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NASA NTRS1978

Modeling structural damping for solids having distinct shear and dilatational loss factors

For steady state time harmonic problems (rigid format 8), the NASTRAN program as currently configured treats internal structural damping through the introduction of a single structural element damping coefficient that typically is viewed as the ratio of the complex to real modulus of elasticity. For problems dealing with two or three dimensional dynamic linear viscoelasticity (e.g. a Kelvin-Voigt viscoelastic model), the present NASTRAN capability cannot directly handle this situation wherein two independent damping coefficients are required to properly model the dissipation phenomenon. A technique is presented whereby the user can adapt the standard versions of NASTRAN (without resorting to either DMAP and/or FORTRAN coding changes) for the purpose of treating this class of problem.

Kalinowski, A. J.↗

NASA NTRS1997

Validation of a Pseudo-Sound Theory for the Pressure-Dilatation in DNS of Compressible Turbulence

The results of an asymptotic theory for statistical closures for compressible turbulence are explored and validated with the direct numerical simulation of the isotropic decay and the homogeneous shear. An excellent collapse of the data is seen. The slow portion is found to scale, as predicted by the theory, with the quantity M(sub t)(sup 2) and epsilon(sub s). The rapid portion has an unambiguous scaling with alpha(sup 2)M(sub t)(sup s)epsilon(sub s)[P(sub k)/epsilon - l](Sk/epsilon)(sup 2). Implicit in the scaling is a dependence, as has been noted by others, on the gradient Mach number. A new feature of the effects of compressibility, that of the Kolmogorov scaling coefficient, alpha, is discussed. It is suggested that alpha may contain flow specific physics associated with large scales that might provide further insight into the structural effects of compressibility.

Ristorcelli, J. R.↗

NASA NTRS2003

Secondary Fracturing of Europa's Crust in Response to Combined Slip and Dilation Along Strike-Slip Faults

A commonly observed feature in faulted terrestrial rocks is the occurrence of secondary fractures alongside faults. Depending on exact morphology, such fractures have been termed tail cracks, wing cracks, kinks, or horsetail fractures, and typically form at the tip of a slipping fault or around small jogs or steps along a fault surface. The location and orientation of secondary fracturing with respect to the fault plane or the fault tip can be used to determine if fault motion is left-lateral or right-lateral.

Kattenhorn, S. A.↗

NASA NTRS2020

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗

NASA NTRS2000

Analysis of shape and motion of the mitral annulus in subjects with and without cardiomyopathy by echocardiographic 3-dimensional reconstruction

The shape and dynamics of the mitral annulus of 10 patients without heart disease (controls), 3 patients with dilated cardiomyopathy, and 5 patients with hypertrophic obstructive cardiomyopathy and normal systolic function were analyzed by transesophageal echocardiography and 3-dimensional reconstruction. Mitral annular orifice area, apico-basal motion of the annulus, and nonplanarity were calculated over time. Annular area was largest in end diastole and smallest in end systole. Mean areas were 11.8 +/- 2.5 cm(2) (controls), 15.2 +/- 4.2 cm(2) (dilated cardiomyopathy), and 10.2 +/- 2.4 cm(2) (hypertrophic cardiomyopathy) (P = not significant). After correction for body surface, annuli from patients with normal left ventricular function were smaller than annuli from patients with dilated cardiomyopathy (5.9 +/- 1.2 cm(2)/m(2) vs 7.7 +/- 1.0 cm(2)/m(2); P <.02). The change in area during the cardiac cycle showed significant differences: 23.8% +/- 5.1% (controls), 13.2% +/- 2.3% (dilated cardiomyopathy), and 32.4% +/- 7.6% (hypertrophic cardiomyopathy) (P <.001). Apico-basal motion was highest in controls, followed by those with hypertrophic obstructive and dilated cardiomyopathy (1.0 +/- 0.3 cm, 0.8 +/- 0.2 cm, 0.3 +/- 0.2 cm, respectively; P <.01). Visual inspection and Fourier analysis showed a consistent pattern of anteroseptal and posterolateral elevations of the annulus toward the left atrium. In conclusion, although area changes and apico-basal motion of the mitral annulus strongly depend on left ventricular systolic function, nonplanarity is a structural feature preserved throughout the cardiac cycle in all three groups.

