Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35

Continental-Scale Validation of Modis-Based and LEDAPS Landsat ETM + Atmospheric Correction Methods

The potential of Landsat data processing to provide systematic continental scale products has been demonstratedby several projects including the NASA Web-enabled Landsat Data (WELD) project. The recent freeavailability of Landsat data increases the need for robust and efficient atmospheric correction algorithms applicableto large volume Landsat data sets. This paper compares the accuracy of two Landsat atmospheric correctionmethods: a MODIS-based method and the Landsat Ecosystem Disturbance Adaptive ProcessingSystem (LEDAPS) method. Both methods are based on the 6SV radiative transfer code but have different atmosphericcharacterization approaches. The MODIS-based method uses the MODIS Terra derived dynamicaerosol type, aerosol optical thickness, and water vapor to atmospherically correct ETM+ acquisitions ineach coincident orbit. The LEDAPS method uses aerosol characterizations derived independently from eachLandsat acquisition and assumes a fixed continental aerosol type and uses ancillary water vapor. Validationresults are presented comparing ETM+ atmospherically corrected data generated using these two methodswith AERONET corrected ETM+ data for 95 10 km10 km 30 m subsets, a total of nearly 8 million 30 mpixels, located across the conterminous United States. The results indicate that the MODIS-based methodhas better accuracy than the LEDAPS method for the ETM+ red and longer wavelength bands.

Atmospheric correction↗

A Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results

A comprehensive review of the available methods for estimating fatigue damage from variable amplitude loading is presented. The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for random processes relevant to real structures such as in offshore or aerospace applications. Beginning with the Rayleigh (or narrow band) approximation, attempts at improved approximations or corrections to the Rayleigh approximation are examined by comparison to rainflow analysis of time histories simulated from psd functions representative of simple theoretical and real world applications. Spectral methods investigated include corrections by Wirsching and Light, Ortiz and Chen, the Dirlik formula, and the Single-Moment method, among other more recent proposed methods. Good agreement is obtained between the spectral methods and the time-domain rainflow identification for most cases, with some limitations. Guidelines are given for using the several spectral methods to increase confidence in the damage estimate.

Larsen, Curtis E.↗

Improved Detection System Description and New Method for Accurate Calibration of Micro-Channel Plate Based Instruments and Its Use in the Fast Plasma Investigation on NASA's Magnetospheric MultiScale Mission

The Fast Plasma Investigation (FPI) on NASAs Magnetospheric MultiScale (MMS) mission employs 16 Dual Electron Spectrometers (DESs) and 16 Dual Ion Spectrometers (DISs) with 4 of each type on each of 4 spacecraft to enable fast (30 ms for electrons; 150 ms for ions) and spatially differentiated measurements of the full 3D particle velocity distributions. This approach presents a new and challenging aspect to the calibration and operation of these instruments on ground and in flight. The response uniformity, the reliability of their calibration and the approach to handling any temporal evolution of these calibrated characteristics all assume enhanced importance in this application, where we attempt to understand the meaning of particle distributions within the ion and electron diffusion regions of magnetically reconnecting plasmas. Traditionally, the micro-channel plate (MCP) based detection systems for electrostatic particle spectrometers have been calibrated using the plateau curve technique. In this, a fixed detection threshold is set. The detection system count rate is then measured as a function of MCP voltage to determine the MCP voltage that ensures the count rate has reached a constant value independent of further variation in the MCP voltage. This is achieved when most of the MCP pulse height distribution (PHD) is located at higher values (larger pulses) than the detection system discrimination threshold. This method is adequate in single-channel detection systems and in multi-channel detection systems with very low crosstalk between channels. However, in dense multi-channel systems, it can be inadequate. Furthermore, it fails to fully describe the behavior of the detection system and individually characterize each of its fundamental parameters. To improve this situation, we have developed a detailed phenomenological description of the detection system, its behavior and its signal, crosstalk and noise sources. Based on this, we have devised a new detection system calibration method that enables accurate and repeatable measurement and calibration of MCP gain, MCP efficiency, signal loss due to variation in gain and efficiency, crosstalk from effects both above and below the MCP, noise margin, and stability margin in one single measurement. More precise calibration is highly desirable as the instruments will produce higher quality raw data that will require less post-acquisition data correction using results from in-flight pitch angle distribution measurements and ground calibration measurements. The detection system description and the fundamental concepts of this new calibration method, named threshold scan, will be presented. It will be shown how to derive all the individual detection system parameters and how to choose the optimum detection system operating point. This new method has been successfully applied to achieve a highly accurate calibration of the DESs and DISs of the MMS mission. The practical application of the method will be presented together with the achieved calibration results and their significance. Finally, it will be shown that, with further detailed modeling, this method can be extended for use in flight to achieve and maintain a highly accurate detection system calibration across a large number of instruments during the mission.

