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NASA NTRS2016

Exergy Based Analysis for the Environmental Control and Life Support Systems of the International Space Station

When optimizing the performance of complex systems, a logical area for concern is improving the efficiency of useful energy. The energy available for a system to perform work is defined as a system's energy content. Interactions between a system's subsystems and the surrounding environment can be accounted for by understanding various subsystem energy efficiencies. Energy balance of reactants and products, and enthalpies and entropies, can be used to represent a chemical process. Heat transfer energy represents heat loads, and flow energy represents system flows and filters. These elements allow for a system level energy balance. The energy balance equations are developed for the subsystems of the Environmental Control and Life Support (ECLS) system aboard the International Space Station (ISS). The use of these equations with system information would allow for the calculation of the energy efficiency of the system, enabling comparisons of the ISS ECLS system to other systems as well as allows for an integrated systems analysis for system optimization.

Clem, Kirk A.↗

NASA NTRS1976

A reliability-based cost effective fail-safe design procedure

The authors have developed a methodology for cost-effective fatigue design of structures subject to random fatigue loading. A stochastic model for fatigue crack propagation under random loading has been discussed. Fracture mechanics is then used to estimate the parameters of the model and the residual strength of structures with cracks. The stochastic model and residual strength variations have been used to develop procedures for estimating the probability of failure and its changes with inspection frequency. This information on reliability is then used to construct an objective function in terms of either a total weight function or cost function. A procedure for selecting the design variables, subject to constraints, by optimizing the objective function has been illustrated by examples. In particular, optimum design of stiffened panel has been discussed.

Hanagud, S.↗

NASA NTRS1991

Measurements and mechanisms of localized aqueous corrosion in aluminum-lithium-copper alloys

Summary information is included for electrochemical aspects of stress corrosion cracking in alloy 2090 and an introduction to the work to be initiated on the new X2095 (Weldalite) alloy system. Stress corrosion cracking (SCC) was studied in both S-T and L-T orientations in alloy 2090. A constant load TTF test was performed in several environments with a potentiostatically applied potential. In the same environments the electrochemical behavior of phases found along subgrain boundaries was assessed. It was found that rapid failure due to SCC occurred when the following criteria was met: E(sub BR,T1) is less than E(sub applied) is less than E(sub Br, matrix phase). Although the L-T orientation is usually considered more resistant to SCC, failures in this orientation occurred when the stated criteria was met. This may be due to the relatively isotropic geometry of the subgrains which measure approximately 12 to 25 microns in diameters. Initial studies of alloy X2095 includes electrochemical characterization of three compositional variations each at three temperatures. The role of T(sub 1) dissolution in SCC behavior is addressed using techniques similar to those used in the research of 2090 described. SCC susceptibility is also studied using alternate immersion facilities at Reynolds Metals Corporation. Pitting is investigated in terms of stability, role of precipitate phases and constituent particles, and as initiation sites for SCC. In all research endeavors, attempts are made to link electrochemistry to microstructure. Previous work on 2090 provides a convenient basis for comparison since both alloys contain T(sub 1) precipitates but with different distributions. In 2090 T(sub 1) forms preferentially on subgrain boundaries whereas in X2095 the microstructure appears to be more homogeneous with finer T(sub 1) particles. Another point for comparison is the delta prime strengthening phase found in 2090 but absent in X2095.

Wall, Douglas↗

NASA NTRS1993

Space research on organs and tissues

Studies in space on various physiological systems have and will continue to provide valuable information on how they adapt to reduced gravitational conditions, and how living in a 1 g (gravity) environment has guided their development. Muscle and bone are the most notable tissues that respond to unweighting caused by lack of gravity. The function of specific muscles and bones relates directly to mechanical loading, so that removal of 'normal forces' in space, or in bedridden patients, causes dramatic loss of tissue mass. The cardiovascular system is also markedly affected by reduced gravity. Adaptation includes decreased blood flow to the lower extremities, thus decreasing the heart output requirement. Return to 1 g is associated with a period of reconditioning due to the deconditioning that occurs in space. Changes in the cardiovascular system are also related to responses of the kidney and certain endocrine (hormone-producing) organs. Changes in respiratory function may also occur, suggesting an effect on the lungs, though this adaptation is poorly understood. The neurovestibular system, including the brain and organs of the inner ear, must adapt to the disorientation caused by lack of gravity. Preliminary findings have been reported for liver. Additionally, endocrine organs responsible for release of hormones such as insulin, growth hormone, glucocorticoids, and thyroid hormone may respond to spaceflight.

