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NASA NTRS2002

Equivalent-Continuum Modeling With Application to Carbon Nanotubes

A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of single-walled carbon nanotubes and the design of nanotube-based devices, the modeling technique has been applied to determine the effective-continuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalent continuum models. As a result, an effective thickness of the continuum model has been determined. This effective thickness has been shown to be significantly larger than the interatomic spacing of graphite. The effective thickness has been shown to be significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the vibrational potential energy of the molecular model of a graphene sheet subjected to cylindrical bending with the strain energy of an equivalent continuum plate subjected to cylindrical bending.

Odegard, Gregory M.↗

NASA NTRS2005

Prediction of Mechanical Properties of Polymers With Various Force Fields

The effect of force field type on the predicted elastic properties of a polyimide is examined using a multiscale modeling technique. Molecular Dynamics simulations are used to predict the atomic structure and elastic properties of the polymer by subjecting a representative volume element of the material to bulk and shear finite deformations. The elastic properties of the polyimide are determined using three force fields: AMBER, OPLS-AA, and MM3. The predicted values of Young s modulus and shear modulus of the polyimide are compared with experimental values. The results indicate that the mechanical properties of the polyimide predicted with the OPLS-AA force field most closely matched those from experiment. The results also indicate that while the complexity of the force field does not have a significant effect on the accuracy of predicted properties, small differences in the force constants and the functional form of individual terms in the force fields determine the accuracy of the force field in predicting the elastic properties of the polyimide.

Odegard, Gregory M.↗

NASA NTRS2005

Multi-Scale Modeling of Cross-Linked Nanotube Materials

The effect of cross-linking single-walled carbon nanotubes on the Young's modulus of a nanotube-reinforced composite is modeled with a multi-scale method. The Young's modulus is predicted as a function of nanotube volume fraction and cross-link density. In this method, the constitutive properties of molecular representative volume elements are determined using molecular dynamics simulation and equivalent-continuum modeling. The Young's modulus is subsequently calculated for cross-linked nanotubes in a matrix which consists of the unreacted cross-linking agent. Two different cross-linking agents are used in this study, one that is short and rigid (Molecule A), and one that is long and flexible (Molecule B). Direct comparisons between the predicted elastic constants are made for the models in which the nanotubes are either covalently bonded or not chemically bonded to the cross-linking agent. At a nanotube volume fraction of 10%, the Young's modulus of Material A is not affected by nanotube crosslinking, while the Young's modulus of Material B is reduced by 64% when the nanotubes are cross-linked relative to the non-cross-linked material with the same matrix.

Frankland, S. J. V.↗

NASA NTRS2006

Multiscale Analysis of Delamination of Carbon Fiber-Epoxy Laminates with Carbon Nanotubes

A multi-scale analysis is presented to parametrically describe the Mode I delamination of a carbon fiber/epoxy laminate. In the midplane of the laminate, carbon nanotubes are included for the purposes of selectively enhancing the fracture toughness of the laminate. To analyze carbon fiber epoxy carbon nanotube laminate, the multi-scale methodology presented here links a series of parameterizations taken at various length scales ranging from the atomistic through the micromechanical to the structural level. At the atomistic scale molecular dynamics simulations are performed in conjunction with an equivalent continuum approach to develop constitutive properties for representative volume elements of the molecular structure of components of the laminate. The molecular-level constitutive results are then used in the Mori-Tanaka micromechanics to develop bulk properties for the epoxy-carbon nanotube matrix system. In order to demonstrate a possible application of this multi-scale methodology, a double cantilever beam specimen is modeled. An existing analysis is employed which uses discrete springs to model the fiber bridging affect during delamination propagation. In the absence of empirical data or a damage mechanics model describing the effect of CNTs on fracture toughness, several tractions laws are postulated, linking CNT volume fraction to fiber bridging in a DCB specimen. Results from this demonstration are presented in terms of DCB specimen load-displacement responses.

