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At least 19 records

A study of solution crystal growth in LOW-g (2-IML-1)

During the International Microgravity Laboratory-1 (IML-1) mission it is planned to grow triglycine sulfate (TGS) crystals from aqueous solution using the modified Fluids Experiment System (FES). A special cooled sting technique will be used for solution crystal growth. The objectives of the experiment are as follows: (1) to grow crystals of TGS using the modified FES; (2) to perform holographic interferometric tomography of the fluid field in three dimensions; (3) to study the fluid motion due to g-jitter by multiple exposure holography of tracer particles; and (4) to study the influence of g-jitter on the growth rate.

Lal, Ravindra B.↗

Examining Metasomatism in Low fO2 Environments: Exploring Sulfidation Reactions in Various Planetary Bodies

Hydrothermal systems are common on Earth in a variety of tectonic environments and at different temperature and pressure conditions. These systems are commonly dominated by H2O, and they are responsible for element transport and the production of ore deposits. Unlike the Earth (fO2~FMQ), many other planetary bodies (e.g., Moon and asteroids) have fO2 environments that are more reduced (IW+/-2), and H2O is not the important solvent responsible for element transport. One example of a texture that could result from element transport and metasomatism, which appears to occur on numerous planetary bodies, is sulfide-silicate intergrowths. These subsolidus assemblages are interpreted to form as a result of sulfidation reactions from a S-rich fluid phase. The composition of fluids may vary within and among parent bodies and could be sourced from magmatic (e.g. Moon) or impact processes (e.g. HED meteorites and Moon). For example, it has been previously demonstrated on the Moon that the interaction of olivine with a hydrogen- and sulfur-bearing vapor phase altered primary mineral assemblages, producing sulfides (e.g. troilite) and orthopyroxene. Formation of these types of "sulfidation" assemblages can be illustrated with the following reaction: Fe2SiO4(ol) + 1/2 S(2 system) = FeS(troi)+ FeSiO3(opx) + 1/2 O2 system. The products of this reaction, as seen in lunar rocks, is a vermicular or "worm-like" texture of intergrown orthopyroxene and troilite. Regardless of the provenance of the S-bearing fluid, the minerals in these various planetary environments reacted in the same manner to produce orthopyroxene and troilite. Although similar textures have been identified in a variety of parent bodies, a comparative study on the compositions and the origins of these sulfide-silicate assemblages has yet to be undertaken. The intent of this study is to examine and compare sulfide-silicate intergrowths from various planetary bodies to explore their petrogenesis and examine the nature of low fO2 (IW+/-2) element migration and sulfidation reactions.

Srinivasan, P.↗

Comparing Wild 2 Particles to Chondrites and IDPS

We compare the observed composition ranges of olivine, pyroxene and Fe-Ni sulfides in Wild 2 grains, comparing these with chondritic IDPs and chondrite classes to explore whether these data suggest affinities to known hydrous materials in particular. Wild 2 olivine has an extremely wide composition range, from Fo4-100 with a pronounced frequency peak at Fo99. The composition range displayed by the low-calcium pyroxene is also very extensive, from En52 to En100, with a significant frequency peak centered at En95. These ranges are as broad or broader than those reported for any other extraterrestrial material. Wild 2 Fe-Ni sulfides mainly have compositions close to that of FeS, with less than 2 atom % Ni - to date, only two pentlandite grains have been found among the Wild-grains suggesting that this mineral is not abundant. The complete lack of compositions between FeS and pentlandite (with intermediate solid solution compositions) suggests (but does not require) that FeS and pentlandite condensed as crystalline species, i.e. did not form as amorphous phases, which later became annealed. While we have not yet observed any direct evidence of water-bearing minerals, the presence of Ni-bearing sulfides, and magnesium-dominated olivine and low-Ca pyroxene does not rule out their presence at low abundance. We do conclude that modern major and minor element compositions of chondrite matrix and IDPs are needed.