Tischler, Marc E.↗

NASA NTRS2004

Preliminary Assessment of Mars Exploration Rover Landing Site Predictions

Selection of the Mars Exploration Rover (MER) landing sites took place over a three year period in which engineering constraints were identified, 155 possible sites were downselected to the final two, surface environments and safety considerations were developed, and the potential science return at the sites was considered. Landing sites in Gusev crater and Meridiani Planum were selected because they appeared acceptably safe for MER landing and roving and had strong morphologic and mineralogical indicators of liquid water in their past and thus appeared capable of addressing the science objectives of the MER missions, which are to determine the aqueous, climatic, and geologic history of sites on Mars where conditions may have been favorable to the preservation of evidence of possible pre-biotic or biotic processes. Engineering constraints important to the selection included: latitude (10 N-15 S) for maximum solar power; elevation (<-1.3 km) for sufficient atmosphere to slow the lander; low horizontal winds, shear and turbulence in the last few kilometers to minimize horizontal velocity; low 10-m scale slopes to reduce airbag spinup and bounce; moderate rock abundance to reduce abrasion or stroke-out of the airbags; and a radar-reflective, load-bearing and trafficable surface safe for landing and roving that is not dominated by fine-grained dust. In selecting the MER landing sites these engineering constraints were addressed via comprehensive evaluation of surface and atmospheric characteristics from existing remote sensing data and models as well as targeted orbital information acquired from Mars Global Surveyor and Mars Odyssey. This evaluation resulted in a number of predictions of the surface characteristics of the sites, which are tested in this abstract. Relating remote sensing signatures to surface characteristics at landing sites allows these sites to be used as ground truth for the orbital data, is essential for selecting and validating landing sites for future missions, and is required for correctly interpreting the surfaces and materials globally present on Mars.

Golombek, M.↗

NASA NTRS2005

Overview of Biomineralization and Nanobacteria

Biomineralization is a frequently used term in nanotechnology, astrobiology, geology, and medicine. In the process of biomineralization, a living organism provides a chemical environment that controls the nucleation and growth of unique mineral phases. Often these materials exhibit hierarchical structural order, leading to superior physical properties, not found either in their inorganic counterparts or in synthetic materials. Biomineralization is widespread in the biosphere and hundreds of different minerals are produced or assisted by a variety of organisms from bacteria to humans. Teeth, bones, kidney stones, and skeletons of algae, mussels, and magnetotactic bacteria are all examples of biomineralization. We do not fully understand the control mechanism of biomineralization either in primitive or in developed organisms. The presence of organic molecules, among other characteristics, can influence the coherence length for X-ray scattering in biogenic crystals. Control over biomineral properties can be accomplished at a myriad of levels, including the regulation of particle size, shape, crystal orientation, polymorphic structure, defect texture, and particle assembly. In the latter case, cellular processes enable control in both the spatial and temporal domain in such a way that hierarchical composite structures can be built which increase the toughness and durability of the material, which is invaluable for load-bearing materials such as bones, teeth, mollusk shells, etc. Durability of biominerals produces remarkably preserved bacterial and cyanobacterial microfossils from billions of years-old samples. The differentiation between microfossils and nonbiogenic artifacts has been a lively discussion subject in astrobiology especially in the last decade. Clearly, more detailed information on the mechanism of biomineralization, and the effect of organic matter on crystal formation/fossilization would help focus such discussions.

Ciftcioglu, N.↗

NASA NTRS2022

International Docking System Standard (IDSS) Interface Definition Document (IDD) Revision F

This IDSS IDD details the physical geometric mating interface and design loads requirements. The physical geometric interface requirements must be strictly followed to ensure physical spacecraft mating compatibility. This includes both defined components and areas that are void of components. The IDD also identifies common design parameters as identified in Section 3.0, e.g., docking initial conditions and vehicle mass properties. This information represents a recommended set of design values enveloping a broad set of design reference missions and conditions, which if accommodated in the docking system design, increases the probability of successful docking between different spacecraft.

