Search NASA⌕ Search

SEARCH · Search NASA

Results for “constitutive relations”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Notes on rotating turbulence

This work investigates the turbulent constitutive relation when turbulence is subjected to solid body rotation. Laws regarding spectra and asymptotic decay of rotating homogeneous turbulence were confirmed through large-eddy simulation (LES) computations. Rotating turbulent flows exist in many industrial, geophysical, and astrophysical applications. From Lagrangian analysis a relation between turbulent stress and strain in rotating homogeneous turbulence was inferred. This relation was used to derive the spectral energy flux and, ultimately, the energy spectrum form. If the rotation wavenumber k(sub Omega) lies in the inertial subrange, then for wavenumbers less than k(sub Omega) the turbulence motions are affected by rotation and the energy spectrum slope is modified. Energy decay laws inferred in other reports and the present results suggest a modification of the epsilon model equation and eddy viscosity in k-epsilon models.

Zeman, Otto↗
NASA NTRS1994

Choked flow effects in the NSI driven pin puller

This paper presents an analysis for pyrotechnic combustion and pin motion in the NASA Standard Initiator (NSI) actuated pin puller. The conservation principles and constitutive relations for a multi-phase system are posed and reduced to a set of eight ordinary differential equations which are solved to predict the system performance. The model tracks the interactions of the unreacted, incompressible solid pyrotechnic, incompressible condensed phase combustion products, and gas phase combustion products. The model accounts for multiple pyrotechnic grains, variable burn surface area, and combustion product mass flow rates through an orifice located within the device. Pressure-time predictions compare favorably with experimental data. Results showing model sensitivity to changes in the cross-sectional area of the orifice are presented.

Gonthier, Keith A.↗
NASA NTRS1995

Haptic interfaces: Hardware, software and human performance

Virtual environments are computer-generated synthetic environments with which a human user can interact to perform a wide variety of perceptual and motor tasks. At present, most of the virtual environment systems engage only the visual and auditory senses, and not the haptic sensorimotor system that conveys the sense of touch and feel of objects in the environment. Computer keyboards, mice, and trackballs constitute relatively simple haptic interfaces. Gloves and exoskeletons that track hand postures have more interaction capabilities and are available in the market. Although desktop and wearable force-reflecting devices have been built and implemented in research laboratories, the current capabilities of such devices are quite limited. To realize the full promise of virtual environments and teleoperation of remote systems, further developments of haptic interfaces are critical. In this paper, the status and research needs in human haptics, technology development and interactions between the two are described. In particular, the excellent performance characteristics of Phantom, a haptic interface recently developed at MIT, are highlighted. Realistic sensations of single point of contact interactions with objects of variable geometry (e.g., smooth, textured, polyhedral) and material properties (e.g., friction, impedance) in the context of a variety of tasks (e.g., needle biopsy, switch panels) achieved through this device are described and the associated issues in haptic rendering are discussed.

Srinivasan, Mandayam A.↗
NASA NTRS1996

Analysis of Compressible Mixing Layers Using Dilatational Covariances Model

Compressible mixing layers are analyzed using a dilatational covariances model based on a pseudo-sound constitutive relation. The calculations are used to evaluate the different physical phenomena affecting compressible mixing layers. The rate of growth of the mixing layer is retarded by both the compressible dissipation and the pressure-dilatational covariances. The pressure-dilatational, essentially a nonequilibrium effect, reduces the amount of excess production over dissipation available for the turbulence energy growth. The pseudo-sound model also includes a history dependent portion: this is also investigated. All constants in the model and used in these computations are predicted by the theory.

Thangam, S.↗
NASA NTRS1996

Non-linear k-epsilon-v(sup 2)(bar) modeling with application to high-lift

The k-epsilon-v(sup 2)(bar) model has been investigated to quantify its predictive performance on two high-lift configurations: 2D flow over a single-element aerofoil, involving closed-type separation; 3D flow over a prolate spheroid, involving open-type separation. A 'code-friendly' modification has been proposed which enhances the numerical stability, in particular, for explicit and uncoupled flow solvers. As a result of introducing Reynolds-number dependence into a coefficient of the s-equation, the skin-friction distribution for the by-pass transitional flow over a flat plate is better predicted. In order to improve deficiencies arising from the Boussinesq approximation, a nonlinear stress-strain constitutive relation was adopted, in which the only one free constant is calibrated on the basis of DNS data, and the Reynolds-stress anisotropy near the wall is fairly well represented.

