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NASA NTRS2015

Evaluating Ammonium, Nitrate and Sulfate Aerosols in 3-Dimensions

The effect aerosols have on climate and air quality is a func-on of their chemical composi-on, concentra-on and spa-al distribu-on. These parameters are controlled by emissions, heterogeneous and homogeneous chemistry, where thermodynamics plays a key role, transport, which includes stratospheric-‐ tropospheric exchange, and deposi-onal sinks. In this work we demonstrate the effect of some of these processes on the SO4‐NH4‐NO3 system using the GISS ModelE2 Global Circula-on Model (GCM).

Aerosols↗

NASA NTRS2014

Implications of Arctic Sea Ice Decline for the Earth System

Arctic sea ice decline has led to an amplification of surface warming and is projected to continue to decline from anthropogenic forcing, although the exact timing of ice-free summers is uncertain owing to large natural variability. Sea ice reductions affect surface heating patterns and the atmospheric pressure distribution, which may alter midlatitude extreme weather patterns. Increased light penetration and nutrient availability during spring from earlier ice breakup enhances primary production in the Arctic Ocean and its adjacent shelf seas. Ice-obligate marine mammals may be losers, whereas seasonally migrant species may be winners from rapid sea ice decline. Tundra greening is occurring across most of the Arctic, driven primarily by warming temperatures, and is displaying complex spatial patterns that are likely tied to other factors. Sea ice changes are affecting greenhouse gas exchanges as well as halogen chemistry in the Arctic. This review highlights the heterogeneous nature of Arctic change, which is vital for researchers to better understand.

Decline↗

NASA NTRS1977

Characterization and Distribution of Lunar Mare Basalt Types Using Remote Sensing Techniques

The types of basal to be found on the moon were identified using reflectance spectra from a variety of lunar mare surfaces and craters as well as geochemical interpretations of laboratory measurements of reflectance from lunar, terrestrial, and meteoritic samples. Findings indicate that major basaltic units are not represented in lunar sample collections. The existence of late stage high titanium basalts is confirmed. All maria contain lateral variations of compositionally heterogenous basalts; some are vertically inhomogenous with distinctly different subsurface composition. Some basalt types are spectrally gradational, suggesting minor variations in composition. Mineral components of unsampled units can be defined if spectra are obtained with sufficient spectral coverage (.3 to 2.5 micron m) and spatial resolution (approximating .5 km).

Pieters, C.↗

NASA NTRSDate not supplied

New insights into PSCs from the nearly 17-year CALIPSO data record

Polar stratospheric clouds (PSCs) play important roles in stratospheric ozone depletion during winter and spring at high latitudes (e.g., the Antarctic ozone hole). PSC particles provide sites for heterogeneous reactions that convert stable chlorine reservoir species to radicals that destroy ozone catalytically. PSCs also prolong ozone depletion by delaying chlorine deactivation through the removal of gas-phase HNO3 and H2O by sedimentation of large nitric acid trihydrate (NAT) and ice particles. A more complete picture of PSC processes on vortex-wide scales has emerged from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) instrument on the CALIPSO satellite that has been observing PSCs at latitudes up to 82 degrees in both hemispheres since June 2006. This nearly 17-year data record has fundamentally improved our knowledge of PSC spatial and temporal distributions, composition, and formation processes. In this presentation, we provide a brief overview of the CALIOP PSC data record and highlight some of the recent advances in our understanding of PSC processes.

polar stratospheric clouds↗

NASA NTRS2022

Lightning Over Central Canada: Skill Assessment for Various Land-Atmosphere Model Configurations and Lightning Indices Over a Boreal Study Area

