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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Extension of continental lithosphere - A model for two scales of basin and range deformation

The development of a model for deformation in an extending continental lithosphere that is stratified in density and strength is described. The lithosphere model demonstrates that the necking instabilities at two wavelengths originate due to a strong upper crust, a mantle layer, and a weak lower crust. It is observed that the dominant wavelengths of necking are controlled by layer thickness and the strength of the layers control the amplitude of the instabilities. The model is applied to the Basin and Range Province of the western U.S. where deformations in ranges and tile domains are detected. The relation between the Bouguer gravity anomaly and the deformations is studied. The data reveal that the horizontal scale of short wavelength necking correlates with the spacings of individual basins and ranges, and the longer wavelength corresponds to the width of tilt domains. The control of the Basin and Range deformation by two scales of extensional instability is proposed.

Zuber, M. T.↗
NASA NTRS1985

The effects of strain heating in lithospheric stretching models

The deformation by stretching of a continental type lithosphere has been formulated so that the problem can be solved by a continuum mechanical approach. The deformation, stress state, and temperature distribution are constrained to satisfy the physical laws of conservation of mass, energy, momentum, and an experimentally defined rheological response. The conservation of energy equation including a term of strain energy dissipation is given. The continental lithosphere is assumed to have the rheology of an isotropic, incompressible, nonlinear viscous, two layered solid.

Stanton, M.↗
NASA NTRS1988

Unified constitutive model for single crystal deformation behavior with applications

Single crystal materials are being used in gas turbine airfoils and are candidates for other hot section components because of their increased temperature capabilities and resistance to thermal fatigue. Development of a constitutive model which assesses the inelastic behavior of these materials has been studied in 2 NASA programs: Life Prediction and Constitutive Models for Engine Hot Section Anisotropic Materials and Biaxial Constitutive Equation Development for Single Crystals. The model has been fit to a large body of constitutive data for single crystal PWA 1480 material. The model uses a unified approach for computing total inelastic strains (creep plus plasticity) on crystallographic slip systems reproducing observed directional and strain rate effects as a natural consequence of the summed slip system quantities. The model includes several of the effects that have been reported to influence deformation in single crystal materials, such as shear stress, latent hardening, and cross slip. The model is operational in a commercial Finite Element code and is being installed in a Boundary Element Method code.

Walker, K. P.↗
NASA NTRS1995

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

Johnson, Arthur R.↗
NASA NTRS1991

Bilinear modeling and state estimation of slew-induced deformations of a flexible multibody system

A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformations are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.

Dwyer, Thomas A. W., III↗
NASA NTRS1999

Strain Rate Dependent Modeling of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Strain rate dependent inelastic constitutive equations have been developed to model the polymer matrix, and have been incorporated into a micromechanics approach to analyze polymer matrix composites. The Hashin failure criterion has been implemented within the micromechanics results to predict ply failure strengths. The deformation model has been implemented within LS-DYNA, a commercially available transient dynamic finite element code. The deformation response and ply failure stresses for the representative polymer matrix composite AS4/PEEK have been predicted for a variety of fiber orientations and strain rates. The predicted results compare favorably to experimentally obtained values.

Goldberg, Robert K.↗
NASA NTRS1983

Crustal deformation, the earthquake cycle, and models of viscoelastic flow in the asthenosphere

The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geometry of the material near the seismogenic zone. The origin of some of these differences are resolved by analyzing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breath of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geometry and structure. Distinguishing among the various models is best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced.

Cohen, S. C.↗
NASA NTRS1984

Crustal deformation, the earthquake cycle, and models of viscoelastic flow in the asthenosphere

The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geometry of the material near the seismogenic zone. The origin of some of these differences are resolved by analyzing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breath of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geometry and structure. Distinguishing among the various models is best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced.