Riddick, Jaret C.↗

NASA NTRS2013

Effects of Microstructural Variability on Thermo-Mechanical Properties of a Woven Ceramic Matrix Composite

The objectives of this paper include identifying important architectural parameters that describe the SiC/SiC five-harness satin weave composite and characterizing the statistical distributions and correlations of those parameters from photomicrographs of various cross sections. In addition, realistic artificial cross sections of a 2D representative volume element (RVE) are generated reflecting the variability found in the photomicrographs, which are used to determine the effects of architectural variability on the thermo-mechanical properties. Lastly, preliminary information is obtained on the sensitivity of thermo-mechanical properties to architectural variations. Finite element analysis is used in combination with a response surface and it is shown that the present method is effective in determining the effects of architectural variability on thermo-mechanical properties.

Goldsmith, Marlana B.↗

NASA NTRSDate not supplied

Multiscale Modeling of Reconstructed Tricalcium Silicate using NASA Multiscale Analysis Tool

To study microstructure characteristics of cementitious materials hydrated in space; previously, cement binder formations were processed under microgravity conditions and was further compared against ground-based experiments. For accurate estimation of process-structure-property linkage, particularly on samples hydrated in the microgravity environment, it is desired to have a high-fidelity volumetric representation of the microstructure. However, owing to small sample size and high porosity of the space-returned samples, conventional experimental characterization techniques are not viable. Hence, a deep learning-based reconstruction algorithm was employed to obtain high fidelity 3D volumes from sparse high resolution 2D Scanning Electron Microscopy (SEM) images, as inputs to micromechanics-based modeling. This machine learning-based reconstruction methodology validated against low-order statistical descriptors, captured the microstructural topology of both sample types (ground, 1g and microgravity, μg). Due to the lack of gravity, hydration products of the samples processed in space differed from those processed-on ground. Such AI-generated virtual samples were analyzed in a multiscale recursive micromechanics approach using the NASA Multiscale Analysis Tool (NASMAT). Here, we present a methodology to rapidly integrate and evaluate these AI-generated volumes in NASMAT. The synthesized microstructural volumes are directly employed as Representative Volume Elements (RVEs) to preserve the fidelity (1 pixel = 0.54 m). Invariably, analysis of such largescale problems (5123 voxels) requires huge amount of computational resources. By taking advantage of the NASMAT architecture, we also focused on systematic multiscale integration of these AI-reconstructed virtual volumes to reduce the computational demands. In this work, this methodology is demonstrated on the ground-based, 1g samples. The estimated stiffness value of 15.90 GPa is comparable to experimentally obtained modulus of hydrated tricalcium silicate sample. The workflow presented here paves the way for utilizing the NASMAT tool to perform multiscale analyses of other multi-phase material systems using either 3D virtual datasets synthesized using AI or obtained via micro-CT.

Machine Learning↗

NASA NTRS2004

Estimation of Length-Scales in Soils by MRI

Soil can be best described as an unconsolidated granular media that forms porous structure. The present macroscopic theory of water transport in porous media rests upon the continuum hypothesis that the physical properties of porous media can be associated with continuous, twice-differentiable field variables whose spatial domain is a set of centroids of Representative Elementary Volume (REV) elements. MRI is an ideal technique to estimate various length-scales in porous media. A 0.267 T permanent magnet at NASA GRC was used for this study. A 2D or 3D spatially-resolved porosity distribution were obtained from the NMR signal strength from each voxel and the spin-lattice relaxation time. A classical spin-warp imaging with Multiple Spin Echos (MSE) was used to evaluate proton density in each voxel. Initial resolution of 256 x 256 was subsequently reduced by averaging neighboring voxels and the porosity convergence was observed. A number of engineered "space candidate" soils such as Isolite(trademark), Zeoponics(trademark), Turface(trademark), and Profile(trademark) were used. Glass beads in the size range between 50 microns to 2 mm were used as well. Initial results with saturated porous samples have shown a good estimate of the average porosity consistent with the gravimetric porosity measurement results. For Profile(trademark) samples with particle sizes ranging between 0.25 to 1 mm and characteristic interparticle pore size of 100 microns the characteristic Darcy scale was estimated to be about delta(sub REV) = 10 mm. Glass beads porosity show clear convergence toward a definite REV which stays constant throughout homogeneous sample. Additional information is included in the original extended abstract.