detection system↗

A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

High-Order↗

Comparison of High-Order and Low-Order Methods for Large-Eddy Simulation of a Compressible Shear Layer

The objective of this work is to compare a high-order solver with a low-order solver for performing Large-Eddy Simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the highorder method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.

large eddy simulations↗

Technology Alignment and Portfolio Prioritization (TAPP): Advanced Methods in Strategic Analysis, Technology Forecasting and Long Term Planning for Human Exploration and Operations, Advanced Exploration Systems and Advanced Concepts

The Advanced Concepts Office (ACO) at NASA, Marshall Space Flight Center is expanding its current technology assessment methodologies. ACO is developing a framework called TAPP that uses a variety of methods, such as association mining and rule learning from data mining, structure development using a Technological Innovation System (TIS), and social network modeling to measure structural relationships. The role of ACO is to 1) produce a broad spectrum of ideas and alternatives for a variety of NASA's missions, 2) determine mission architecture feasibility and appropriateness to NASA's strategic plans, and 3) define a project in enough detail to establish an initial baseline capable of meeting mission objectives ACO's role supports the decision­-making process associated with the maturation of concepts for traveling through, living in, and understanding space. ACO performs concept studies and technology assessments to determine the degree of alignment between mission objectives and new technologies. The first step in technology assessment is to identify the current technology maturity in terms of a technology readiness level (TRL). The second step is to determine the difficulty associated with advancing a technology from one state to the next state. NASA has used TRLs since 1970 and ACO formalized them in 1995. The DoD, ESA, Oil & Gas, and DoE have adopted TRLs as a means to assess technology maturity. However, "with the emergence of more complex systems and system of systems, it has been increasingly recognized that TRL assessments have limitations, especially when considering [the] integration of complex systems." When performing the second step in a technology assessment, NASA requires that an Advancement Degree of Difficulty (AD2) method be utilized. NASA has used and developed or used a variety of methods to perform this step: Expert Opinion or Delphi Approach, Value Engineering or Value Stream, Analytical Hierarchy Process (AHP), Technique for the Order of Prioritization by Similarity to Ideal Solution (TOPSIS), and other multi­‐criteria decision-making methods. These methods can be labor-intensive, often contain cognitive or parochial bias, and do not consider the competing prioritization between mission architectures. Strategic Decision-Making (SDM) processes cannot be properly understood unless the context of the technology is understood. This makes assessing technological change particularly challenging due to the relationships "between incumbent technology and the incumbent (innovation) system in relation to the emerging technology and the emerging innovation system." The central idea in technology dynamics is to consider all activities that contribute to the development, diffusion, and use of innovations as system functions. Bergek defines system functions within a TIS to address what is actually happening and has a direct influence on the ultimate performance of the system and technology development. ACO uses similar metrics and is expanding these metrics to account for the structure and context of the technology. At NASA technology and strategy is strongly interrelated. NASA's Strategic Space Technology Investment Plan (SSTIP) prioritizes those technologies essential to the pursuit of NASA's missions and national interests. The SSTIP is strongly coupled with NASA's Technology Roadmaps to provide investment guidance during the next four years, within a twenty-year horizon. This paper discusses the methods ACO is currently developing to better perform technology assessments while taking into consideration Strategic Alignment, Technology Forecasting, and Long Term Planning.

Funaro, Gregory V.↗

Comparison of High-Order and Low-Order Methods for Large-Eddy Simulation of a Compressible Shear Layer

The objective of this work is to compare a high-order solver with a low-order solver for performing large-eddy simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the high-order method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.

large eddy simulations↗

Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method

Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity so that they are being frequently employed for specific real world applications within NASA. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by highly complex geometries. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the peculiarities of applying the immersed boundary method to this moving boundary problem, we will provide a detailed aeroacoustic analysis of the noise generation mechanisms encountered in the open rotor flow. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. The noise generation mechanisms are analyzed employing spectral analysis, proper orthogonal decomposition and the causality method.

