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NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Ols- son & Oliger (1994), Gerritsen & Olsson (1996), and Yee et al. (2000) is revisited. The entropy splitting is a form of skew-symmetric splitting of the nonlinear Euler flux derivatives. Central differencing applied to the entropy splitting form of the Euler flux derivatives together with SBP difference operators will, hereafter, be referred to as entropy split schemes. This study is prompted by the recent growing interest in numerical methods for which a discrete entropy conservation law holds, a discrete global entropy conservation can be proved and/or the numerical method possesses a stable entropy in the framework of SBP difference operators and L2-energy norm estimate. The objective of this paper is to recast the entropy split scheme as the re- cent definition of an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for non- linear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grub- ber splitting.

Sjogreen, Bjorn↗
NASA NTRS1983

An investigation of coronal active region loop structures using AS&E rocket X-ray images

Simultaneous high spatial resolution observations at 6 cm in soft X-rays, in photospheric magnetograms, and in optical filtergrams were used to compare the most intense sources of centimetric emission in two active regions to coronal loops, sunspots, chromospheric structures, and photospheric magnetic fields. Results show that the majority of the bright microwave components are not associated with sunspots or X-ray emission. A nonthermal mechanism appears necessary to explain the brightest microwave components, discrete regions of continuous particle acceleration may be common in active regions. Studies of the plasma parameters of selected loops imply that the radio emission is consistent with gyro-resonance absorption at the third and fourth harmonic, at least from part of each loop. Results are presented for: (1) X-ray and microwave observations of active regions; (2) comparison of coronal holes observed in soft X-rays and Hel 10830 A spectrosheliograms; and (3) the reappearance of polar coronal holes and the evolution of the solar magnetic field.

Webb, D. F.↗
NASA NTRS1993

A multi-dimensional kinetic-based upwind solver for the Euler equations

A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.

Eppard, W. M.↗
NASA NTRS2016

Organic Analysis in Miller Range 090657 and Buckley Island 10933 CR2 Chondrites: Part 1 In-Situ Observation of Carbonaceous Material

Primitive carbonaceous chondrites contain a wide variety of organic material, ranging from soluble discrete molecules to insoluble unstructured kerogen-like component as well as structured nano-globules of macromolecular carbon. The relationship between the soluble organic molecules, macromolecular organic material, and host minerals are poorly understood. Due to the differences in extractability of soluble and insoluble organic materials, the analysis methods for each differ and are often performed independently. The combination of soluble and insoluble analyses, when performed concurrently, can provide a wider understanding on spatial distribution, and elemental, structural and isotopic composition of organic material in primitive meteorites. Furthermore, they can provide broader perspective on how extraterrestrial organic ma-terials potentially contributed to the synthesis of life's essential compounds such as amino acids, sugar acids, activated phosphates and nucleobases.

Cao, T.↗
NASA NTRS2016

Organic Analysis in the Miller Range 090657 CR2 Chondrite: Part 2 Amino Acid Analyses

Primitive carbonaceous chondrites contain a wide variety of organic material, ranging from soluble discrete molecules to insoluble, unstructured kerogen-like components, as well as structured nano-globules of macromolecular carbon. The relationship between the soluble organic molecules, macromolecular organic material, and host minerals are poorly understood. Due to the differences in extractability of soluble and insoluble organic materials, the analysis methods for each differ and are often performed independently. The combination of soluble and insoluble analyses, when performed concurrently, can provide a wider understanding of spatial distribution, and elemental, structural and isotopic composition of organic material in primitive meteorites. Using macroscale extraction and analysis techniques in combination with in situ microscale observation, we have been studying both insoluble and soluble organic material in the primitive CR2 chondrite Miller Range (MIL) 090657. In accompanying abstracts (Cao et al. and Messenger et al.) we discuss insoluble organic material in the samples. By performing the consortium studies, we aim to improve our understanding of the relationship between the meteorite minerals and the soluble and insoluble organic phases and to delineate which species formed within the meteorite and those that formed in nebular or presolar environments. In this abstract, we present the results of amino acid analyses of MIL 090657 by ultra performance liquid chromatography with fluorescence detection and quadrupole-time of flight mass spectrometry. Amino acids are of interest because they are essential to life on Earth, and because they are present in sufficient structural, enantiomeric and isotopic diversity to allow insights into early solar system chemical processes. Furthermore, these are among the most isotopically anomalous species, yet at least some fraction are thought to have formed by aqueously-mediated processes during parent body alteration.