N E Daidzic↗

NASA NTRS2010

Instability of a Supersonic Boundary-Layer with Localized Roughness

A localized 3-D roughness causes boundary-layer separation and (weak) shocks. Most importantly, streamwise vortices occur which induce streamwise (low U, high T) streaks. Immersed boundary method (volume force) suitable to represent roughness element in DNS. Favorable comparison between bi-global stability theory and DNS for a "y-mode" Outlook: Understand the flow physics (investigate "z-modes" in DNS through sinuous spanwise forcing, study origin of the beat in DNS).

Marxen, Olaf↗

NASA NTRS1997

Trans-Laminar-Reinforced (TLR) Composites

A Trans-Laminar-Reinforced (TLR) composite is defined as composite laminate with up to five percent volume of fibrous reinforcement oriented in a 'trans-laminar' fashion in the through-thickness direction. The TLR can be continuous threads as in 'stitched laminates', or it can be discontinuous rods or pins as in 'Z-Fiber(TM) materials. It has been repeatedly documented in the literature that adding TLR to an otherwise two dimensional laminate results in the following advantages: substantially improved compression-after-impact response; considerably increased fracture toughness in mode 1 (double cantilever beam) and mode 2 (end notch flexure); and severely restricted size and growth of impact damage and edge delamination. TLR has also been used to eliminate catastrophic stiffener disbonding in stiffened structures. TLR directly supports the 'Achilles heel' of laminated composites, that is delamination. As little as one percent volume of TLR significantly alters the mechanical response of laminates. The objective of this work was to characterize the effects of TLR on the in-plane and inter-laminar mechanical response of undamaged composite laminates. Detailed finite element models of 'unit cells', or representative volumes, were used to study the effects of adding TLR on the elastic constants; the in-plane strength; and the initiation of delamination. Parameters investigated included TLR material, TLR volume fraction, TLR diameter, TLR through-thickness angle, ply stacking sequence, and the microstructural features of pure resin regions and curved in-plane fibers. The work was limited to the linear response of undamaged material with at least one ply interface. An inter-laminar dominated problem of practical interest, a flanged skin in bending, was also modeled.

Hinders, Mark↗

NASA NTRS1989

Moment method with isoparametric elements for three-dimensional anisotropic scatterers

A novel method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatters is presented. The method is based on a general volume integrodifferential formulation of the scattering problem and consists of the numerical solution of the coupled integral equations by the moment method and point matching. The numerical model of the scatterer is obtained by parametric volume elements, and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples.

Graglia, Roberto D.↗

NASA NTRS1977

Space station systems analysis study. Part 2, Volume 3: Appendixes, Book 1. Program requirements documentation

The objective elements representative of the kinds of space activities that will be supported by the space construction base (SCB) are discussed in (1) a brief mission overview including the primary purpose and general objectives; (2) descriptions of the processes involved (where applicable), the mission hardware, the principal activities to be undertaken, the test requirements, and the principal tests; and (3) the SCB requirements including such items as special devices (e.g., fabrication modules, assembly or construction fixtures, cranes, and airlocks), power, data management and communications, waste management, environmental control, safety, and logistics. Each program option is then described in terms of the objective elements it supports, its orbit, the general makeup of the SCB, the transportation approach, and the program schedule goals. The specific requirements that are imposed on the SCB in order to support program option L are given.