Computational↗

An Efficient Ray-Tracing Method for Determining Terrain Intercepts in EDL Simulations

The calculation of a ray's intercept from an arbitrary point in space to a prescribed surface is a common task in computer simulations. The arbitrary point often represents an object that is moving according to the simulation, while the prescribed surface is fixed in a defined frame. For detailed simulations, this surface becomes complex, taking the form of real-world objects such as mountains, craters or valleys which require more advanced methods to accurately calculate a ray's intercept location. Incorporation of these complex surfaces has commonly been implemented in graphics systems that utilize highly optimized graphics processing units to analyze such features. This paper proposes a simplified method that does not require computationally intensive graphics solutions, but rather an optimized ray-tracing method for an assumed terrain dataset. This approach was developed for the Mars Science Laboratory mission which landed on the complex terrain of Gale Crater. First, this paper begins with a discussion of the simulation used to implement the model and the applicability of finding surface intercepts with respect to atmosphere modeling, altitude determination, radar modeling, and contact forces influencing vehicle dynamics. Next, the derivation and assumptions of the intercept finding method are presented. Key assumptions are noted making the routines specific to only certain types of surface data sets that are equidistantly spaced in longitude and latitude. The derivation of the method relies on ray-tracing, requiring discussion on the formulation of the ray with respect to the terrain datasets. Further discussion includes techniques for ray initialization in order to optimize the intercept search. Then, the model implementation for various new applications in the simulation are demonstrated. Finally, a validation of the accuracy is presented along with the corresponding data sets used in the validation. A performance summary of the method will be shown using the analysis from the Mars Science Laboratory's terminal descent sensing model. Alternate uses will also be shown for determining horizon maps and orbiter set times.

Shidner, Jeremy D.↗

California Reservoir Inflow Projections Using a Hybrid EMD-Matalas Method

Inflow projections provide scenarios for future water availability and are integral to operational reservoir management. They can aid water practitioners in decision-making for conservation efforts, multiyear storage retention, managing flood risk, downstream water releases, and regional growth planning. However, conventional methods are often limited in terms of their ability to incorporate non-stationarity, long run persistence, and the cross-correlation of multiple series in a region. This research aims to address these issues with a hybrid approach that integrates Empirical Mode Decomposition (EMD) with the Matalas multisite generation method. Multiple long-run inflows were examined for the Shasta/Trinity Reservoirs and Oroville Reservoir of California. EMD is used to decompose each inflow series into a set of independent intrinsic mode functions (IMFs) that have different timescales and frequencies. These IMFs were grouped into intradecadal (less-than- 10-year average periodicity) and interdecadal (greater-than-10-year average periodicity) series for each site. The IMF projections at each site were then combined to produce replicates of the historical data. This preserves the correlation structure of the intra- and interdecadal components of the series. The hybrid EMD-Matalas method was compared to a traditional autoregressive lag-one model. Both methods were found to retain the statistical characteristics of the historical data. However, the EMD-Matalas method retained the multiyear wet and dry periods to a greater degree. This was examined by comparing the 5-year and 10-year sums from the traditional model with the hybrid EMD-Matalas model. An advantage of the EMD-Matalas method is the ability to explicitly incorporate modes of non-stationary long-run persistence often associated with large-scale climate drivers such as the El Nino Southern Oscillation (ENSO) or the Pacific Decadal Oscillation (PDO). This contributes to scenario planning that may be particularly important for managing multiyear low flow periods.

inflow projections↗

X-Ray Diffraction (XRD) Characterization Methods for Sigma=3 Twin Defects in Cubic Semiconductor (100) Wafers

An X-ray defraction (XRD) characterization method for sigma=3 twin defects in cubic semiconductor (100) wafers includes a concentration measurement method and a wafer mapping method for any cubic tetrahedral semiconductor wafers including GaAs (100) wafers and Si (100) wafers. The methods use the cubic semiconductor's (004) pole figure in order to detect sigma=3/{111} twin defects. The XRD methods are applicable to any (100) wafers of tetrahedral cubic semiconductors in the diamond structure (Si, Ge, C) and cubic zinc-blend structure (InP, InGaAs, CdTe, ZnSe, and so on) with various growth methods such as Liquid Encapsulated Czochralski (LEC) growth, Molecular Beam Epitaxy (MBE), Organometallic Vapor Phase Epitaxy (OMVPE), Czochralski growth and Metal Organic Chemical Vapor Deposition (MOCVD) growth.

