unfractured rock). The actual behavior of geologic materials is more complex than in our rheological model, so the uncertainties in the plasticity do not represent the state-of-the-art error. Additional information is contained in the original.

Dombard, A. J.↗