Stanley R Donahoe↗

NASA NTRS2018

Efficacy of FTIR Analysis in Determining CO2 Loading on Diglycolamine

In support of advanced air revitalization technologies to enable human spaceflight beyond low earth orbit, performance studies have been conducted using a liquid amine, Diglycolamine (DGA) between teams at NASA's Johnson Spaceflight Center (JSC) and Ames Research Center (ARC). Liquid amines have been used in regenerable earth-based systems to remove CO2 from industrial systems as well as for closed-environment air revitalization because they can be regenerated at lower temperatures than solid sorbent systems. As an additional advantage to solid sorbent-based systems, liquid sorbents can be cycled between an adsorbing contactor and degassing chamber, thereby reducing system complexity by operation in a continuous loop. In an effort to inform a regeneration system design for micro-gravity applications, ARC has performed a number of tests to characterize the degas mechanics of DGA. In order to accurately measure the amount of CO2 captured or released by the amine, methods such as gravimetric weighing and chemical desorption are reasonable, however the first iteration test setup for a scaled down degas system required analysis on small sample sizes. Fourier-transform infrared spectroscopy (FTIR) analysis was experimentally evaluated to analyze CO2 concentration because it can produce measurements with sample sizes on the order of 100's of μL. Calibration against chemical desorption showed relatively good correlation and test data showed reasonable adherence to expected trends, however more extensive testing should be conducted to fully validate the usage of FTIR to determine CO2 loading on DGA.

Diglycolamine↗

NASA NTRS2008

Update on Development of SiC Multi-Chip Power Modules

Progress has been made in a continuing effort to develop multi-chip power modules (SiC MCPMs). This effort at an earlier stage was reported in 'SiC Multi-Chip Power Modules as Power-System Building Blocks' (LEW-18008-1), NASA Tech Briefs, Vol. 31, No. 2 (February 2007), page 28. The following recapitulation of information from the cited prior article is prerequisite to a meaningful summary of the progress made since then: 1) SiC MCPMs are, more specifically, electronic power-supply modules containing multiple silicon carbide power integrated-circuit chips and silicon-on-insulator (SOI) control integrated-circuit chips. SiC MCPMs are being developed as building blocks of advanced expandable, reconfigurable, fault-tolerant power-supply systems. Exploiting the ability of SiC semiconductor devices to operate at temperatures, breakdown voltages, and current densities significantly greater than those of conventional Si devices, the designs of SiC MCPMs and of systems comprising multiple SiC MCPMs are expected to afford a greater degree of miniaturization through stacking of modules with reduced requirements for heat sinking; 2) The stacked SiC MCPMs in a given system can be electrically connected in series, parallel, or a series/parallel combination to increase the overall power-handling capability of the system. In addition to power connections, the modules have communication connections. The SOI controllers in the modules communicate with each other as nodes of a decentralized control network, in which no single controller exerts overall command of the system. Control functions effected via the network include synchronization of switching of power devices and rapid reconfiguration of power connections to enable the power system to continue to supply power to a load in the event of failure of one of the modules; and, 3) In addition to serving as building blocks of reliable power-supply systems, SiC MCPMs could be augmented with external control circuitry to make them perform additional power-handling functions as needed for specific applications. Because identical SiC MCPM building blocks could be utilized in such a variety of ways, the cost and difficulty of designing new, highly reliable power systems would be reduced considerably. This concludes the information from the cited prior article. The main activity since the previously reported stage of development was the design, fabrication, and testing a 120- VDC-to-28-VDC modular power-converter system composed of eight SiC MCPMs in a 4 (parallel)-by-2 (series) matrix configuration, with normally-off controllable power switches. The SiC MCPM power modules include closed-loop control subsystems and are capable of operating at high power density or high temperature. The system was tested under various configurations, load conditions, load-transient conditions, and failure-recovery conditions. Planned future work includes refinement of the demonstrated modular system concept and development of a new converter hardware topology that would enable sharing of currents without the need for communication among modules. Toward these ends, it is also planned to develop a new converter control algorithm that would provide for improved sharing of current and power under all conditions, and to implement advanced packaging concepts that would enable operation at higher power density.