Zolensky, Michael↗

Hydrothermal alteration of CM carbonaceous chondrites: Implications of the identification of tochilinite as one type of meteoritic PCP

Poorly characterized phases (PCP's) constitute up to 30 volume percent of some CM carbonaceous chondrites, and are therefore an important key to an understanding of the physico-chemical conditions attending matrix evolution. An iron rich form of the terrestrial phase tochilinite was recently identified as a common type of PCP. Tochilinite has the general formula 6Fe(0.9)S.5(Mg,Fe)(OH)2 and consists of alternating machinawite (FeS) and brucite ((Mg,Fe)(OH)2) sheets, with iron vacancies in the sulfide sheets. In iron rich tochilinite, ferrous hydroxide, called amakinite, replaces brucite. If CM carbonaceous kchondrites have underdone hydrothermal alteration, iron rich tochilinite, at least, probably grew from aqueous solutions characterized by low FO2, high FS2, pH 10 to 12, and at a temperature at or below 170 C.

Zolensky, M. E.↗

Melt Redistribution in Dynamic Systems: Applications to Core Formation

Samples of olivine + Fe-S were fabricated by hot-pressing a mechanical mixture of the two phases. Olivine powders with a starting grain size of approx. 10 microns were prepared by crushing crystals of San Carlos olivine followed by pulverization in a fluid energy mill. Iron sulfide powder with a particle size of approx. 5 microns was prepared from a 2:1 mixture of reagent grade iron sulfide (FeS) plus iron. Rods 20 mm in length by 10 mm in diameter were cold-pressed into iron capsules with a uniaxial stress of approx. 200 MPa. These rods were then hot-pressed at 1523 K and 300 MPa for 4 h to obtain a starting material with <2% porosity. Samples for shear experiments were cut perpendicular to the long axis of these rods. The discs were shaped into ellipses approx. 6 mm by approx. 8 mm with a thickness ranging from 0.6 to 1.0 mm. An iron foil strain marker was inserted into a cut made along the minor axis. The sample was placed between two thoriated tungsten pistons cut at 45 deg to the long axis and then placed into an iron sleeve capped by alumina discs. The sample was then sheared in a gas pressure-medium apparatus at a temperature of 1523 K and a confining pressure of 300 MPa.

Hustoft, J. W.↗

Relative Sputtering Rates of FeS, MgS, and Mg Silicates: Implications for ISM Gas Phase Depletions of Rock-Forming Elements

Astronomical measurements of S abundances in the diffuse interstellar medium (ISM) indicate ionized S is a dominant species with little (< 5%) S residing in grains (e.g. Jenkins 2009). This is an enigmatic result, given that abundant Fe-sulfide grains are observed in dust around pre- and post-main sequence stars and are also observed as major components of primitive meteoritic and cometary samples. These disparate observations suggest that the lifetime of sulfide grains in the ISM is short because of destruction processes. Our previous work has shown that FeS and MgS retain their crystallinity and do not amorphize during radiation processing, whereas enstatite and forsterite are readily amorphized. We have extended this study to measure the relative sputtering rates of FeS and MgS compared to enstatite and forsterite. Irradiation of FeS with 4 keV He+ results in preferential sputtering of S and the formation of a thin 2-3 nm, compact Fe metal layer that armors the surface. The zone of S loss extends to a depth of ~8-10 nm below the exposed surface. Despite this S loss, the FeS retains its crystallinity and shows no sign of incipient amorphization. Irradiation of FeS with 5kV Ga+ in a focused ion beam (FIB) instrument resulted in preferential sputtering of S and the formation of a 5-8-nm thick surface layer of nanophase Fe metal. X-ray mapping shows that the zone of S sputtering extends to a depth of nearly 20 nm, but there is no evidence for FeS amorphization, consistent with our previous work. The irradiation experiments show that the relative sputtering rate of FeS and MgS are much higher than olivine or enstatite. Sputtering experiments utilizing 30 kV and 5 kV Ga ions in the FIB produced volume loss in troilite that was ~4X greater than in enstatite or forsterite. The sputter yield under these conditions is such that for every Si atom sputtered from enstatite, ~14 S atoms are sputtered from FeS. We have performed similar sputtering experiments on Fe-bearing niningerite (MgS) and co-existing enstatite from the ALH 84170 EH3 chondrite. MgS also sputters much more rapidly than enstatite with a relative Si:S sputter yield of 1:8. For MgS, sulfur is highly depleted at the surface and the S-depletion zone extends to a depth of ~15 nm (using 5 kV Ga+). There is a corresponding zone of Mg and especially Fe enrichment that extends from 5 to ~10 nm below the surface, respectively. The dominant grain destruction mechanism in the ISM is sputtering from passage of supernova-generated shock waves. This process also results in the amorphization of crystalline silicates in the ISM. Our results indicate that FeS and MgS grains produced in evolved stars and injected into the ISM will be destroyed more rapidly than crystalline silicates. This process may account for the lack of significant depletion of S from the gas phase in the ISM. However, rare nanophase FeS grains occur as inclusions in circumstellar amorphous silicate grains found in comet dust particles analyzed in the laboratory. These results show that a finite amount of S in the ISM is sequestered in solid grains.