Non-NASA Center↗

NASA NTRS2008

Arterial Structure and Function in Women and Men Following Long Duration Bed Rest

Orthostatic intolerance is a well-recognized consequence of space flight and bed rest (BR), with a greater incidence reported in women. We hypothesized that leg, but not arm, arterial structure and function would be altered following prolonged BR, as a model of space flight, and that women would be more susceptible to BR-induced deconditioning than men. METHODS: Ten volunteers (5 males, 5 females) completed 90 d of 6 head-down BR. Subjects participated in tests of brachial (BA) and anterior tibial (AT) artery endothelium-dependent (flow mediated dilation [FMD] following 5-7 min of arterial occlusion) and endothelium-independent (0.4 mg sublingual nitroglycerin [SN]) vasodilation before BR (PRE) and on days 7 (BR7), 21 (BR21), and 90 (BR90) of BR. Vessel diameter and intimal medial thickness (IMT) were measured by ultrasound. IMT, baseline diameter, and percent change in diameter from baseline during FMD and SN tests were compared across BR and between genders using repeated measures two-way ANOVA with Bonferroni post-hoc tests in which PRE and women were control conditions. RESULTS: Baseline vessel diameter was lower in women than in men in both the BA (p=0.005) and AT (p=0.01) across all days. Baseline AT diameter decreased during BR (p=0.01) and tended to be more profound in women (interaction, p=0.06). AT diameter was reduced in women at BR21 and BR90 (p<0.01) but not in men. In contrast, there was no BR effect on baseline BA diameter. IMT also decreased in the AT (p<0.001) but not in the BA during BR; AT IMT was reduced by BR21 (p<0.05). As a group, there was no effect of BR on AT FMD, BA FMD, and AT SN-dilation, although BA SN-dilation was significantly reduced on BR21 (p=0.01). Across all BR days, women exhibited higher AT FMD (p=0.03), BA FMD (p=0.02), and BA SN-dilation (p=0.01) and tended to demonstrate greater AT SN-dilation (p=0.11). CONCLUSIONS: These preliminary results suggest that arterial remodeling occurs during BR in the leg (decreased diameter and IMT), but not in the arm, and that women appear to be more responsive to BR than men. These changes in the leg, coupled with larger responses to direct and indirect stimulation of the arterial smooth muscle, may be related to the greater incidence of orthostatic intolerance in women after BR and space flight.

Lee, Stuart M. C.↗

NASA NTRS1991

Direct simulation of compressible turbulence in a shear flow

Compressibility effects on the turbulence in homogeneous shear flow are investigated. The growth of the turbulent kinetic energy was found to decrease with increasing Mach number: a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. Previously, the following results were obtained for isotropic turbulence: (1) the normalized compressible dissipation is of O(M(sub t)(exp 2)); and (2) there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both of these results were substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.

Sarkar, S.↗

NASA NTRS1990

Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence

The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.

Aupoix, B.↗

NASA NTRS1985

Influence of the resin on interlaminar mixed-mode fracture

Both literature review data and new data on toughness behavior of seven matrix and adhesive systems in four types of tests were studied in order to assess the influence of the resin on interlaminar fracture. Mixed mode (i.e., various combinations of opening mode 1, G sub 1, and shearing mode 2; G sub 2) fracture toughness data showed that the mixed mode relationship for failure appears to be linear in terms of G sub 1 and G sub 2. The study further indicates that fracture of brittle resins is controlled by the G sub 1 component, and that fracture of many tough resins is controlled by total strain-energy release rate, G sub T. Regarding the relation of polymer structure and the mixed mode fracture: high mode 1 toughness requires resin dilatation; dilatation is low in unmodified epoxies at room temperature/dry conditions; dilatation is higher in plasticized epoxies, heated epoxies, and in modified epoxies; modification improves mode 2 toughness only slightly compared with mode 1 improvements. Analytical aspects of the cracked lap shear test specimen were explored.

Johnson, W. S.↗

NASA NTRS1987

Influence of the resin on interlaminar mixed-mode fracture

Johnson, W. S.↗

NASA NTRS1989

A dual potential formulation of the Navier-Stokes equations

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

Gegg, S. G.↗

NASA NTRS1990

A study of turbulence on compression ramps with k-epsilon and Reynolds stress models

A theoretical study was conducted to determine the effects of adverse pressure gradient and compressibility in modeling turbulent compressible flows. The kinetic energy/dissipation and Reynolds stress model predictions are presented and compared with experimental data. The effects of compressibility, which include the mass averaged fluctuation term, the pressure dilatation term, and the dilatation dissipation, are important in modeling the turbulent compressible flows. The normal stresses and longitudinal strain rates also have an effect in the prediction of turbulent energy productions on the curved surfaces. A new compressible formulation of the pressure strain term, which includes the dilatation effects, in the Reynolds stress equation is presented.