Lostetter, Alexander↗

NASA NTRS1978

Energy consumption program: A computer model simulating energy loads in buildings

The JPL energy consumption computer program developed as a useful tool in the on-going building modification studies in the DSN energy conservation project is described. The program simulates building heating and cooling loads and computes thermal and electric energy consumption and cost. The accuracy of computations are not sacrificed, however, since the results lie within + or - 10 percent margin compared to those read from energy meters. The program is carefully structured to reduce both user's time and running cost by asking minimum information from the user and reducing many internal time-consuming computational loops. Many unique features were added to handle two-level electronics control rooms not found in any other program.

Stoller, F. W.↗

NASA NTRS1985

A global model of carbon-nutrient interactions

The global biogeochemical model presented has two primary objectives. First, it characterizes natural elemental cycles and their linkages for the four elements significant to Earth's biota: C, N, S, and P. Second, it describes changes in these cycles due to human activity. Global nutrient cycles were studied within the drainage basins of several major world rivers on each continent. The initial study region was the Mississippi drainage basin, concentrating on carbon and nitrogen. The model first establishes the nutrient budgets of the undisturbed ecosystems in a study region. It then uses a data set of land use histories for that region to document the changes in these budgets due to land uses. Nutrient movement was followed over time (1800 to 1980) for 30 ecosystems and 10 land use categories. A geographically referenced ecological information system (GREIS) was developed to manage the digital global data bases of 0.5 x 0.5 grid cells needed to run the model: potential vegetation, drainage basins, precipitation, runoff, contemporary land cover, and FAO soil maps of the world. The results show the contributions of land use categories to river nutrient loads on a continental scale; shifts in nutrient cycling patterns from closed, steady state systems to mobile transient or open, steady state systems; soil organic matter depletion patterns in U.S. agricultural lands; changing nutrient ratios due to land use changes; and the effect of using heavy fertilizer on aquatic systems.

Moore, Berrien, III↗

NASA NTRS2014

Engine Power Turbine and Propulsion Pod Arrangement Study

A study has been conducted for NASA Glenn Research Center under contract NNC10BA05B, Task NNC11TA80T to identify beneficial arrangements of the turboshaft engine, transmissions and related systems within the propulsion pod nacelle of NASA's Large Civil Tilt-Rotor 2nd iteration (LCTR2) vehicle. Propulsion pod layouts were used to investigate potential advantages, disadvantages, as well as constraints of various arrangements assuming front or aft shafted engines. Results from previous NASA LCTR2 propulsion system studies and tasks performed by Boeing under NASA contracts are used as the basis for this study. This configuration consists of two Fixed Geometry Variable Speed Power Turbine Engines and related drive and rotor systems (per nacelle) arranged in tilting nacelles near the wing tip. Entry-into-service (EIS) 2035 technology is assumed for both the engine and drive systems. The variable speed rotor system changes from 100 percent speed for hover to 54 percent speed for cruise by the means of a two speed gearbox concept developed under previous NASA contracts. Propulsion and drive system configurations that resulted in minimum vehicle gross weight were identified in previous work and used here. Results reported in this study illustrate that a forward shafted engine has a slight weight benefit over an aft shafted engine for the LCTR2 vehicle. Although the aft shafted engines provide a more controlled and centered CG (between hover and cruise), the length of the long rotor shaft and complicated engine exhaust arrangement outweighed the potential benefits. A Multi-Disciplinary Analysis and Optimization (MDAO) approach for transmission sizing was also explored for this study. This tool offers quick analysis of gear loads, bearing lives, efficiencies, etc., through use of commercially available RomaxDESIGNER software. The goal was to create quick methods to explore various concept models. The output results from RomaxDESIGNER have been successfully linked to Boeing spreadsheets that generate gear tooth geometry in Catia 3D environment. Another initial goal was to link information from RomaxDESIGNER (such as hp, rpm, gear ratio) to populate Boeing's parametric weight spreadsheet and create an automated method to estimate drive system weight. This was only partially achieved due to the variety of weight models, number of manual inputs, and qualitative assessments required. A simplified weight spreadsheet was used with data inputs from RomaxDESIGNER along with manual inputs to perform rough weight calculations.