Park, Yeonjoon↗

Historical Perspective on Fast Coupled Loads Analysis Methods

Spacecraft structural designs are typically verified through a coupled loads analysis (CLA) process, which couples the spacecraft model with the launch vehicle (LV) model to predict low-frequency quasi-static and dynamic responses. The CLA calculations are typically the responsibility of the LV organization, but the spacecraft organization has a vested interest in being able to calculate approximate CLA results during the design of the spacecraft. Because of this, there has long been interest in a method that would allow a spacecraft organization to perform a CLA without access to the full set of LV models and forcing functions. One such method is the Norton-Thevenin Receptance Coupling (NTRC) approach, which is specifically designed to accurately transform LV free accelerations (no payload) into coupled system accelerations (LV plus payload). The purpose of this report is to provide historical context for the NTRC method and compare it with methods that have been used in the past. In particular, it is compared to a frequency-domain substitution method that had been used for a long period of time at the Jet Propulsion Laboratory, and a component-mode-based equivalent to that method.

Blelloch, Paul A.↗

Application of a Temperature-Dependent Load Prediction Method to a RUAG Six-Component Block-Type Balance

Temperature-dependent data of a RUAG six-component block-type balance was analyzed to assess the accuracy of two load prediction methods for temperature-dependent balance data. The supplied data was prepared for the analysis by splitting it into calibration and check load data subsets. The first calibration data subset was obtained at a temperature of 294 Kelvin. The second calibration data subset was obtained at a temperature of 315 Kelvin. A subset of 38 points was extracted from the second data set and used as check loads so that the accuracy of the two load prediction methods could be tested. First, the Iterative Method in combination with an extended independent and dependent variable set was used for the balance load prediction. This approach fits electrical outputs as a function of loads and the temperature and, afterwards, constructs a load iteration scheme from the regression coefficients so that loads can be predicted from outputs and the temperature during a wind tunnel test. The Non-Iterative Method was also used for the load prediction. This alternate method can more easily be implemented in a data system as loads are directly fitted as a function of electrical outputs and the temperature. Analysis results for the axial force are only discussed in the paper as similar results were obtained for the other five load components. Results for both methods clearly show that the cross-product term constructed from either a primary gage load or a primary gage output and the temperature explains the majority of the temperature-dependent part of the predicted balance load. This term models the temperature dependent nature of the gage sensitivity. Therefore, it is recommended to apply primary gage loadings at different temperatures during a balance calibration whenever temperature effects need to be described. These loadings will contain information about the temperature-dependent nature of the gage sensitivities that can be quantified by related cross-product terms in regression models of the data.

strain-gage balance↗

Intercomparison of Field Methods for Acquiring Ground Reflectance at Railroad Valley Playa for Spectral Calibration of Satellite Data

Ground reflectance was acquired at the Railroad Valley Playa calibration site in Nevada USA using different methods of collection. The data was collected near the time and date of Landsat 8 OLI and Sentinel-2 satellite overpasses so an inter-comparison could be made with the reflectance products to determine which method was more suitable for vicarious calibration. The field spectrometers and reference panels were characterized before the field campaign. A continuous acquisition method was compared to stop and measure collections. Both acquisition methods were collected along an 80 m east-west transect as well as for a series of north-south transects over an 80 x 320 m area, with the stop and measure method being performed at random sampling locations. The measurements were performed using two field spectrometers by three teams of two people to compare the repeatability. The aim of the field campaign was to determine the variability due to the operator and the method of collection.

Lau, Ian C.↗

Intercomparison of Field Methods for Acquiring Ground Reflectance at Railroad Valley Playa for Spectral Calibration of Satellite Data

Ground reflectance was acquired at the Railroad Valley Playa calibration site in Nevada USA using different methods of collection. The data was collected near the time and date of Landsat 8 OLI and Sentinel-2 satellite overpasses so an inter-comparison could be made with the reflectance products to determine which method was more suitable for vicarious calibration. The field spectrometers and reference panels were characterized before the field campaign. A continuous acquisition method was compared to stop and measure collections. Both acquisition methods were collected along an 80 m east-west transect as well as for a series of north-south transects over an 80 x 320 m area, with the stop and measure method being performed at random sampling locations. The measurements were performed using two field spectrometers by three teams of two people to compare the repeatability. The aim of the field campaign was to determine the variability due to the operator and the method of collection.

