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NASA NTRS1994

A spectral formalism for computing three-dimensional deformations due to surface loads. 1: Theory

We outline a complete spectral formalism for computing high spatial resolution three-dimensional deformations arising from the surface mass loading of a spherically symmetric planet. The main advantages of the formalism are that all surface mass loads are always described using a consistent mathematical representation and that calculations of deformation fields for various spatial resolutions can be performed by simpley altering the spherical harmonic degree truncation level of the procedure. The latter may be important when incorporating improved observational constraints on a particular surface mass load, when considering potential errors in the computed field associated with mass loading having a spatial scale unresolved by the observational constraints, or when treating a number of global surface mass loads constrained with different spatial resolutions. The advantages do not extend to traditional 'Green's function' approaches which involve surface element discretizations of the global mass loads. Another advantage of the spectral formalism, over the Green's function approach, is that a posteriori analyses of the computed deformation fields are easily performed. In developing the spectral formalism, we consider specific cases where the Earth's mantle is assumed to respond as an elastic, slightly anelastic, or linear viscoelastic medium. In the case of an elastic or slightly anelastic mantle rheology the spectral response equations incorporate frequency dependent Love numbers. The formalism can therefore be used, for example, to compute the potentially resonant deformational response associated with the free core nutation and Chandler wobble eigenfunctions. For completeness, the spectral response equations include both body forces, as arise from the gravitational attraction of the Sun and the Moon, and surface mass loads. In either case, and for both elastic and anelastic mantle rheologies, we outline a pseudo-spectral technique for computing the ocean adjustment associated with the total gravitational perturbation induced by the external forcing. Three-dimensional deformations computed using the usual Love number approach are generally referenced to an origin at the center of mass of the undeformed planet. We derive a spectral technique for transforming the results to an origin located at the center of mass of the deformed planet.

Mitrovica, J. X.↗

NASA NTRS1998

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Goldberg, Robert K.↗

NASA NTRS1996

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Wang, P. K. C.↗

NASA NTRS1999

Dynamic Deformation of ETNA Volcano Observed by GPS and SAR Interferometry

Synthetic aperture radar (SAR) interferometry and GPS have shown that during the quiescent period from 1993-1995 Mt. Etna volcano, Italy, inflated. Since the initiation of eruptive activity since late 1995 the deformation has been more contentious. We will explore the detailed deformation during the period from 1995-1996 spanning the late stages of inflation and the beginning of eruptive activity. We use SAR interferometry and GPS data to measure the volcano deformation. We invert the observed deformation for both simple point source. le crack elastic sources or if warranted for a spheroidal pressure So In particular, we will examine the evolution of the inflation and the transition to a lesser deflation observed at the end of 1995. We use ERS-1/2 SAR data from both ascending and descending passes to allow for dense temporal 'sampling of the deformation and to allow us to critically assess atmospheric noise. Preliminary results from interferometry suggest that the inflation rate accelerated prior to resumption of activity in 1995, while GPS data suggest a more steady inflation with some fluctuation following the start of activity. This study will compare and contrast the interferometric SAR and GPS results and will address the strengths and weaknesses of each technique towards volcano deformation studies.

Lundgren, P.↗

NASA NTRS2003

Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites

The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.

Goldberg, Robert K.↗

NASA NTRS2009

Electron Backscatter Diffraction (EBSD) Analysis and U-Pb Geochronology of the Oldest Lunar Zircon: Constraining Early Lunar Differentiation and Dating Impact-Related Deformation