Lien, F. S.↗
NASA NTRS1998

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Simmonds, James G.↗
NASA NTRS1999

An Analysis of the Macroscopic Tensile Behavior of a Nonlinear Nylon Reinforced Elastomeric Composite System Using MAC/GMC

A special class of composite laminates composed of soft rubbery matrices and stiff reinforcements made of steel wires or synthetic fibers is examined, where each constituent behaves in a nonlinear fashion even in the small strain domain. Composite laminates made of piles stacked at alternating small orientation angles with respect to the applied axial strain are primarily dominated by the nonlinear behavior of the reinforcing fibers. However; composites with large ply orientations or those perpendicular to the loading axis, will approximate the behavior of the matrix phase and respond in even a more complex fashion for arbitrarily stacked piles. The geometric nonlinearity due to small cord rotations during loading was deemed here to have a second order effect and consequently dropped from any consideration. The user subroutine USRMAT within the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC), was utilized to introduce the constituent material nonlinear behavior. Stress-strain behavior at the macro level was experimentally generated for single and multi ply composites comprised of continuous Nylon-66 reinforcements embedded in a carbon black loaded rubbery matrix. Comparisons between the predicted macro composite behavior and experimental results are excellent when material nonlinearity is included in the analysis. In this paper, a brief review of GMC is provided, along with a description of the nonlinear behavior of the constituents and associated constituent constitutive relations, and the improved macro (or composite) behavior predictions are documented and illustrated.

Assaad, Mahmoud↗
NASA NTRS1999

A Hysteresis Model for Piezoceramic Materials

This paper addresses the modeling of nonlinear constitutive relations and hysteresis inherent to piezoceramic materials at moderate to high drive levels. Such models are, necessary to realize the, full potential of the materials in high performance control applications, and a necessary prerequisite is the development of techniques which permit control implementation. The approach employed here is based on the qualification of reversible and irreversible domain wall motion in response to applied electric fields. A comparison with experimental data illustrates that because the resulting ODE model is physics-based, it can be employed for both characterization and prediction of polarization levels throughout the range of actuator operation. Finally, the ODE formulation is amenable to inversion which facilitates the development of an inverse compensator for linear control design.

Smith, Ralph C.↗
NASA NTRS2000

Experiment Evaluation of Bifurcation in Sands

The basic principles of bifurcation analysis have been established by several investigators, however several issues remain unresolved, specifically how do stress level, grain size distribution, and boundary conditions affect general bifurcation phenomena in pressure sensitive and dilatant materials. General geometrical and kinematics conditions for moving surfaces of discontinuity was derived and applied to problems of instability of solids. In 1962, the theoretical framework of bifurcation by studying the acceleration waves in elasto-plastic (J2) solids were presented. Bifurcation analysis for more specific forms of constitutive behavior was examined by studying localization in pressure-sensitive, dilatant materials, however, analyses were restricted to plane deformation states only. Bifurcation analyses were presented and applied to predict shear band formations in sand under plane strain condition. The properties of discontinuous bifurcation solutions for elastic-plastic solids under axisymmetric and plane strain loading conditions were studied. The study focused on theory, but also references and comparisons to experiments were made. The current paper includes a presentation of a summary of bifurcation analyses for biaxial and triaxial (axisymmetric) loading conditions. The Coulomb model is implemented using incremental piecewise scheme to predict the constitutive relations and shear band inclination angles. Then, a comprehensive evaluation of bifurcation phenomena is presented based on data from triaxial experiments performed under microgravity conditions aboard the Space Shuttle under very low effective confining pressure (0.05 to 1.30 kPa), in which very high peak friction angles (47 to 75 degrees) and dilatancy angles (30 to 31 degrees) were measured. The evaluation will be extended to include biaxial experiments performed on the same material under low (10 kPa) and moderate (100 kPa) confining pressures. A comparison between the behavior under biaxial and triaxial loading conditions will be presented, and related issues concerning influence of confining pressure will be discussed.