Burton, A. S.↗
NASA NTRS2001

Modelling of Trapped Radiation Near Jupiter

Energetic (62 to approx. 130 MeV) proton fluxes measured with the Galileo Probe inside Jupiter's main ring (radii 122,500 to 128,940 km) show a modest increase as Jupiter is approached. Solutions of a reduced (1-d) equatorial diffusion equation with-constant losses described by a lifetime tau match those data for tau greater than or equal to 10(exp 9) s for diffusion coefficient D(sub LL) = 10(exp -9) L(exp 4)/s, 10(exp -9) L(exp -3)/s, or 10(exp -10) L(exp 4)/s (this particle population may be undergoing nearly loss-free inward radial diffusion). Tau would increase as Jupiter is approached if its value were determined by pitch angle scattering due to EM wave-particle interactions. if the absolute amplitudes of the waves' magnetic fluctuations did not vary with radial distance. Exploration of numerical solutions of the diffusive transport equation for Jupiter's magnetospheric ions at die planetary ring and closer to Jupiter has been done. Explicit range-energy relationships for energy loss in ring matter (SiO2), modeled as a continuous disk, are incorporated. A spatial resolution of approx. 1000 km in the radial direction is used in the vicinity of the main ring; off-equatorial ion fluxes have been included (assuming the atmosphere is a perfect absorber). For protons the maximum effect of energy loss in the microscopic size range of ring particles is expected at energies approx. 0.1 Mev. Presumably there could be sufficiently large, unobserved bodies within the ring that would have to be modeled as discrete objects, as planetary satellites would be. Within limitations of the model and computational resources it's planned to characterize solutions for transport of magnetospheric ions past the planetary ring; the procedures that are used are fairly well known and may be applied generally to the simpler magnetospheric models.

Mihalov, John D.↗
NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗
NASA NTRS2011

High Frequency Acoustic Response Characterization and Analysis of the Deep Throttling Common Extensible Cryogenic Engine

The Common Extensive Cryogenic Engine program demonstrated the operation of a deep throttling engine design. The program, spanning five years from August 2005 to July 2010, funded testing through four separate engine demonstration test series. Along with successful completion of multiple objectives, a discrete response of approximately 4000 Hz was discovered and explored throughout the program. The typical low-amplitude acoustic response was evident in the chamber measurement through almost every operating condition; however, at certain off-nominal operating conditions, the response became discrete with higher amplitude. This paper summarizes the data reduction, characterization, and analysis of the 4,000 Hz response for the entire program duration, using the large amount of data collected. Upon first encountering the response, new objectives and instrumentation were incorporated in future test series to specifically collect 4,000 Hz data. The 4,000 Hz response was identified as being related to the first tangential acoustic mode by means of frequency estimation and spatial decomposition. The latter approach showed that the effective node line of the mode was aligned with the manifold propellant inlets with standing waves and quasi-standing waves present at various times. Contour maps that contain instantaneous frequency and amplitude trackings of the response were generated as a significant improvement to historical manual approaches of data reduction presentation. Signal analysis and dynamic data reduction also uncovered several other features of the response including a stable limit cycle, the progressive engagement of subsequent harmonics, the U-shaped time history, an intermittent response near the test-based neutral stability region, other acoustic modes, and indications of modulation with a separate subsynchronous response. Although no engine damage related to the acoustic mode was noted, the peak-to-peak fluctuating pressure amplitude achieved 12.1% of the mean chamber pressure at its highest. The identification of this response in terms of an instability is also discussed.

Casiano, M. J.↗
NASA NTRS1992

Mapping the Moon in Soft x Rays: Promises and Challenges

Recent ROSAT images reported by Schmitt et el. show that the sunlit part of the Moon is a significant source of very soft x rays. Stimulated by these observations, Edwards et al. have made an analysis of the response of the Moon to the solar soft x ray and EUV spectrum. They argue that much of the observed emission is in the form of discrete fluorescence lines in the energy range 25 to 100 eV, and that these lines are generally much stronger than the adjacent directly scattered solar background. On this basis they suggest that soft x ray fluorescence can be used to remotely obtain high-precision elemental maps of the lunar surface. Edwards et al. have continued to develop this idea and have suggested a system using soft x ray telescopes in lunar orbit, which could also obtain very good spatial resolution. This combination could be extremely valuable in furthering our understanding of lunar chemistry and potential resource distributions. High spatial resolution combined with the thin surface layer from which these soft x rays arise suggests the exciting possibility that x ray telescopes could map lunar volcanic volatiles from orbit.