The evolution of the early moon was dominated by two processes (i) crystallization of the Lunar Magma Ocean (LMO) and differentiation of potassium-rare earth element-phosphorous-rich residual magma reservoir referred to as KREEP, and (ii) an intense meteorite bombardment referred to as lunar cataclysm . The exact timing of these processes is disputed, and resolution relies on collection and interpretation of precise age data. This study examines the microstructure and geochronology of zircon from lunar impact breccias collected during the Apollo 17 mission. A large zircon clast within lunar breccia 72215,195 shows sector zoning in optical microscopy, cathodoluminescence (CL) imaging and Raman mapping, and indicates that it was a relict fragment of a much larger magmatic grain. Sensitive high resolution ion microprobe (SHRIMP) U-Pb analysis of the zircon shows that U and Th concentration correlate with sector zoning, with darkest CL domains corresponding with high-U and Th (approx.150 and approx.100 ppm respectively), and the brightest-CL sectors containing approx.30-50 ppm U and approx.10-20 ppm Th. This indicates that variations in optical CL and Raman properties correspond to differential accumulation of alpha-radiation damage in each sector. Electron backscatter diffraction (EBSD) mapping shows that the quality of electron backscatter patterns (band contrast) varies with sector zoning, with the poorest quality patterns obtained from high-U and Th, dark-CL zones. EBSD mapping also reveals a deformation microstructure that is cryptic in optical, CL and Raman imaging. Two orthogonal sets of straight discrete and gradational low-angle boundaries accommodate approx.12 misorientation across the grain. The deformation bands are parallel to the crystallographic {a}-planes of the zircon, have misorientation axes parallel to the c-axis, and are geometrically consistent with formation by dislocation creep associated with <100>{010} slip. The deformation bands are unlike curved morphology of crystal-plastic microstructures in tectonically deformed terrestrial zircon, and geometrically similar to dislocation microstructures reported in experimentally shocked zircon. We interpret these crystal-plastic deformation microstructures to have resulted from a significant impact, either directly from impact shock, or during ductile flow directly following the impact. The deformation bands appear to continue undeflected through the non-indexed, radiation-damaged areas of the grain, which suggests that the orientation variation predates any significant mechanical weakening from radiation damage in the grain, and therefore occurred early in its history.

Timms, Nick↗

NASA NTRS2012

Deformation and Phase Transformation Processes in Polycrystalline NiTi and NiTiHf High Temperature Shape Memory Alloys

The deformation and transformation mechanisms of polycrystalline Ni49.9Ti50.1 and Ni50.3Ti29.7Hf20 (in at.%) shape memory alloys were investigated by combined experimental and modeling efforts aided by an in situ neutron diffraction technique at stress and temperature. The thermomechanical response of the low temperature martensite, the high temperature austenite phases, and changes between these two states during thermomechanical cycling were probed and reported. In the cubic austenite phase, stress-induced martensite, deformation twinning and slip processes were observed which helped in constructing a deformation map that contained the limits over which each of the identified mechanisms was dominant. Deformation of the monoclinic martensitic phase was also investigated where the microstructural changes (texture, lattice strains, and phase fractions) during room-temperature deformation and subsequent thermal cycling were compared to the bulk macroscopic response. When cycling between these two phases, the evolution of inelastic strains, along with the shape setting procedures were examined and used for the optimization of the transformation properties as a function of deformation levels and temperatures. Finally, this work was extended to the development of multiaxial capabilities at elevated temperatures for the in situ neutron diffraction measurements of shape memory alloys on the VULCAN Diffractometer at Oak Ridge National Laboratory.