Alshibi, Khalid A.↗
NASA NTRS1997

Predictive Modeling in Plasma Reactor and Process Design

Research continues toward the improvement and increased understanding of high-density plasma tools. Such reactor systems are lauded for their independent control of ion flux and energy enabling high etch rates with low ion damage and for their improved ion velocity anisotropy resulting from thin collisionless sheaths and low neutral pressures. Still, with the transition to 300 mm processing, achieving etch uniformity and high etch rates concurrently may be a formidable task for such large diameter wafers for which computational modeling can play an important role in successful reactor and process design. The inductively coupled plasma (ICP) reactor is the focus of the present investigation. The present work attempts to understand the fundamental physical phenomena of such systems through computational modeling. Simulations will be presented using both computational fluid dynamics (CFD) techniques and the direct simulation Monte Carlo (DSMC) method for argon and chlorine discharges. ICP reactors generally operate at pressures on the order of 1 to 10 mTorr. At such low pressures, rarefaction can be significant to the degree that the constitutive relations used in typical CFD techniques become invalid and a particle simulation must be employed. This work will assess the extent to which CFD can be applied and evaluate the degree to which accuracy is lost in prediction of the phenomenon of interest; i.e., etch rate. If the CFD approach is found reasonably accurate and bench-marked with DSMC and experimental results, it has the potential to serve as a design tool due to the rapid time relative to DSMC. The continuum CFD simulation solves the governing equations for plasma flow using a finite difference technique with an implicit Gauss-Seidel Line Relaxation method for time marching toward a converged solution. The equation set consists of mass conservation for each species, separate energy equations for the electrons and heavy species, and momentum equations for the gas. The sheath is modeled by imposing the Bohm velocity to the ions near the walls. The DSMC method simulates each constituent of the gas as a separate species which would be analogous in CFD to employing separate species mass, momentum, and energy equations. All particles including electrons are moved and allowed to collide with one another with the stipulation that the electrons remain tied to the ions consistent with the concept of ambipolar diffusion. The velocities of the electrons are allowed to be modified during collisions and are not confined to a Maxwellian distribution. These benefits come at a price in terms of computational time and memory. The DSMC and CFD are made as consistent as possible by using similar chemistry and power deposition models. Although the comparison of CFD and DSMC is interesting, the main goal of this work is the increased understanding of high-density plasma flowfields that can then direct improvements in both techniques. This work is unique in the level of the physical models employed in both the DSMC and CFD for high-density plasma reactor applications. For example, the electrons are simulated in the present DSMC work which has not been done before for low temperature plasma processing problems. In the CFD approach, for the first time, the charged particle transport (discharge physics) has been self-consistently coupled to the gas flow and heat transfer.

Hash, D. B.↗
NASA NTRS2003

Fundamentals of Polarized Light

The analytical and numerical basis for describing scattering properties of media composed of small discrete particles is formed by the classical electromagnetic theory. Although there are several excellent textbooks outlining the fundamentals of this theory, it is convenient for our purposes to begin with a summary of those concepts and equations that are central to the subject of this book and will be used extensively in the following chapters. We start by formulating Maxwell's equations and constitutive relations for time- harmonic macroscopic electromagnetic fields and derive the simplest plane-wave solution that underlies the basic optical idea of a monochromatic parallel beam of light. This solution naturally leads to the introduction of such fundamental quantities as the refractive index and the Stokes parameters. Finally, we define the concept of a quasi-monochromatic beam of light and discuss its implications.

Mishchenko, Michael↗
NASA NTRS2000

Vascular mechanics of the coronary artery

This paper describes our research into the vascular mechanics of the coronary artery and plaque. The three sections describe the determination of arterial mechanical properties using intravascular ultrasound (IVUS), a constitutive relation for the arterial wall, and finite element method (FEM) models of the arterial wall and atheroma. METHODS: Inflation testing of porcine left anterior descending coronary arteries was conducted. The changes in the vessel geometry were monitored using IVUS, and intracoronary pressure was recorded using a pressure transducer. The creep and quasistatic stress/strain responses were determined. A Standard Linear Solid (SLS) was modified to reproduce the non-linear elastic behavior of the arterial wall. This Standard Non-linear Solid (SNS) was implemented into an axisymetric thick-walled cylinder numerical model. Finite element analysis models were created for five age groups and four levels of stenosis using the Pathobiological Determinants of Atherosclerosis Youth (PDAY) database. RESULTS: The arteries exhibited non-linear elastic behavior. The total tissue creep strain was epsilon creep = 0.082 +/- 0.018 mm/mm. The numerical model could reproduce both the non-linearity of the porcine data and time dependent behavior of the arterial wall found in the literature with a correlation coefficient of 0.985. Increasing age had a strong positive correlation with the shoulder stress level, (r = 0.95). The 30% stenosis had the highest shoulder stress due to the combination of a fully formed lipid pool and a thin cap. CONCLUSIONS: Studying the solid mechanics of the arterial wall and the atheroma provide important insights into the mechanisms involved in plaque rupture.

NASA Program Biomedical Research and Countermeasur↗
NASA NTRS2004

Two-Fluid Models and Interfacial Area Transport in Microgravity Condition

The objective of the present study is to develop a two-fluid model formulation with interfacial area transport equation applicable for microgravity conditions. The new model is expected to make a leapfrog improvement by furnishing the constitutive relations for the interfacial interaction terms with the interfacial area transport equation, which can dynamically model the changes of the interfacial structures. In the first year of this three-year project supported by the U.S. NASA, Office of Biological and Physics Research, the primary focus is to design and construct a ground-based, microgravity two-phase flow simulation facility, in which two immiscible fluids with close density will be used. In predicting the two-phase flow behaviors in any two-phase flow system, the interfacial transfer terms are among the most essential factors in the modeling. These interfacial transfer terms in a two-fluid model specify the rate of phase change, momentum exchange, and energy transfer at the interface between the two phases. For the two-phase flow under the microgravity condition, the stability of the fluid particle interface and the interfacial structures are quite different from those under normal gravity condition. The flow structure may not reach an equilibrium condition and the two fluids may be loosely coupled such that the inertia terms of each fluid should be considered separately by use of the two-fluid model. Previous studies indicated that, unless phase-interaction terms are accurately modeled in the two-fluid model, the complex modeling does not necessarily warrant an accurate solution.