Cohen, S. C.↗
NASA NTRS2004

Development of an Intelligent Videogrammetric Wind Tunnel Measurement System

A videogrammetric technique developed at NASA Langley Research Center has been used at five NASA facilities at the Langley and Ames Research Centers for deformation measurements on a number of sting mounted and semispan models. These include high-speed research and transport models tested over a wide range of aerodynamic conditions including subsonic, transonic, and supersonic regimes. The technique, based on digital photogrammetry, has been used to measure model attitude, deformation, and sting bending. In addition, the technique has been used to study model injection rate effects and to calibrate and validate methods for predicting static aeroelastic deformations of wind tunnel models. An effort is currently underway to develop an intelligent videogrammetric measurement system that will be both useful and usable in large production wind tunnels while providing accurate data in a robust and timely manner. Designed to encode a higher degree of knowledge through computer vision, the system features advanced pattern recognition techniques to improve automated location and identification of targets placed on the wind tunnel model to be used for aerodynamic measurements such as attitude and deformation. This paper will describe the development and strategy of the new intelligent system that was used in a recent test at a large transonic wind tunnel.

Graves, Sharon S.↗
NASA NTRS2000

Analysis and modeling of Southern California deformation

The large and rich quantity of data now becoming available through the Southern California Integrated GPS Network (SCIGN) makes possible a wide variety of research involving analysis and modeling.

geodesy earthquakes finite elements↗
NASA NTRS2001

Comparison of Angle of Attack Measurements for Wind Tunnel Testing

Two optical systems capable of measuring model attitude and deformation were compared to inertial devices employed to acquire wind tunnel model angle of attack measurements during the sting mounted full span 30% geometric scale flexible configuration of the Northrop Grumman Unmanned Combat Air Vehicle (UCAV) installed in the NASA Langley Transonic Dynamics Tunnel (TDT). The overall purpose of the test at TDT was to evaluate smart materials and structures adaptive wing technology. The optical techniques that were compared to inertial devices employed to measure angle of attack for this test were: (1) an Optotrak (registered) system, an optical system consisting of two sensors, each containing a pair of orthogonally oriented linear arrays to compute spatial positions of a set of active markers; and (2) Video Model Deformation (VMD) system, providing a single view of passive targets using a constrained photogrammetric solution whose primary function was to measure wing and control surface deformations. The Optotrak system was installed for this test for the first time at TDT in order to assess the usefulness of the system for future static and dynamic deformation measurements.

Jones, Thomas, W.↗
NASA NTRS1980

Interpretation of postseismic deformation with a viscoelastic relaxation model

A viscoelastic relaxation model is used to interpret postseismic surface deformation for the large-magnitude Aleutian earthquakes of 1957 and 1965. The lithosphere and asthenosphere are modeled as elastic solids with an anomalous viscoelastic inclusion below the island arc volcanoes. It is found that the observed postseismic surface deformation is a corollary of the known island arc structure. A satisfactory fit to the uplift following the 1957 earthquake is found for a viscoelastic volume with 80-km width extending from a depth of 50 to 200 km.

Wahr, J.↗
NASA NTRS1985

Earthquake deformation cycle in the Andean Back Arc, western Argentina

It is pointed out that the 1977 Caucete earthquake was an east-west compressive event which occurred at a depth of about 17 km in the Andean back arc approximately 450 km east of the Chile trench. The present study is primarily concerned with the mechanics of fault behavior prior to and after the 1977 earthquake, as evidenced by preseismic and postseismic vertical deformation. Simple fault models for each phase of deformation are presented. The models of preseismic slip, coseismic slip, and postseismic slip consist of uniform dislocations in an elastic half-space following the method of Chinnery (1961). The basically elastic models presented demonstrate that deformations in the vicinity of the 1977 Caucete, Argentina, earthquake are consistent with activity on some portion of the coseismic fault. This is evidence that these deformations are directly related to the processes of strain accumulation and release associated with the event.

Reilinger, R.↗
NASA NTRS1988

An internal variable constitutive model for the large deformation of metals at high temperatures

The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.