SPUTTERING RATES↗

Chromium on Mercury: New Results From the MESSENGER X-Ray Spectrometer and Implications for the Innermost Planet’s Geochemical Evolution

Mercury, the innermost planet, formed under highly reduced conditions, based mainly on surface Fe, S, and Si abundances determined from MESSENGER mission data. The minor element Cr may serve as an independent oxybarometer but only very limited Cr data have been previously reported for Mercury. We report Cr/Si abundances across Mercury's surface based on MESSENGER X-Ray Spectrometer data throughout the spacecraft's orbital mission. The heterogeneous Cr/Si ratio ranges from 3.6 × 10 -5 in the Caloris Basin to 0.0012 within the high-magnesium region, with an average southern hemisphere value of 0.0008 (corresponding to about 200 ppm Cr). Absolute Cr/Si values have systematic uncertainty of at least 30%, but relative variations are more robust. By combining experimental Cr partitioning data along with planetary differentiation modeling, we find that if Mercury formed with bulk chondritic Cr/Al, Cr must be present in the planet's core and differentiation must have occurred at log ƒO 2 in the range of IW-6.5 to IW-2.5 in the absence of sulfides in its interior and a range of IW-5.5 to IW-2 with an FeS layer at the core-mantle boundary. Models with large fractions of Mg-Ca-rich sulfides in Mercury's interior are more compatible with moderately reducing conditions (IW-5.5 to IW-4) owing to the instability of Mg-Ca-rich sulfides at elevated ƒO 2 . These results indicate that if Mercury differentiated at a log ƒO 2 lower than IW-5.5, the presence of sulfides whether in the form of a FeS layer at the top of the core or Mg-Ca-rich sulfides within the mantle would be unlikely.

Larry R. Nittler↗

Opaque Minerals in the Matrix of the Bishunpur (LL3.1) Chondrite: Constraints on the Chondrule Formation Environment

The chemistry and mineralogy of a group of opaque mineral assemblages in the matrix of the Bishunpur LL3.1 ordinary chondrite provide insight into the nebular environment in which they formed. The assemblages consist of a kamacite (Fe,Ni) core that is rimmed by troilite (FeS) and fayalite (Fe2Si04). Accessory phases in the rims include silica (Si02), chromite (FeCr204), whitlockite (Ca3(P04)2), maricite (FeNaP04), magnetite (Fe304), and tetrataenite (FeNi). We suggest that the metal melted in and equilibrated with an igneous chondrule under high- temperature, reducing conditions. In this environment the molten alloys incorporated varied amounts of Si, Ni, P, Cr, and Co, depending on the oxygen fugacity and temperature of the melt. Some of the metal was subsequently expelled from the chondrule interiors into the surrounding nebular gas. As the temperature dropped, the alloy solidified and volatile elements corroded the metal. The main reaction products were troilite and fayalite. Thermodynamic equilibrium calculations are used to constrain the conditions under which these two phases can form simultaneously in the solar nebula. Kinetic factors are used to place a lower limit on the formation temperature. We determine that the metal corroded between 1173 and 1261 K at a total pressure in the range of 1025.0 to 1024.1 bars and a dust/gas ratio of 302 to 355 x relative to solar composition. These conditions are consistent with our model that the metal corroded in a dust- rich region of the solar nebula that was cooling after a chondrule formation event.

Lauretta, D. S.↗

Density of the mantle of Mars

The range of zero pressure densities of the Martian mantle which are compatible with the mean density and moment of inertia factor of Mars has been explored by: (1) considering the full range of plausible core compositions and densities, and (2) investigating the sensitivity of computed mantle densities to uncertainties in the input parameters. Ni, Fe, Fe3O4, and FeS cores were considered; corresponding zero pressure mantle densities range from 3.47 to 3.41 g/cu cm. Uncertainty in the mantle density of about 0.04 g/cu cm for the Fe core model and about 0.05 g/cu cm for the FeS core model results from uncertainties in the input parameters. The zero pressure density of the Martian mantle is estimated to be 3.44 plus or minus 0.06 g/cu cm.