Housley, R. M.↗
NASA NTRS1995

CNR LARA project, Italy: Airborne laboratory for environmental research

The increasing interest for the environmental problems and the study of the impact on the environment due to antropic activity produced an enhancement of remote sensing applications. The Italian National Research Council (CNR) established a new laboratory for airborne hyperspectral imaging, the LARA Project (Laboratorio Aero per Ricerche Ambientali - Airborne Laboratory for Environmental Research), equipping its airborne laboratory, a CASA-212, mainly with the Daedalus AA5000 MIVIS (Multispectral Infrared and Visible Imaging Spectrometer) instrument. MIVIS's channels, spectral bandwidths, and locations are chosen to meet the needs of scientific research for advanced applications of remote sensing data. MIVIS can make significant contributions to solving problems in many diverse areas such as geologic exploration, land use studies, mineralogy, agricultural crop studies, energy loss analysis, pollution assessment, volcanology, forest fire management and others. The broad spectral range and the many discrete narrow channels of MIVIS provide a fine quantization of spectral information that permits accurate definition of absorption features from a variety of materials, allowing the extraction of chemical and physical information of our environment. The availability of such a hyperspectral imager, that will operate mainly in the Mediterranean area, at the present represents a unique opportunity for those who are involved in environmental studies and land-management to collect systematically large-scale and high spectral-spatial resolution data of this part of the world. Nevertheless, MIVIS deployments will touch other parts of the world, where a major interest from the international scientific community is present.

Bianchi, R.↗
NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗
NASA NTRS1990

Empirical relationships between gas abundances and UV selective extinction

Several studies of gas-phase abundances in lines of sight through the outer edges of dense clouds are summarized. These lines of sight have 0.4 less than E(B-V) less than 1.1 and have inferred spatial densities of a few hundred cm(-3). The primary thrust of these studies has been to compare gaseous abundances in interstellar clouds that have various types of peculiar selective extinction. To date, the most notable result has been an empirical relationship between the CN/Fe I abundance ratio and the depth of the 2200 A extinction bump. It is not clear at the present time, however, whether these two parameters are linearly correlated or the data are organized into two discrete ensembles. Based on 19 samples and assuming the clouds form discrete ensembles, lines of sight that have a CN/Fe I abundance ratio greater than 0.3 (dex) appear to have a shallow 2.57 plus or minus 0.55 bump compared to 3.60 plus or minus 0.36 for other dense clouds and compared to the 3.6 Seaton (1979) average. The difference in the strength of the extinction bump between these two ensembles is 1.03 plus or minus 0.23. Although a high-resolution IUE survey of dense clouds is far from complete, the few lines of sight with shallow extinction bumps all show preferential depletion of certain elements, while those lines of sight with normal 2200 A bumps do not. Ca II, Cr II, and Mn II appear to exhibit the strongest preferential depletion compared to S II, P II, and Mg II. Fe II and Si II depletions also appear to be enhanced somewhat in the shallow-bump lines of sight. It should be noted that Copernicus data suggest all elements, including the so-called nondepletors, deplete in diffuse clouds (Snow and Jenkins 1980, Joseph 1988). Those lines of sight through dense clouds that have normal 2200 A extinction bumps appear to be extensions of the depletions found in the diffuse interstellar medium. That is, the overall level of depletion is enhanced, but the element-to-element abundances are similar to those in diffuse clouds. In a separate study, the abundances of neutral atoms were studied in a dense cloud having a shallow 2200 A bump and in one with a normal strength bump.

Joseph, Charles L.↗
NASA NTRS1992

Spectral analysis for automated exploration and sample acquisition

Future space exploration missions will rely heavily on the use of complex instrument data for determining the geologic, chemical, and elemental character of planetary surfaces. One important instrument is the imaging spectrometer, which collects complete images in multiple discrete wavelengths in the visible and infrared regions of the spectrum. Extensive computational effort is required to extract information from such high-dimensional data. A hierarchical classification scheme allows multispectral data to be analyzed for purposes of mineral classification while limiting the overall computational requirements. The hierarchical classifier exploits the tunability of a new type of imaging spectrometer which is based on an acousto-optic tunable filter. This spectrometer collects a complete image in each wavelength passband without spatial scanning. It may be programmed to scan through a range of wavelengths or to collect only specific bands for data analysis. Spectral classification activities employ artificial neural networks, trained to recognize a number of mineral classes. Analysis of the trained networks has proven useful in determining which subsets of spectral bands should be employed at each step of the hierarchical classifier. The network classifiers are capable of recognizing all mineral types which were included in the training set. In addition, the major components of many mineral mixtures can also be recognized. This capability may prove useful for a system designed to evaluate data in a strange environment where details of the mineral composition are not known in advance.

Eberlein, Susan↗
NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗
NASA NTRS1984

A new multifunction acousto-optic signal processor

An acousto-optic architecture for simultaneously obtaining time integration correlation and high-speed power spectrum analysis was constructed using commercially available TeO2 modulators and photodiode detector-arrays. The correlator section of the processor uses coherent interferometry to attain maximum bandwidth and dynamic range while achieving a time-bandwidth product of 1 million. Two correllator outputs are achieved in this system configuration. One is optically filtered and magnified 2 : 1 to decrease the spatial frequency to a level where a 25-MHz bandwidth may be sampled by a 62-mm array with elements on 25-micro centers. The other output is magnified by a factor of 10 such that the center 4 microseconds of information is available for estimation of time-difference-of-arrival to within 10 ns. The Bragg cell spectrum-analyzer section, which also has two outputs, resolves a 25-MHz instantaneous bandwidth to 25 kHz and can determine discrete-frequency reception time to within 15 microseconds. A microprocessor combines spectrum analysis information with that obtained from the correlator.