Robuck, Mark↗

NASA NTRS2013

Aerodynamic Characterization of New Parachute Configurations for Low-Density Deceleration

The Low Density Supersonic Decelerator project performed a wind tunnel experiment on the structural design and geometric porosity of various sub-scale parachutes in order to inform the design of the 110ft nominal diameter flight test canopy. Thirteen different parachute configurations, including disk-gap-band, ring sail, disk sail, and star sail canopies, were tested at the National Full-scale Aerodynamics Complex 80- by 120-foot Wind Tunnel at NASA Ames Research Center. Canopy drag load, dynamic pressure, and canopy position data were recorded in order to quantify there lative drag performance and stability of the various canopies. Desirable designs would yield increased drag above the disk-gap-band with similar, or improved, stability characteristics. Ring sail parachutes were tested at geometric porosities ranging from 10% to 22% with most of the porosity taken from the shoulder region near the canopy skirt. The disk sail canopy replaced the rings lot portion of the ring sail canopy with a flat circular disk and wastested at geometric porosities ranging from 9% to 19%. The star sail canopy replaced several ringsail gores with solid gores and was tested at 13% geometric porosity. Two disk sail configurations exhibited desirable properties such as an increase of 6-14% in the tangential force coefficient above the DGB with essentially equivalent stability. However, these data are presented with caveats including the inherent differences between wind tunnel and flight behavior and qualitative uncertainty in the aerodynamic coefficients.

parachute↗

NASA NTRS2020

Inversion of multiangular polarimetric measurements from the ACEPOL campaign: an application of improving aerosol property and hyperspectral ocean color retrievals

NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, scheduled for launch in the time frame of late 2022 to early 2023, will carry the Ocean Color Instrument (OCI), a hyperspectral scanning radiometer, and two multiangle polarimeters (MAPs), the UMBC Hyper-Angular Rainbow Polarimeter 2 (HARP2) and the SRON Spectro-Polarimeter for Planetary EXploration one (SPEXone). One purpose of the PACE MAPs is to better characterize aerosol properties, which can then be used to improve atmospheric correction for the retrieval of ocean color in coastal waters. Though this is theoretically promising, the use of MAP data in the atmospheric correction of colocated hyperspectral ocean color measurements have not yet been well demonstrated. In this work, we performed aerosol retrievals using the MAP measurements from the Research Scanning Polarimeter (RSP) and demonstrate its application to the atmospheric correction of hyperspectral radiometric measurements from SPEX airborne. Both measurements were collected on the same aircraft from the Aerosol Characterization from Polarimeter and Lidar (ACEPOL) field campaign in 2017. Two cases over ocean with small aerosol loading (aerosol optical depth ∼0.04) are identified including colocated RSP and SPEX airborne measurements and Aerosol Robotic Network (AERONET) ground-based observations. The aerosol retrievals are performed and compared with two options: one uses reflectance measurement only and the other uses both reflectance and polarization. It is demonstrated that polarization information helps reduce the uncertainties of aerosol microphysical and optical properties. The retrieved aerosol properties are then used to compute the contribution of atmosphere and ocean surface for atmospheric correction over the discrete bands from RSP measurements and the hyperspectral SPEX airborne measurements. The water-leaving signals determined this way are compared with both AERONET and Moderate Resolution Imaging Spectroradiometer (MODIS) ocean color products for performance analysis. The results and lessons learned from this work will provide a basis to fully exploit the information from the unique combination of sensors on PACE for aerosol characterization and ocean ecosystem research.

Meng Gao↗

NASA NTRSDate not supplied

Validation of Self-Scheduling Countermeasures in NASA's HERA Campaign 6

Enhancing crew capabilities for planning and scheduling activities is critical for periods of increased crew autonomy in future long-duration missions where communication delays preclude real-time ground support from Earth. Our study focuses on how to empower astronauts to manage their timelines independently from the experts in the mission control center (MCC). Our objective was to evaluate the impact of scheduling countermeasures on crew scheduling performance, workload, and usability in an analog mission environment. The study involved 16 crew members across four missions in the Limited Autonomy phase of Human Exploration Research Analog (HERA) Campaign 6. Crew members used Playbook to schedule one operational day for the entire crew. Half the participants accessed scheduling aids, and we compared their performance to a control group with no aids. Performance, workload, and usability were assessed using time on task, violation counts, NASA Task Load Index (NASA-TLX), and System Usability Scale (SUS). Participants using scheduling aids completed sessions 20% faster and committed 33% fewer violations. While these differences were not statistically significant due to the study’s operational limitations, trends indicate that scheduling aids may reduce errors and improve efficiency. These results can inform the design of scheduling tools to enhance astronauts’ autonomy in long-duration space missions, contributing to improved crew performance and reduced reliance on ground support.