Goettel, K. A.↗

The origin of KREEP

KREEP is a lunar material having very high concentrations of incompatible elements; its name is an acronym for the incompatibles K, rare-earth elements (REE), and P. Although a few pristine (endogenously igneous) KREEPy samples were returned from the Apollo 15 and 17 sites, most KREEPy samples are polymict breccias. Most models of KREEP petrogenesis have been based on partial melting of a variety of sources. Such models fail to explain the veritable absence of variations in incompatible element patterns over the sampled portion of the moon. We have defined a KREEP component based on the average composition of Apollo 14 breccias having extremely high concentrations of incompatible elements. Normalization of accurate incompatible data for KREEPy samples from the Apollo 12, 14, 15, 16, and 17 sites to this component virtually always shows no resolvable fractionation (e.g., <10% variation in the La/Lu ratio), whereas partial melting models typically produce larger fractionations (±20–25% in La/Lu) from a factor of 2 difference in degree of partial melting. Required is a single major source that could provide KREEP to widely separated locations on the nearside of the moon. The anorthositic crust of the moon is commonly attributed to the flotation of plagioclase on a deep, moon-wide magma ocean. Fractional crystallization of this magma ocean would have produced large enrichments of incompatibles in a residual liquid. No other plausible major source of incompatibles has been proposed. We borrow the German prefix ur—meaning primeval and designate this residual liquid ‘urKREEP.’ We propose that all KREEPy rocks originated by dilution of urKREEP with crustal or mantle materials during assimilation, or zone-refining (pristine samples), or impact-induced brecciation (breccias and melt rocks). The formation of urKREEP cannot be dated precisely. Correction of breccia Rb-Sr model ages for Rb loss or gain during the early intense bombardments yields ages that cluster in the range 4.4–4.5 Gy. This implies that crystallization of the magma ocean was essentially complete at this time and is in general agreement with U-Pb evidence indicating crustal formation at 4.4 Gy. Assuming that the moon had the composition of an H-group chondrite depleted in Fe-Ni and FeS and that half the incompatibles fractionated into materials other than urKREEP, the thickness of a moon-wide urKREEP layer was <2 km. Thorium concentrations determined by gamma ray spectroscopy indicate that about 4% of the incompatibles in an H chondritic moon are now in the outermost kilometer.

Paul H. Warren↗

Solution Growth of Crystals in Zero-Gravity

In a low-g environment, buoyancy driven convection effects in solution crystal growth are greatly reduced and, thus, one can study diffusion mass transport which in 1-g is masked by convective phenomena. Crystals of triglycine sulfate (TGS) will be grown aboard the Spacelab 3 mission, using a specially developed Fluids Experiments System (FES). The objectives of the experiment are: (1) to develop a technique for solution crystal growth in a low-g environment, (2) to characterize the growth environment provided by an orbiting spacecraft and to determine the influence of the environment on the growth behavior, and (3) to determine how gravity in a low-gravity environment influences the properties of a resulting TGS crystal. Single crystals of TGS have been grown using conventional low-temperature solution crystal growth method and the growth process has been extensively characterized. Various physical properties of TGS solution have been measured. Also, a unique technique of growing solution growth crystals by extracting heat at a programmed rate from the crystal through a semi-insulating sting has been developed and tested in 1-g environment.

Lal, R. B.↗

Oxidation states of iron in the terrestrial planets: Evidence and implications for accretion models

Analyses of Mars spectra reveal that primary minerals may be more iron rich than average basalts on Earth, and the oxidation state of iron in the pyroxines suggests equally high or higher oxygen fugacities on Mars than Earth. Analysis of Mercury spectra reveal that silicate iron contents are substantially lower than those on Mars. Mercury, however, probably has a substantial iron core. This is consistent with a lower oxidation state of iron on Mercury than on Mars. These findings are consistent with predictions of models of equilibrium condensation and homogeneous accretion. Those models predict that Mercury would have negligible Fe(2+) in silicates (Fe/Fe+Mg approx. 0.5). For Mercury iron should be virtually all metallic, while for Mars the iron would be all oxidized as FeS and silicate. Surface measurements of Fe/Fe+Mg on Venus, Earth, and Mars further support the predicted relative increase in Fe/Fe+Mg ratio (increased oxidation state) with distance from the Sun. The implied high oxygen fugacities on Mars (Fe(3+) in silicates) provide additional consistence with the model predictions.