Source record↗

NASA NTRS1977

Numerical calculation of transonic flow past a swept wing by a finite volume method

The utility of numerical methods for predicting transonic flows over wings and bodies is well established. The computer program FLO22, based on a method presented earlier, has actually been widely used to calculate the aerodynamic performance of wings of transport aircraft. Provided that a correction is made for the displacement effect of the viscous boundary layer, this code has been found to give predictions which are accurate enough to serve as a useful design guide. The main disadvantages of the scheme used in FLO22 are the use of nonconservative difference formulas, which result in a failure to satisfy conservation of mass across shock waves, and the difficulty of finding suitable transformations of coordinates to permit the treatment of more complex geometric configurations. The method described here is an attempt to overcome these shortcomings, while retaining the successful features of the previous method. The basic idea is to use a discrete approximation which directly represents a balance of the mass flow through small volume elements. This leads to a relatively simple treatment of the potential flow equation in conservation form.

Jameson, A.↗

NASA NTRS1989

Definition of NASTRAN sets by use of parametric geometry

Many finite element preprocessors describe finite element model geometry with points, lines, surfaces and volumes. One method for describing these basic geometric entities is by use of parametric cubics which are useful for representing complex shapes. The lines, surfaces and volumes may be discretized for follow on finite element analysis. The ability to limit or selectively recover results from the finite element model is extremely important to the analyst. Equally important is the ability to easily apply boundary conditions. Although graphical preprocessors have made these tasks easier, model complexity may not lend itself to easily identify a group of grid points desired for data recovery or application of constraints. A methodology is presented which makes use of the assignment of grid point locations in parametric coordinates. The parametric coordinates provide a convenient ordering of the grid point locations and a method for retrieving the grid point ID's from the parent geometry. The selected grid points may then be used for the generation of the appropriate set and constraint cards.

Baughn, Terry V.↗

NASA NTRS1973

Three isoparametric solid elements for NASTRAN

Linear, quadratic, and cubic isoparametric hexahedral solid elements have been added to the element library of NASTRAN. These elements are available for static, dynamic, buckling, and heat-transfer analyses. Because the isoparametric element matrices are generated by direct numerical integration over the volume of the element, variations in material properties, temperatures, and stresses within the elements are represented in the computations. In order to compare the accuracy of the new elements, three similar models of a slender cantilever were developed, one for each element. All elements performed well. As expected, however, the linear element model yielded excellent results only when shear behavior predominated. In contrast, the results obtained from the quadratic and cubic element models were excellent in both shear and bending.

Johnson, S. E.↗

NASA NTRS1975

PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual

The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.

Pifko, A.↗

NASA NTRS1971

Reference Earth Orbital Research and Applications Investigations (Blue Book). Volume 2: Astronomy

Representative astronomy objectives, experiments, facilities, and instruments for use in the space station are discussed. The specific program elements describe a coordinated multiwavelength, multisensor approach needed to locate, observe, and interpret radiation from extragalactic, galactic, solar, and planetary sources in the different parts of the spectrum with spectral, angular, and temporal resolution not achievable from earth sites. Items of astronomy equipment are identified for the experiments to be conducted.

Source record↗

NASA NTRS2002

Deployment Simulation of Ultra-Lightweight Inflatable Structures

Dynamic deployment analyses of folded inflatable tubes are conducted to investigate modeling issues related to the deployment of solar sail booms. The analyses are necessary because ground tests include gravity effects and may poorly represent deployment in space. A control volume approach, available in the LS-DYNA nonlinear dynamic finite element code, and the ideal gas law are used to simulate the dynamic inflation deployment process. Three deployment issues are investigated for a tube packaged in a Z-fold configuration. The issues are the effect of the rate of inflation, the effect of residual air, and the effect of gravity. The results of the deployment analyses reveal that the time and amount of inflation gas required to achieve a full deployment are related to these issues.

Wang, John T.↗

NASA NTRS2013

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