space robotics↗

NASA NTRSDate not supplied

Validation of Self-Scheduling Countermeasures in NASA's HERA Campaign 6

space robotics↗

NASA NTRS2013

The Digital Astronaut Project Computational Bone Remodeling Model (Beta Version) Bone Summit Summary Report

Under the conditions of microgravity, astronauts lose bone mass at a rate of 1% to 2% a month, particularly in the lower extremities such as the proximal femur [1-3]. The most commonly used countermeasure against bone loss in microgravity has been prescribed exercise [4]. However, data has shown that existing exercise countermeasures are not as effective as desired for preventing bone loss in long duration, 4 to 6 months, spaceflight [1,3,5,6]. This spaceflight related bone loss may cause early onset of osteoporosis to place the astronauts at greater risk of fracture later in their lives. Consequently, NASA seeks to have improved understanding of the mechanisms of bone demineralization in microgravity in order to appropriately quantify this risk, and to establish appropriate countermeasures [7]. In this light, NASA's Digital Astronaut Project (DAP) is working with the NASA Bone Discipline Lead to implement well-validated computational models to help predict and assess bone loss during spaceflight, and enhance exercise countermeasure development. More specifically, computational modeling is proposed as a way to augment bone research and exercise countermeasure development to target weight-bearing skeletal sites that are most susceptible to bone loss in microgravity, and thus at higher risk for fracture. Given that hip fractures can be debilitating, the initial model development focused on the femoral neck. Future efforts will focus on including other key load bearing bone sites such as the greater trochanter, lower lumbar, proximal femur and calcaneus. The DAP has currently established an initial model (Beta Version) of bone loss due to skeletal unloading in femoral neck region. The model calculates changes in mineralized volume fraction of bone in this segment and relates it to changes in bone mineral density (vBMD) measured by Quantitative Computed Tomography (QCT). The model is governed by equations describing changes in bone volume fraction (BVF), and rates of changes in bone cell populations that remove and replace bone in packets within the bone region. The DAP bone model is unique in several respects. In particular in takes former models of volume fraction changes one step higher in fidelity and separates BVF into separate equations for mineralized and osteoid volume fractions governed by a mineralization rate. This more closely follows the physiology of the remodeling unit cycles where bone is first resorbed and then followed by the action of osteoblasts to lay down collagen matrix which eventually becomes mineralized. In another respect, the modules allow the functional description of the time rate of change of other parameters and variables in the model during a computational simulation. More detailed description of the model, preliminary validation results, current limitation and caveats, and planned advancements are provided in sections 2 through 5. The DAP bone model is being developed primarily as a research tool, and not as a clinical tool like QCT. Even if it transitions to a clinical tool, it is not intended to replace QCT or any other clinical tool. Moreover, the DAP bone model does not predict bone fracture. Its purpose is to provide valuable additional data via "forward prediction" simulations for during and after spaceflight missions to gain insight on, (1) mechanisms of bone demineralization in microgravity, and (2) the volumetric changes at the various bone sites in response to in-flight and post-flight exercise countermeasures. This data can then be used as input to the Keyak [8] (or equivalent) FE analysis method to gain insight on how bone strength may change during and after flight. This information can also be useful to help optimize exercise countermeasure protocols to minimize changes in bone strength during flight, and improve regain of bone strength post-flight. To achieve this goal, the bone model will be integrated with DAP's exercise countermeasure models to simulate the effect of exercise prescriptions on preserving bone. More specifically, the model will accept loading history due to muscle and joint force on bone and produce quantified remodeling within the bone region under influence of the applied stress. Furthermore, because they tend to respond differently, the bone remodeling model includes both trabecular bone and cortical bone.

Pennline, James↗

NASA NTRS1974

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Osias, J. R.↗