Current lightning predictions are uncertain because they rely on empirical diagnostic relationships and often use coarse-scale climate scenario simulations in which deep convection is parameterized. Previous studies demonstrated that simulations with convection permitting resolutions improve lightning predictions compared to coarser-grid simulations using convection parameterizations for different geographical locations but not over the boreal zone. In this study, lightning simulations with the NASA Unified-Weather Research and Forecasting (NU-WRF) model are evaluated over a domain including the Great Slave Lake in Canada, for six lightning seasons. The simulations are performed at convection parameterized (9 km) and convection-permitting (3 km) resolution using the Goddard 4ICE and the Thompson microphysics schemes. Four lightning indices are evaluated against observations from the Canadian Lightning Detection Network, in terms of spatiotemporal frequency distribution, spatial pattern, daily climatology, and an event-based overall skill assessment. The Thompson scheme is, regardless of the spatial resolution, superior to the Goddard 4ICE scheme in predicting daily climatology but worse in predicting the spatial patterns of lightning occurrence. Results indicate that lightning estimation benefits from modeling at convection-permitting resolution, in particular for the ice based lightning indices. In contrast, the product of convective available potential energy and precipitation rate proved to be the most robust index that was largely invariant to varying spatial resolution. Finally, this study reveals issues of the models to reproduce the observed spatial pattern of lightning well, which might be related to an insufficient representation of land surface heterogeneity, including peatlands, in the study area.

Jonas Mortelmans↗

NASA NTRS2017

Evaluation of Satellite Remote Sensing Albedo Retrievals over the Ablation Area of the Southwestern Greenland Ice Sheet

MODerate resolution Imaging Spectroradiometer (MODIS) albedo products have been validated over spatially uniform, snow-covered areas of the Greenland ice sheet (GrIS) using the so-called single 'point-to-pixel' method. This study expands on this methodology by applying a 'multiple-point-to-pixel' method and examination of spatial autocorrelation (here using semivariogram analysis) by using in situ observations, high-resolution World- View-2 (WV-2) surface reflectances, and MODIS Collection V006 daily blue-sky albedo over a spatially heterogeneous surfaces in the lower ablation zone in southwest Greenland. Our results using 232 ground-based samples within two MODIS pixels, one being more spatial heterogeneous than the other, show little difference in accuracy among narrow and broad band albedos (except for Band 2). Within the more homogenous pixel area, in situ and MODIS albedos were very close (error varied from −4% to +7%) and within the range of ASD standard errors. The semivariogram analysis revealed that the minimum observational footprint needed for a spatially representative sample is 30 m. In contrast, over the more spatially heterogeneous surface pixel, a minimum footprint size was not quantifiable due to spatial autocorrelation, and far exceeds the effective resolution of the MODIS retrievals. Over the high spatial heterogeneity surface pixel, MODIS is lower than ground measurements by 4-7%, partly due to a known in situ undersampling of darker surfaces that often are impassable by foot (e.g., meltwater features and shadowing effects over crevasses). Despite the sampling issue, our analysis errors are very close to the stated general accuracy of the MODIS product of 5%. Thus, our study suggests that the MODIS albedo product performs well in a very heterogeneous, low-albedo, area of the ice sheet ablation zone. Furthermore, we demonstrate that single 'point-to-pixel' methods alone are insufficient in characterizing and validating the variation of surface albedo displayed in the lower ablation area. This is true because the distribution of in situ data deviations from MODIS albedo show a substantial range, with the average values for the 10th and 90th percentiles being −0.30 and 0.43 across all bands. Thus, if only single point is taken for ground validation, and is randomly selected from either distribution tails, the error would appear to be considerable. Given the need for multiple in-situ points, concurrent albedo measurements derived from existing AWSs, (low-flying vehicles (airborne or unmanned) and high-resolution imagery (WV-2)) are needed to resolve high sub-pixel variability in the ablation zone, and thus, further improve our characterization of Greenland's surface albedo.

Ablation zone↗

NASA NTRS2015

9+ Years of CALIOP PSC Data: An Evolving Climatology

Polar stratospheric clouds (PSCs) play key roles in the springtime chemical depletion of ozone at high latitudes. PSC particles provide sites for heterogeneous chemical reactions that transform stable chlorine and bromine reservoir species into highly reactive ozone-destructive forms. Furthermore, large nitric acid trihydrate (NAT) PSC particles can irreversibly redistribute odd nitrogen through gravitational sedimentation, which prolongs the ozone depletion process by slowing the reformation of the stable chlorine reservoirs. However, there are still significant gaps in our understanding of PSC processes, particularly concerning the details of NAT particle formation. Spaceborne observations from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar on the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite are providing a rich new dataset for studying PSCs on unprecedented vortex-wide scales. In this paper, we examine the vertical and spatial distribution of PSCs in the Antarctic and Arctic on vortex-wide scales for entire PSC seasons over the more than nine-year data record.