Lau, Ian C.↗

Elemental Variation and Petrogenesis of Pyroxenes in HED Meteorites by Multivariable Discriminant Analysis Method

HED (Howardite, Eucrite and Diogenite) are meteorites with mafic and ultramafic igneous composition. Previous studies suggested HED came from asteroid (4) Vesta and they were generated by magmatic melting followed by differentiation crystallization, metamorphic, and impact. Uniform oxygen isotopic composition of HED samples favors global magma ocean for (4) Vesta. However, the petrological diversity of HED may indicate more complex magma processes in the meteorites. In general, most of the geochemical studies are using traditional methods (e.g. element to element or ratio to ratio plots) to classify the different rock type and groups. With the traditional methods, only limited elements can be shown in a figure. As such, some meteorites may have been identified as HED by a traditional method but found different either in isotopic composition or other elemental characteristic. These anomalous HED meteorites may or may not come from asteroid (4) Vesta. In fact, magma is a unit system where any elemental change should affect to all other elements as a whole, it would be reasonable to consider all elements together to look for the systematical changes. Using multivariable discriminant analysis (MDA) method is one of such testing for their geochemical variation. The method may be able to help us to better understand the petrologic processes and the relationship among elements. This study is to test the MDA method by focus mainly on pyroxene composition of eucrite and diogenite.

Peng, Z. X.↗

Extending A Correction Method for Unsteady Transonic Aerodynamics to Variable Camber Continuous Trailing Edge Flap

In this study, we have extended our correction method for transonic aerodynamics to baseline and variable camber continuous trailing edge (VCCTEF) geometries of super-critical airfoils at cruise conditions. This correction method modifies Theodorsen theory, which is based on incompressible potential flow over a flat plate. The method is partly based on CFD RANS simulations of oscillating NASA generic transport model (GTM) baseline cruise and VCCTEF airfoil geometries in pitch and shows promise for addressing transonic flutter problems of aeroelasticity. In the earlier study1, the Theodorsen functions were modulated with non-linear functions of Mach number, M, and reduced frequency, k, and thus the correction was demonstrated for the symmetrical NACA0012 airfoil. In the present study, the modulation functions are also allowed to account for the effects of camber and thickness of the airfoil. This is demonstrated by applying the correction method to various symmetric NACA00xx airfoil geometries (NACA001, NACA0002, NACA0012, NACA0015 and NACA0018), the NASA GTM super-critical baseline and VCCTEF airfoil geometries, e.g., the circular airfoil, VCCTEF222. First results indicate that the correction method accounts for a large variation of thickness of airfoils and camber. The present correction method will guide the development of a new state space model for the VCCTEF system and eventually a new transfer function that will be incorporated in a new aeroelastic framework leading to an appropriate transonic flutter model for use in the future aircraft systems in development under the NASA Advanced Air Transportation Technologies (AATT) project.

Kaul, Upender K.↗

Benchmarking Mixed Mode Failure in Progressive Damage and Failure Analysis Methods

The verification and validation of progressive-damage-analysis finite element methods are difficult but critical tasks to undertake during their development. Verification exercises assess whether a predictive analysis tool produces results that are consistent with the fundamental concepts and assumptions of the tool under evaluation. Ideally, closed-form analytical solutions can be derived for which method verification results can be compared. Problems selected for computational tool verification are often simple and isolate individual features of the tool. In the case of progressive damage finite element methods, verifications should be performed to evaluate the ability of the model to predict the initiation of damage and its growth through the finite element mesh under a variety of conditions. Mabson et al. proposed a test case of a unidirectional, fiber-reinforced plate with a center crack subjected to tensile loads to evaluate matrix crack propagation predictions. The problem was modeled using the Abaqus Hashin continuum damage mechanics (CDM) model for fiber-reinforced composites. Different combinations of matrix strengths and element sizes were used in the simulations, and the results were compared to a closed-form solution based on linear elastic fracture mechanics (LEFM). It was determined that the Abaqus CDM model could predict the LEFM solution of Mode I cracks only when the finite element mesh density met specific requirements based on the material properties. This paper presents closed-form LEFM solutions for a center notch mixed mode (CNMM) verification problem. Parametric finite element analyses were developed using progressive damage analysis methods of both the Discrete Damage Mechanics (DDM) and CDM classes. The progressive damage analysis methods applied in the analyses of the CNMM problem include CompDam and the Floating Node Method. Analyses were conducted with various mode mixities and element sizes to verify that the damage models were working as intended and to identify any limits of applicability.

Leone, Frank↗