Huguenin, R. L.↗

Affordable Development and Demonstration of a Small NTR Engine and Stage: How Small is Big Enough?

The Nuclear Thermal Rocket (NTR) derives its energy from fission of uranium-235 atoms contained within fuel elements that comprise the engine's reactor core. It generates high thrust and has a specific impulse potential of approximately 900 seconds - a 100% increase over today's best chemical rockets. The Nuclear Thermal Propulsion (NTP) project, funded by NASA's AES program, includes five key task activities: (1) Recapture, demonstration, and validation of heritage graphite composite (GC) fuel (selected as the "Lead Fuel" option); (2) Engine Conceptual Design; (3) Operating Requirements Definition; (4) Identification of Affordable Options for Ground Testing; and (5) Formulation of an Affordable Development Strategy. During FY'14, a preliminary DDT&E plan and schedule for NTP development was outlined by GRC, DOE and industry that involved significant system-level demonstration projects that included GTD tests at the NNSS, followed by a FTD mission. To reduce cost for the GTD tests and FTD mission, small NTR engines, in either the 7.5 or 16.5 klbf thrust class, were considered. Both engine options used GC fuel and a "common" fuel element (FE) design. The small approximately 7.5 klbf "criticality-limited" engine produces approximately 157 megawatts of thermal power (MWt) and its core is configured with parallel rows of hexagonal-shaped FEs and tie tubes (TTs) with a FE to TT ratio of approximately 1:1. The larger approximately 16.5 klbf Small Nuclear Rocket Engine (SNRE), developed by LANL at the end of the Rover program, produces approximately 367 MWt and has a FE to TT ratio of approximately 2:1. Although both engines use a common 35 inch (approximately 89 cm) long FE, the SNRE's larger diameter core contains approximately 300 more FEs needed to produce an additional 210 MWt of power. To reduce the cost of the FTD mission, a simple "1-burn" lunar flyby mission was considered to reduce the LH2 propellant loading, the stage size and complexity. Use of existing and flight proven liquid rocket and stage hardware (e.g., from the RL10B-2 engine and Delta Cryogenic Second Stage) was also maximized to further aid affordability. This paper examines the pros and cons of using these two small engine options, including their potential to support future human exploration missions to the Moon, near Earth asteroids, and Mars, and recommends a preferred size. It also provides a preliminary assessment of the key activities, development options, and schedule required to affordably build, ground test and fly a small NTR engine and stage within a 10-year timeframe.

Spacecraft design↗

An optical study of grain formation: Casting and solidification technology (2-IML-1)

By studying the unidirectional growth of a metal-model material in microgravity, an attempt is made to characterize alloy solidification. Using holograms and supporting temperature measurements obtained during processing in the Fluids Experiment System (FES), the solute and thermal fields associated with the dendrite growth front and extraneous nucleation will be measured and compared to a theoretical (computational) model. Ground based supporting experiments include particle tracking to measure the velocity fields, and optical phase shift techniques (confocal optical signal processing, interferometry, and Schlieren) to study thermal and solutal fields.

Mccay, Mary H.↗

Prebiotic Nitrogen Fixation by FeS Reduction of Nitrite Under Acidic Conditions

Theories for the origin of life require the availability of reduced nitrogen for the formation of such species as amino acid and nucleic acids. In a strongly reducing atmosphere, compounds essential to the chemical evolution of life, such as amino acids, can form by reactions between HCN, NH3, and carbonyl compounds produced in spark discharges. However, under non-reducing atmospheres, electric discharges produced NO rather than HCN or NH3. This raises the questions of; how ammonia can be formed under a neutral atmosphere, and what conditions are needed such formation to occur? On possibility is the conversion of NO into nitric and nitrous acids (through HNO) and rained into the oceans. The reduction of nitrite by aqueous Fe(II) (6 Fe(+2) + 7 H(+) + NO2(-) yields 6 Fe(III) + 2 H2O + NH3) such as was present on the early Earth could then have produced ammonia. However, this reaction does not proceed at pHs less than 7.3. An alternative is reduction by other forms of Fe(II), such as FeS. We will present results that show that FeS can reduce nitrite to ammonia at pHs as low as pH 5 under a variety of conditions.