Pitts, Michael C.↗

NASA NTRS1972

A simulation study exploring the effects of sensor spatial resolution on estimates of cloud cover from satellites.

Investigation of the effects of sensor spatial resolution on estimating the amount of clouds covering the earth by simulating various cloud distributions and sizes, and measuring the known cloud amount with resolution of different sizes using a cloud-no cloud threshold technique often applied in automatic data processing. Cloud amount statistics have been tabulated for a three-orders-of-magnitude range in the ratio (R) of areal cloud size to areal resolution size for seven cloud amounts between 6 and 90%. Three different cloud patterns were used. These were 1) a regularly spaced pattern of homogeneous dots arranged in rows and columns (to simulate cloud streets), 2) a randomly spaced pattern of the same dots (to simulate randomly oriented cumulus clouds), and 3) a heterogeneous cloud size distribution irregularly spaced (to simulate a view of different cloud types and sizes). Two cloud amount estimation techniques were tested. Cloud amounts of 100% (method 1) and 50% (method 2) were assigned to partially filled resolution elements. Using criteria applicable to some studies carried out in the past, it is shown that cloud amount estimations can be in error by as much as 86 and 38%, respectively, for the two methods. Nomograms have been developed which subtantially improve the estimate of the true cloud cover for R less than 100, provided that R can be determined.

Shenk, W. E.↗

NASA NTRS1997

Mineralogy of the Martian Surface: Crustal Composition to Surface Processes

The main results have been published in the refereed literature, and thus this report serves mainly to summarize the main findings and indicate where the detailed papers may be found. Reflectance spectroscopy has been an important tool for determining the mineralogic makeup of the near surface materials on Mars. Analysis of the spectral properties of the surface have demonstrated that these attributes are heterogeneous from the coarse spatial but high spectral resolution spectra obtained with telescopes to the high spatial but coarse spectral resolution Viking data (e.g. Arvidson et al., 1989; McEwen et al., 1989). Low albedo materials show strong evidence for the presence of igneous rock forming minerals while bright materials are generally interpreted as representing heavily altered crustal material. How these materials are physically and genetically related has important implications for understanding martian surface properties and processes, weathering histories and paths, and crustal composition. The goal of this research is to characterize the physical and chemical properties of low albedo materials on Mars and the relationship to intermediate and high albedo materials. Fundamental science questions to be pursued include: (1) the observed distributions of soil, rock, and dust a function of physical processes or weathering and (2) different stages of chemical and physical alteration fresh rock identified. These objectives will be addressed through detailed analyses and modelling of the ISM data from the Phobos-2 mission with corroborating evidence of surface composition and properties provided by data from the Viking mission.

Mustard, John F.↗

NASA NTRS2000

BOREAS RSS-8 BIOME-BGC SSA Simulation of Annual Water and Carbon Fluxes

The BOREAS RSS-8 team performed research to evaluate the effect of seasonal weather and landcover heterogeneity on boreal forest regional water and carbon fluxes using a process-level ecosystem model, BIOME-BGC, coupled with remote sensing-derived parameter maps of key state variables. This data set contains derived maps of landcover type and crown and stem biomass as model inputs to determine annual evapotranspiration, gross primary production, autotrophic respiration, and net primary productivity within the BOREAS SSA-MSA, at a 30-m spatial resolution. Model runs were conducted over a 3-year period from 1994-1996; images are provided for each of those years. The data are stored in binary image format. The data files are available on a CD-ROM (see document number 20010000884), or from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC).