Benafan, Othmane↗

NASA NTRS2013

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Nemeth, Michael P.↗

NASA NTRS2013

Fabrication Methods for Adaptive Deformable Mirrors

Previously, it was difficult to fabricate deformable mirrors made by piezoelectric actuators. This is because numerous actuators need to be precisely assembled to control the surface shape of the mirror. Two approaches have been developed. Both approaches begin by depositing a stack of piezoelectric films and electrodes over a silicon wafer substrate. In the first approach, the silicon wafer is removed initially by plasmabased reactive ion etching (RIE), and non-plasma dry etching with xenon difluoride (XeF2). In the second approach, the actuator film stack is immersed in a liquid such as deionized water. The adhesion between the actuator film stack and the substrate is relatively weak. Simply by seeping liquid between the film and the substrate, the actuator film stack is gently released from the substrate. The deformable mirror contains multiple piezoelectric membrane layers as well as multiple electrode layers (some are patterned and some are unpatterned). At the piezolectric layer, polyvinylidene fluoride (PVDF), or its co-polymer, poly(vinylidene fluoride trifluoroethylene P(VDF-TrFE) is used. The surface of the mirror is coated with a reflective coating. The actuator film stack is fabricated on silicon, or silicon on insulator (SOI) substrate, by repeatedly spin-coating the PVDF or P(VDFTrFE) solution and patterned metal (electrode) deposition. In the first approach, the actuator film stack is prepared on SOI substrate. Then, the thick silicon (typically 500-micron thick and called handle silicon) of the SOI wafer is etched by a deep reactive ion etching process tool (SF6-based plasma etching). This deep RIE stops at the middle SiO2 layer. The middle SiO2 layer is etched by either HF-based wet etching or dry plasma etch. The thin silicon layer (generally called a device layer) of SOI is removed by XeF2 dry etch. This XeF2 etch is very gentle and extremely selective, so the released mirror membrane is not damaged. It is possible to replace SOI with silicon substrate, but this will require tighter DRIE process control as well as generally longer and less efficient XeF2 etch. In the second approach, the actuator film stack is first constructed on a silicon wafer. It helps to use a polyimide intermediate layer such as Kapton because the adhesion between the polyimide and silicon is generally weak. A mirror mount ring is attached by using adhesive. Then, the assembly is partially submerged in liquid water. The water tends to seep between the actuator film stack and silicon substrate. As a result, the actuator membrane can be gently released from the silicon substrate. The actuator membrane is very flat because it is fixed to the mirror mount prior to the release. Deformable mirrors require extremely good surface optical quality. In the technology described here, the deformable mirror is fabricated on pristine substrates such as prime-grade silicon wafers. The deformable mirror is released by selectively removing the substrate. Therefore, the released deformable mirror surface replicates the optical quality of the underlying pristine substrate.

Toda, Risaku↗

NASA NTRS2014

Virtual Deformation Control of the X-56A Model with Simulated Fiber Optic Sensors

A robust control law design methodology is presented to stabilize the X-56A model and command its wing shape. The X-56A was purposely designed to experience flutter modes in its flight envelope. The methodology introduces three phases: the controller design phase, the modal filter design phase, and the reference signal design phase. A mu-optimal controller is designed and made robust to speed and parameter variations. A conversion technique is presented for generating sensor strain modes from sensor deformation mode shapes. The sensor modes are utilized for modal filtering and simulating fiber optic sensors for feedback to the controller. To generate appropriate virtual deformation reference signals, rigid-body corrections are introduced to the deformation mode shapes. After successful completion of the phases, virtual deformation control is demonstrated. The wing is deformed and it is shown that angle-ofattack changes occur which could potentially be used to an advantage. The X-56A program must demonstrate active flutter suppression. It is shown that the virtual deformation controller can achieve active flutter suppression on the X-56A simulation model.

Suh, Peter M.↗

NASA NTRS2013

Virtual Deformation Control of the X-56A Model with Simulated Fiber Optic Sensors

A robust control law design methodology is presented to stabilize the X-56A model and command its wing shape. The X-56A was purposely designed to experience flutter modes in its flight envelope. The methodology introduces three phases: the controller design phase, the modal filter design phase, and the reference signal design phase. A mu-optimal controller is designed and made robust to speed and parameter variations. A conversion technique is presented for generating sensor strain modes from sensor deformation mode shapes. The sensor modes are utilized for modal filtering and simulating fiber optic sensors for feedback to the controller. To generate appropriate virtual deformation reference signals, rigid-body corrections are introduced to the deformation mode shapes. After successful completion of the phases, virtual deformation control is demonstrated. The wing is deformed and it is shown that angle-of-attack changes occur which could potentially be used to an advantage. The X-56A program must demonstrate active flutter suppression. It is shown that the virtual deformation controller can achieve active flutter suppression on the X-56A simulation model.

Modal Filter↗

NASA NTRS2013

Effect of Temperature on the Deformation Behavior of B2 Austenite in a Polycrystalline Ni49.9Ti50.1 (at.Percent) Shape Memory Alloy

Superelasticity in austenitic B2-NiTi is of great technical interest and has been studied in the past by several researchers [1]. However, investigation of temperature dependent deformation in B2-NiTi is equally important since competing mechanisms of stress-induced martensite (SIM), retained martensite, plastic and deformation twinning can lead to unusual mechanical behaviors. Identification of the role of various mechanisms contributing to the overall deformation response of B2-NiTi is imperative to understanding and maturing SMA-enabled technologies. Thus, the objective of this work was to study the deformation of polycrystalline Ni49.9Ti50.1 (at. %) above A(sub f) (105 C) in the B2 state at temperatures between 165-440 C, and generate a B2 deformation map showing active deformation mechanisms in different temperature-stress regimes.