Summers, David P.↗

Lunar evolution - How well do we know it now.

The currently known astronomical, chemical, and magnetic data are not uniquely indicative of an extensively and globally molten moon. It is argued that an accretional layering occurred in the moon, but at temperatures below solidus. The excess mass in the near side of the moon compatible with a 2-km displacement in the center of mass relative to the center of figure and the moment of inertia data is considered to be due to Fe-FeS liquid formation and inhomogeneous segregation. These Fe-FeS bodies, termed 'fescons,' are shown to be capable of accounting for the presently available magnetization data, by acting as small regenerative dynamos with a time-stability less than that of the terrestrial equivalent. The chemical characteristics of the highly differentiated materials, are considered to be due to small-scale localized melting caused by collisional events, from sources in which accessory phases play a significant role. Mare basalts are considered to be melts in the overlying material produced at a later time by K-40 radioactivity in the fescons. Some consequences of the present hypothesis are suggested. It is concluded that these and other characteristics of the lunar materials are reconcilable with a 'cold' moon, such as discussed by Urey over the past two decades.

Murthy, V. R.↗

Affordable Development and Demonstration of a Small Nuclear Thermal Rocket (NTR) Engine and Stage: How Small Is Big Enough?

The Nuclear Thermal Rocket (NTR) derives its energy from fission of uranium-235 atoms contained within fuel elements that comprise the engine's reactor core. It generates high thrust and has a specific impulse potential of approximately 900 specific impulse - a 100 percent increase over today's best chemical rockets. The Nuclear Thermal Propulsion (NTP) project, funded by NASA's Advanced Exploration Systems (AES) program, includes five key task activities: (1) Recapture, demonstration, and validation of heritage graphite composite (GC) fuel (selected as the Lead Fuel option); (2) Engine Conceptual Design; (3) Operating Requirements Definition; (4) Identification of Affordable Options for Ground Testing; and (5) Formulation of an Affordable Development Strategy. During fiscal year (FY) 2014, a preliminary Design Development Test and Evaluation (DDT&E) plan and schedule for NTP development was outlined by the NASA Glenn Research Center (GRC), Department of Energy (DOE) and industry that involved significant system-level demonstration projects that included Ground Technology Demonstration (GTD) tests at the Nevada National Security Site (NNSS), followed by a Flight Technology Demonstration (FTD) mission. To reduce cost for the GTD tests and FTD mission, small NTR engines, in either the 7.5 or 16.5 kilopound-force thrust class, were considered. Both engine options used GC fuel and a common fuel element (FE) design. The small approximately 7.5 kilopound-force criticality-limited engine produces approximately157 thermal megawatts and its core is configured with parallel rows of hexagonal-shaped FEs and tie tubes (TTs) with a FE to TT ratio of approximately 1:1. The larger approximately 16.5 kilopound-force Small Nuclear Rocket Engine (SNRE), developed by Los Alamos National Laboratory (LANL) at the end of the Rover program, produces approximately 367 thermal megawatts and has a FE to TT ratio of approximately 2:1. Although both engines use a common 35-inch (approximately 89-centimeters) -long FE, the SNRE's larger diameter core contains approximately 300 more FEs needed to produce an additional 210 thermal megawatts of power. To reduce the cost of the FTD mission, a simple one-burn lunar flyby mission was considered to reduce the liquid hydrogen (LH2) propellant loading, the stage size and complexity. Use of existing and flight proven liquid rocket and stage hardware (e.g., from the RL10B-2 engine and Delta Cryogenic Second Stage) was also maximized to further aid affordability. This paper examines the pros and cons of using these two small engine options, including their potential to support future human exploration missions to the Moon, near Earth asteroids (NEA), and Mars, and recommends a preferred size. It also provides a preliminary assessment of the key activities, development options, and schedule required to affordably build, ground test and fly a small NTR engine and stage within a 10-year timeframe.

Spacecraft design↗

Coupling finite and boundary element methods for 2-D elasticity problems

A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.

Krishnamurthy, T.↗