Lee, J.↗

NASA NTRS1991

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. It is found that the growth of the turbulent kinetic energy decreases with increasing Mach number, a phenomenon similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance.

Sarkar, S.↗

NASA NTRS1992

Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow

For the numerical simulation of inhomogeneous turbulent flows, a method is developed for generating stochastic inflow boundary conditions with a prescribed power spectrum. Turbulence statistics from spatial simulations using this method with a low fluctuation Mach number are in excellent agreement with the experimental data, which validates the procedure. Turbulence statistics from spatial simulations are also compared to those from temporal simulations using Taylor's hypothesis. Statistics such as turbulence intensity, vorticity, and velocity derivative skewness compare favorably with the temporal simulation. However, the statistics of dilatation show a significant departure from those obtained in the temporal simulation. To directly check the applicability of Taylor's hypothesis, space-time correlations of fluctuations in velocity, vorticity, and dilatation are investigated. Convection velocities based on vorticity and velocity fluctuations are computed as functions of the spatial and temporal separations. The profile of the space-time correlation of dilatation fluctuations is explained via a wave propagation model.

Lee, Sangsan↗

NASA NTRS1995

Relativistic timescale analysis suggests lunar theory revision

The SI second of the atomic clock was calibrated to match the Ephemeris Time (ET) second in a mutual four year effort between the National Physical Laboratory (NPL) and the United States Naval Observatory (USNO). The ephemeris time is 'clocked' by observing the elapsed time it takes the Moon to cross two positions (usually occultation of stars relative to a position on Earth) and dividing that time span into the predicted seconds according to the lunar equations of motion. The last revision of the equations of motion was the Improved Lunar Ephemeris (ILE), which was based on E. W. Brown's lunar theory. Brown classically derived the lunar equations from a purely Newtonian gravity with no relativistic compensations. However, ET is very theory dependent and is affected by relativity, which was not included in the ILE. To investigate the relativistic effects, a new, noninertial metric for a gravitated, translationally accelerated and rotating reference frame has three sets of contributions, namely (1) Earth's velocity, (2) the static solar gravity field and (3) the centripetal acceleration from Earth's orbit. This last term can be characterized as a pseudogravitational acceleration. This metric predicts a time dilation calculated to be -0.787481 seconds in one year. The effect of this dilation would make the ET timescale run slower than had been originally determined. Interestingly, this value is within 2 percent of the average leap second insertion rate, which is the result of the divergence between International Atomic Time (TAI) and Earth's rotational time called Universal Time (UT or UTI). Because the predictions themselves are significant, regardless of the comparison to TAI and UT, the authors will be rederiving the lunar ephemeris model in the manner of Brown with the relativistic time dilation effects from the new metric to determine a revised, relativistic ephemeris timescale that could be used to determine UT free of leap second adjustments.

Deines, Steven D.↗

NASA NTRS1996

Modeling of Inhomogeneous Compressible Turbulence Using a Two-Scale Statistical Theory

Turbulence modeling plays an important role in the study of high-speed flows in engineering and aerodynamic problems; they include flows in supersonic combustion engines and over hypersonic transport aircraft. The enhancement of the kinetic energy dissipation by the dilatational terms is one of the typical compressibility effects. Zeman (1990) and Sarkar et al. (1991) proposed that the dilatation dissipation is proportional to the solenoidal dissipation and is a function of the turbulent Mach number. Sarkar (1992) also modeled the pressure-dilatation correlation using the turbulent Mach number. Zeman (1991) related the correlation to the rate of change of the pressure variance.

Hamba, Fujihiro↗

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 NTRS1999

Damping of drop oscillations by surfactants and surface viscosity

An energy equation is derived for the general case of a viscous drop suspended in a viscous medium with surfactants contaminating the interface. It contains terms that clearly identify dissipation contributions from the viscous effects in the bulk fluids, surface shear and dilatational viscosity effects at the interface, and surfactant transport. An efficient boundary integral method is developed which incorporates the effects of a constant surface dilatational viscosity in simulations of an oscillating two-dimensional inviscid drop. Surface dilatational viscosity is shown to have a significant damping effect on the otherwise undamped inviscid oscillations.

Rush, Brian M.↗