Hall, Forrest G.↗

NASA NTRS2016

Impact of Spatial Sampling on Continuity of MODIS-VIIRS Land Surface Reflectance Products: A Simulation Approach

With the increasing need to construct long-term climate-quality data records to understand, monitor, and predict climate variability and change, it is vital to continue systematic satellite measurements along with the development of new technology for more quantitative and accurate observations. The Suomi National Polar-orbiting Partnership mission provides continuity in monitoring the Earths surface and its atmosphere in a similar fashion as the heritage MODIS instruments onboard the National Aeronautics and Space Administrations Terra and Aqua satellites. In this paper, we aim at quantifying the consistency of Aqua MODIS and Suomi-NPP Visible Infrared Imaging Radiometer Suite (VIIRS) Land Surface Reflectance (LSR) and NDVI products as related to their inherent spatial sampling characteristics. To avoid interferences from sources of measurement and/or processing errors other than spatial sampling, including calibration, atmospheric correction, and the effects of the bidirectional reflectance distribution function, the MODIS and VIIRSLSR products were simulated using the Landsat-8s Operational Land Imager (OLI) LSR products. The simulations were performed using the instruments point spread functions on a daily basis for various OLI scenes over a 16-day orbit cycle. It was found that the daily mean differences due to discrepancies in spatial sampling remain below 0.0015 (1) in absolute surface reflectance at subgranule scale (i.e., OLI scene size).We also found that the MODISVIIRS product intercomparisons appear to be minimally impacted when differences in the corresponding view zenith angles (VZAs) are within the range of -15deg to -35deg (VZA(sub v) - VZA(sub m)), where VIIRS and MODIS footprints resemble in size. In general, depending on the spatial heterogeneity of the OLI scene contents, per-grid-cell differences can reach up to 20.Further spatial analysis of the simulated NDVI and LSR products revealed that, depending on the user accuracy requirements for product intercomparisons, spatial aggregations may be used. It was found that if per-grid-cell differences on the order of 10(in LSR or NDVI) are tolerated, the product intercomparisons are expected to be immune from differences in spatial sampling.

VIIRS↗

NASA NTRSDate not supplied

TEMPERATURE CONSTRAINT OF THE MISTASTIN LAKE IMPACT STRUCTURE IMPACT MELT ROCKS

Impact melt is a product of hypervelocity cratering events formed by the instantaneous melting of near-surface target rocks. The temperatures of impact melt upon formation are believed to be superheated, vastly exceeding the liquidus temperature of igneous rocks formed via endogenic processes. However, quantitative understanding of the formation and duration of superheated temperatures remains incomplete. To date, only one datum on the hottest post-shock temperature (>2370 °C) has been derived by Timms et al. (2017) [1]. These authors studied the microstructures and crystallographic orientations preserved within a rim of vermicular ZrO2 of a zircon grain entrained within impact glass at the Mistastin Lake impact structure, Canada. Diagnostic crystallographic orientation indicated the presence of cubic zirconia, requiring a minimum temperature for the impact melt of >2370°C from the dissociation of zircon to cubic zirconia and liquid SiO2. With only one temperature datum, it cannot be stated whether the temperature of the impact melt sheet was homogenous across the entire structure or if the thermal history of the melt varied with spatial distribution. In this study, we present a preliminary investigation of 70 zircon grains, 22 of which exhibit rims of vermicular ZrO2 dissociation textures, similar to those studied by Timms et al. (2017). To acquire a more accurate temperature profile representative of impact melt, zircon crystals were collected from different types of impact melt bearing units, including additional samples of the impact glass studied by Timms et al. (2017). Of the 22 zircon grains with dissociation textures, at least 4 grains in the impact glass show diagnostic evidence of pre-existing cubic zirconia, and 1 grain from a glass-bearing breccia exhibits granular zircon textures, possible evidence of a transition from high-P to high-T conditions. These results show the heterogeneous post-shock temperature distribution of superheated impact melt within the Mistastin impact structure. [1] Timms, N.E., Erickson, T.M., Zanetti, M.R., Pearce, M.A., Cayron, C., Cavosie, A.J., Reddy, S.M., Wittmann, A. and Carpenter, P.K., 2017. Cubic zirconia in> 2370° C impact melt records Earth's hottest crust. Earth and Planetary Science Letters, 477, pp.52-58.