Ishii, Mamoru↗
NASA NTRS1994

Finite Element Analysis of the Random Response Suppression of Composite Panels at Elevated Temperatures using Shape Memory Alloy Fibers

A feasibility study on the use of shape memory alloys (SMA) for suppression of the random response of composite panels due to acoustic loads at elevated temperatures is presented. The constitutive relations for a composite lamina with embedded SMA fibers are developed. The finite element governing equations and the solution procedures for a composite plate subjected to combined acoustic and thermal loads are presented. Solutions include: 1) Critical buckling temperature; 2) Flat panel random response; 3) Thermal postbuckling deflection; 4) Random response of a thermally buckled panel. The preliminary results demonstrate that the SMA fibers can completely eliminate the thermal postbuckling deflection and significantly reduce the random response at elevated temperatures.

Turner, Travis L.↗
NASA NTRS1992

Finite Element Modeling of the Bulk Magnitization of Railroad Wheels to Improve Test Conditions for Magnetoacoustic Residual Stress Measurements

The magnetoacoustic measurement technique has been used successfully for residual stress measurements in laboratory samples. However, when used to field test samples with complex geometries, such as railroad wheels, the sensitivity of the method declines dramatically. It has been suggested that the decrease in performance may be due, in part, to an insufficient or nonuniform magnetic induction in the test sample. The purpose of this paper is to optimize the test conditions by using finite element modeling to predict the distribution of the induced bulk magnetization of railroad wheels. The results suggest that it is possible to obtain a sufficiently large and uniform bulk magnetization by altering the shape of the electromagnet used in the tests. Consequently, problems associated with bulk magnetization can be overcome, and should not prohibit the magnetoacoustic technique from being used to make residual stress measurements in railroad wheels. We begin by giving a brief overview of the magnetoacoustic technique as it applies to residual stress measurements of railroad wheels. We then define the finite element model used to predict the behavior of the current test configuration along with the nonlinear constitutive relations which we obtained experimentally through measurements on materials typically used to construct both railroad wheels and electromagnets. Finally, we show that by modifying the pole of the electromagnet it is possible to obtain a significantly more uniform bulk magnetization in the region of interest.

Fulton, J. P.↗
NASA NTRS2004

Mechanical Properties of Plasma-Sprayed ZrO2-8 wt% Y2O3 Thermal Barrier Coatings

Mechanical behavior of free standing, plasma-sprayed ZrO2-8 wt% Y2O3 thermal barrier coatings, including strength, fracture toughness, fatigue, constitutive relation, elastic modulus, and directionality, has been determined under various loading-specimen configurations. This report presents and describes a summary of mechanical properties of the plasma-sprayed coating material to provide them as a design database.

Choi, Sung R.↗
NASA NTRS2011

The Effect of Boundary Support and Reflector Dimensions on Inflatable Parabolic Antenna Performance

For parabolic antennas with sufficient surface accuracy, more power can be radiated with a larger aperture size. This paper explores the performance of antennas of various size and reflector depth. The particular focus is on a large inflatable elastic antenna reflector that is supported about its perimeter by a set of elastic tendons and is subjected to a constant hydrostatic pressure. The surface accuracy of the antenna is measured by an RMS calculation, while the reflector phase error component of the efficiency is determined by computing the power density at boresight. In the analysis, the calculation of antenna efficiency is not based on the Ruze Equation. Hence, no assumption regarding the distribution of the reflector surface distortions is presumed. The reflector surface is modeled as an isotropic elastic membrane using a linear stress-strain constitutive relation. Three types of antenna reflector construction are considered: one molded to an ideal parabolic form and two different flat panel design patterns. The flat panel surfaces are constructed by seaming together panels in a manner that the desired parabolic shape is approximately attained after pressurization. Numerical solutions of the model problem are calculated under a variety of conditions in order to estimate the accuracy and efficiency of these antenna systems. In the case of the flat panel constructions, several different cutting patterns are analyzed in order to determine an optimal cutting strategy.

Coleman, Michael J.↗
NASA NTRS2014

NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

Rodio, J. J.↗