Brown, Stuart↗
NASA NTRS1993

Research on Earth's rotation and the effect of atmospheric pressure on vertical deformation and sea level variability

The work done under NASA grant NAG5-485 included modelling the deformation of the earth caused by variations in atmospheric pressure. The amount of deformation near coasts is sensitive to the nature of the oceanic response to the pressure. The PSMSL (Permanent Service for Mean Sea Level) data suggest the response is inverted barometer at periods greater than a couple months. Green's functions were constructed to describe the perturbation of the geoid caused by atmospheric and oceanic loading and by the accompanying load-induced deformation. It was found that perturbation of up to 2 cm are possible. Ice mass balance data was used for continental glaciers to look at the glacial contributions to time-dependent changes in polar motion, the lod, the earth's gravitational field, the position of the earth's center-of-mass, and global sea level. It was found that there can be lateral, non-hydrostatic structure inside the fluid core caused by gravitational forcing from the mantle, from the inner core, or from topography at the core/mantle or inner core/outer core boundaries. The nutational and tidal response of a non-hydrostatic earth with a solid inner core was modeled. Monthly, global tide gauge data from PSMSL was used to look at the 18.6-year ocean tide, the 14-month pole tide, the oceanic response to pressure, the linear trend and inter-annual variability in the earth's gravity field, the global sea level rise, and the effects of post glacial rebound. The effects of mantle anelasticity on nutations, earth tides, and tidal variation in the lod was modeled. Results of this model can be used with Crustal Dynamics observations to look at the anelastic dissipation and dispersion at tidal periods. The effects of surface topography on various components of crustal deformation was also modeled, and numerical models were developed of post glacial rebound.

Wahr, John↗
NASA NTRS1983

Estimating crustal deformations from a combination of baseline measurements and geophysical models

Three possible estimation algorithms are presented for the monitoring of crustal deformations from a combination of repeated baseline measurements and prior deformation information. Attention is given to best linear minimum bias estimation, best linear estimation, and Bayesian estimation. The application of the deformation estimators to the maintenance of a conventional terrestrial reference system is considered. It is shown that if no prior deformation model is available, the free adjustment is the preferred algorithm. In the presence of prior information, however, it is better to use a somewhat incorrect model than to ignore it altogether. The best estimation model of the ones tested is the best linear estimation.

Bock, Y.↗
NASA NTRS1994

Modeling of periodic great earthquakes on the San Andreas fault: Effects of nonlinear crustal rheology

We analyze the cycle of great earthquakes along the San Andreas fault with a finite element numerical model of deformation in a crust with a nonlinear viscoelastic rheology. The viscous component of deformation has an effective viscosity that depends exponentially on the inverse absolute temperature and nonlinearity on the shear stress; the elastic deformation is linear. Crustal thickness and temperature are constrained by seismic and heat flow data for California. The models are for anti plane strain in a 25-km-thick crustal layer having a very long, vertical strike-slip fault; the crustal block extends 250 km to either side of the fault. During the earthquake cycle that lasts 160 years, a constant plate velocity v(sub p)/2 = 17.5 mm yr is applied to the base of the crust and to the vertical end of the crustal block 250 km away from the fault. The upper half of the fault is locked during the interseismic period, while its lower half slips at the constant plate velocity. The locked part of the fault is moved abruptly 2.8 m every 160 years to simulate great earthquakes. The results are sensitive to crustal rheology. Models with quartzite-like rheology display profound transient stages in the velocity, displacement, and stress fields. The predicted transient zone extends about 3-4 times the crustal thickness on each side of the fault, significantly wider than the zone of deformation in elastic models. Models with diabase-like rheology behave similarly to elastic models and exhibit no transient stages. The model predictions are compared with geodetic observations of fault-parallel velocities in northern and central California and local rates of shear strain along the San Andreas fault. The observations are best fit by models which are 10-100 times less viscous than a quartzite-like rheology. Since the lower crust in California is composed of intermediate to mafic rocks, the present result suggests that the in situ viscosity of the crustal rock is orders of magnitude less the rock viscosity determined in the laboratory.

Reches, Ze'ev↗