rock↗

NASA NTRS2000

The Decomposition of Carbonates and Organics on Mars

The return and analysis of pristine material that is relict of a putative period of chemical evolution is a fumdamental goal of the exobiological exploration of Mars. In order to accomplish this objective, it is desirable to find oxidant-free regions where pristine material can be accessed at the shallowest possible depth (ideally directly from the surface). The objective of our ongoing research is to understand the spatial and temporal distribution of oxidants in the martian regolith and the redox chemistry of the soil; in effect to understand the chemical mechanisms and kinetics relating to the in-situ destruction of organics and the formation of the reactive species responsible for the Viking biology results. In this work, we report on experimental studies of oxidizing processes that may contribute to carbonate and organic degradation on Mars. Organic molecules directly exposed to solar UV may decomposed either directly into CO2, or into more volatile organic fragments. Organic macromolecules not directly exposed to high UV flux are most likely to be affected by atmospheric oxidants which can diffuse to their surfaces. The oxidizing processes examined include: gas-phase oxidants, UV photolysis, and UV-assisted heterogeneous catalysis. For example, assuming a meteroritic infall rate of 4 x 10(exp -4) g/m^2yr (Flynn and McKay 1990) and a flux of organic carbon of 2 x 10(exp -5) g/m^2yr, laboratory measurements of the UV-assisted decomposition of benzenehexacarboxylic acid (mellitic acid, a likely intermediate of kerogen oxidation), indicate its decomposition rate on Mars would exceed the total flux of organic carbon to the planet by over four orders of magnitude. Our measurements indicate that although the decomposition temperature of kerogens in some cases exceeds the temperature limit of the Viking GCMS, it is unlikely kerogens or their decomposition intermediates were present at the Viking landings sites at levels above the GCMS detection limits.

Quinn, Richard C.↗

NASA NTRSDate not supplied

Bridging the Last Mile with Open-Source Advancements: Empowering Communities through Fusion of Aerosol Optical Depth (AOD) Products from Multi-Satellite Sensors

Aerosol Optical Depth (AOD) is a crucial parameter for understanding atmospheric aerosol distribution and their impact on climate and air quality. With the growing number of Earth observation satellites, there is an abundance of AOD products derived from various sensors onboard both geostationary and low-orbit satellites. The availability of multiple datasets provides an opportunity to harness the strengths of each sensor and create comprehensive and accurate AOD datasets for climate and air quality studies at different temporal and spatial scales. Our NASA aerosol MEaSURES project has made significant strides in recent years by undertaking the ambitious task of developing an open-source package tailored for fusing AOD products from different sources. The package is based on OOP (Object-Oriented Programming) design and is implemented in Python modules. Generic interfaces enable easy inclusion of large and heterogeneous data. The package may be utilized to produce harmonized AOD datasets with enhanced spatial and temporal coverage. The latest version of the package is able to process and integrate the dark-target AOD data from six different sensors: AHI Himawari-8, ABI GOES-West, ABI GOES-East, MODIS AQUA, MODIS TERRA, and VIIRS SNPP. Rigorous validation and intercomparison studies have been performed to assess the accuracy and reliability of the fused AOD product against ground-based measurements and reference datasets. The open-source nature of the developed package ensures transparency, reproducibility, and community engagement. The research community and stakeholders can access, contribute to, and further improve the fusion methodology, making it adaptable to other studies, or expanding it to include new satellite data as they become available. In this poster presentation, we will introduce the accomplishments and challenges faced during the development of the open-source package for AOD data fusion, and demonstrate the advantages of combining AOD products from the six aforementioned satellite sensors. The presentation aims to foster discussions, collaborations, and future directions in integrating Earth observation and remote sensing data, which may contribute to a better understanding of atmospheric aerosols and their impacts on our environment.