Berg, N. J.↗
NASA NTRS1999

Preliminary Performance of CdZnTe Imaging Detector Prototypes

The promise of good energy and spatial resolution coupled with high efficiency and near-room-temperature operation has fuelled a large International effort to develop Cadmium-Zinc-Telluride (CdZnTe) for the hard-x-ray region. We present here preliminary results from our development of small-pixel imaging arrays fabricated on 5x5x1-mm and 5x5x2-mm spectroscopy and discriminator-grade material. Each array has 16 (4x4) 0.65-mm gold readout pads on a 0.75-mm pitch, with each pad connected to a discrete preamplifier via a pulse-welded gold wire. Each array is mounted on a 3-stage Peltier cooler and housed in an ion-pump-evacuated housing which also contains a hybrid micro-assembly for the 16 channels of electronics. We have investigated the energy resolution and approximate photopeak efficiency for each pixel at several energies and have used an ultra-fine beam x-ray generator to probe the performance at the pixel boundaries. Both arrays gave similar results, and at an optimum temperature of -20 C we achieved between 2 and 3% FWHM energy resolution at 60 keV and around 15% at 5.9 keV. We found that all the charge was contained within 1 pixel until very close to the pixels edge, where it would start to be shared with its neighbor. Even between pixels, all the charge would be appropriately shared with no apparently loss of efficiency or resolution. Full details of these measurements will be presented, together with their implications for future imaging-spectroscopy applications.

Ramsey, B.↗
NASA NTRS2009

Development of Countermeasures to Aid Functional Egress from the Crew Exploration Vehicle Following Long Duration Spaceflight

Astronauts experience disturbances in sensorimotor function following their return to Earth due to adaptive responses that occur during exposure to the microgravity conditions of space flight. As part of the Crew Exploration Vehicle design requirements, the crewmember adapted to the microgravity state may need to egress the vehicle within a few minutes for safety and operational reasons in various sea state conditions following a water landing. The act of emergency egress includes and is not limited to rapid motor control tasks (including both fine motor such as object manipulation and gross motor such as opening a hatch) and visual acuity tasks while maintaining spatial orientation and postural stability in time to escape safely. Exposure to even low frequency motions (0.2-2.0 Hz) induced by sea conditions surrounding a vessel can cause significant fine and gross motor control problems affecting critical functions. These motion frequencies coupled with the varying sea state conditions (frequencies ranging from 0.125-0.5 Hz) cause performance deficits by affecting the efficacy of motor and visual acuity dependent skills in tasks critical to emergency egress activities such as visual monitoring of displays, actuating discrete controls, operating auxiliary equipment and communicating with Mission Control and recovery teams. Thus, during exploration class missions the sensorimotor disturbances due to the crewmember's adaptation to microgravity may lead to disruption in the ability to maintain postural stability and perform functional egress tasks during the initial introduction to the Earth's gravitational environment. At present, the functional implication of the interactions between a debilitated crewmember during readaptation to Earth s gravity and the environmental constraints imposed by a water landing scenario is not defined and no operational countermeasure has been implemented to mitigate this risk. Stochastic resonance (SR) is a mechanism whereby noise can assist and hence enhance the response of neural systems to relevant, subthreshold sensory signals. Application of subthreshold stochastic resonance noise coupled to sensory input either through the proprioceptive, visual or vestibular sensory systems, has been shown to improve motor function. Crew members who have adapted to microgravity have acquired new sensorimotor strategies that take time to discard. We hypothesize that detection of time-critical subthreshold sensory signals will play a crucial role in improving strategic responses and thus the rate of skill re-acquisition will be faster, leading to faster recovery of function during their re-adaptation to Earth G. Therefore, we expect the use of stochastic resonance mechanisms will enhance the acquisition of new strategic abilities. This process should ensure rapid restoration of functional egress capabilities during the initial return to Earth G after prolonged space flight. Therefore, the overall goals of this project are to investigate performance of motor and visual tasks during varying sea state conditions and develop a countermeasure based on stochastic resonance that could be implemented to enhance sensorimotor capabilities with the aim of facilitating rapid adaptation to Earth s gravity, allowing rapid CEV egress on water in varying sea states following long-duration space flight.

Mulavara, Ajitkumar↗
NASA NTRS2014

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

Generalized Method of Cells↗