Zhaohui Zhang↗

NASA NTRS2001

Quantitative molecular characterization of bovine vitreous and lens with non-invasive dynamic light scattering

The non-invasive technique of dynamic light scattering (DLS) was used to quantitatively characterize vitreous and lens structure on a molecular level by measuring the sizes of the predominant particles and mapping the three-dimensional topographic distribution of these structural macromolecules in three spatial dimensions. The results of DLS measurements in five fresh adult bovine eyes were compared to DLS measurements in model solutions of hyaluronan (HA) and collagen (Coll). In the bovine eyes DLS measurements were obtained from excised samples of gel and liquid vitreous and compared to the model solutions. Measurements in whole vitreous were obtained at multiple points posterior to the lens to generate a three-dimensional 'map' of molecular structure. The macromolecule distribution in bovine lens was similarly characterized.In each bovine vitreous (Bo Vit) specimen, DLS predominantly detected two distinct particles, which differed in diffusion properties and hence size. Comparisons with model vitreous solutions demonstrated that these most likely corresponded to the Coll and HA components of vitreous. Three-dimensional mapping of Bo Vit found heterogeneity throughout the vitreous body, with different particle size distributions for Coll and HA at different loci. In contrast, the three-dimensional distribution of lens macromolecules was more homogeneous. Thus, the non-invasive DLS technique can quantitate the average sizes of vitreous and lens macromolecules and map their three-dimensional distribution. This method to assess quantitatively the macromolecular structure of vitreous and lens should be useful for clinical as well as experimental applications in health and disease. Copyright 2001 Academic Press.

Models, Molecular↗

NASA NTRS1993

Variations in the Fe mineralogy of bright Martian soil

Bright regions on Mars are interpreted as 'soil' derived by chemical alteration of crustal rocks, whose main pigmentary component is ferric oxide or oxyhydroxide. The mineralogy and mineralogic variability of ferric iron are important evidence for the evolution of Martian soil: mineralogy of ferric phases is sensitive to chemical conditions in their genetic environments, and the spatial distributions of different ferric phases would record a history of both chemical environments and physical mixing. Reflectance spectroscopic studies provide several types of evidence that discriminate possible pigmentary phases, including the position of a crystal field absorption near 0.9 microns and position and strengths of absorptions in the UV-visible wavelength region. Recent telescopic spectra and laboratory measurements of Mars soil analogs suggest that spectral features of bright soil can be explained based on a single pigmentary phase, hematite (alpha-Fe2O3), occurring in both 'nanophase' and more crystalline forms. Here we report on a systematic investigation of Martian bright regions using ISM imaging spectrometer data, in which we examined spatial variations in the position and shape of the approximately 0.9 microns absorption. We found both local and regional heterogeneities that indicate differences in Fe mineralogy. These results demonstrate that bright soils do not represent a single lithology that has been homogenized by eolian mixing, and suggest that weathering of soils in different geologic settings has followed different physical and chemical pathways.

Murchie, Scott↗

NASA NTRS1994

The impact of land-surface wetness heterogeneity on mesoscale heat fluxes

Vertical heat fluxes associated with mesoscale circulations generated by land-surface wetness discontinuities are often stronger than turbulent fluxes, especially in the upper part of the atmospheric planetary boundary layer. As a result, they contribute significantly to the subgrid-scale fluxes in large-scale atmospheric models. Yet they are not considered in these models. To provide some insights into the possible parameterization of these fluxes in large-scale models, a state-of-the-art mesoscale numerical model was used to investigate the relationships between mesoscale heat fluxes and atmospheric and land-surface characteristics that play a key role in the generation of mesoscale circulations. The distribution of land-surface wetness, the wavenumber and the wavelength of the land-surface discontinuities, and the large-scale wind speed have a significant impact on the mesoscale heat fluxes. Empirical functions were derived to characterize the relationships between mesoscale heat fluxes and the spatial distribution of land-surface wetness. The strongest mesoscale heat fluxes were obtained for a wavelength of forcing corresponding approximately to the local Rossby deformation radius. The mesoscale heat fluxes are weakened by large-scale background winds but remain significant even with moderate winds.

Chen, Fei↗

NASA NTRS1989

Nonlinear mesomechanics of composites with periodic microstructure

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

Walker, Kevin P.↗