Garg, A.↗

NASA NTRS2015

Active Beam Shaping System and Method Using Sequential Deformable Mirrors

An active optical beam shaping system includes a first deformable mirror arranged to at least partially intercept an entrance beam of light and to provide a first reflected beam of light, a second deformable mirror arranged to at least partially intercept the first reflected beam of light from the first deformable mirror and to provide a second reflected beam of light, and a signal processing and control system configured to communicate with the first and second deformable mirrors. The first deformable mirror, the second deformable mirror and the signal processing and control system together provide a large amplitude light modulation range to provide an actively shaped optical beam.

Norman, Colin A.↗

NASA NTRS2021

Exep: Environmental Testing of High-Actuator-Count Mems Deformable Mirrors for Space-Based Applications

Coronagraph instruments on future space telescopes will rely on deformable mirrors to create high contrast images for the direct detection of exoplanets. As part of the NASA Exoplanet Explorations Program’s coronagraph technology development efforts, two sets of Micro-electro-mechanical systems (MEMS) deformable mirrors manufactured by Boston Micromachines Corporation were exposed to vibration and thermal cycles representative of launch conditions. The first set were 952-actuator Kilo-DMs that successfully demonstrated 100% actuator survival and achieved ~1e-8 contrast after the environment test. The second round used an engineering-grade 2048-actuator deformable mirror on which few changes were identified after the environmental test. However, each actuator that changed behavior was flagged as anomalous beforehand or was directly adjacent to a defective actuator. From this result, we hypothesized that typical actuators on a science grade deformable mirror are robust to environmental testing. A third set of 2048-actuator deformable mirror have been procured for a planned test to characterize the deformable mirrors using interferometric measurements, contrast results on a new in-air coronagraph testbed, and infrared microscopy on the internal structure of the MEMS devices.

Lam, Charlie↗

NASA NTRS2006

Contrasts in Sea Ice Deformation and Production in the Arctic Seasonal and Perennial Ice Zones

Four years (1997-2000) of RADARSAT Geophysical Processor System (RGPS) data are used to contrast the sea ice deformation and production regionally, and in the seasonal (SIZ) and perennial (PIZ) ice zones. Ice production is of seasonal ice in openings during the winter. Three-day estimates of these quantities are provided within Lagrangian elements initially 10 km on a side. A distinct seasonal cycle is seen in both zones with these estimates highest in the late fall and with seasonal minimums in the midwinter. Regional divergence over the winter could be up to 30%. Spatially, the highest deformation is seen in the SIZ north of coastal Alaska. Both ice deformation and production are higher in the SIZ: deformation-related ice production in the SIZ (approx.0.5 m) is 1.5-2.3 times that of the PIZ (approx.0.3 m): this is connected to ice strength and thickness. Atmospheric forcing and boundary layer structure contribute to only the seasonal and interannual variability. Seasonal ice growth in ice fractures accounts for approx.25-40% of the total ice production of the Arctic Ocean. Uncertainties in these estimates are discussed. By itself, this deformation-ice production relationship could be considered a negative feedback when thickness is perturbed. However, the overall effect on ice production in the face of increasing seasonal and thinner/weaker ice coverage could be modified by local destabilization of the water column promoting overturning of warmer water due to increased brine rejection; and the upwelling of the pynocline associated with increased occurrence of large shear motion in sea ice. Divergence is shown to be negligibly correlated to cyclonic motion in summer and winter in both ice zones.

Arctic Ocean↗

NASA NTRS1980

Effect of propellant deformation on ignition and combustion processes in solid propellant cracks

A comprehensive theoretical model was formulated to study the development of convective burning in a solid propellant crack which continually deforms due to burning and pressure loading. In the theoretical model, the effect of interrelated structural deformation and combustion processes was taken into account by considering (1) transient, one dimensional mass, momentum, and energy conservation equations in the gas phase; (2) a transient, one dimensional heat conduction equation in the solid phase; and (3) quasi-static deformation of the two dimensional, linear viscoelastic propellant crack caused by pressure loading. Partial closures may generate substantial local pressure peaks along the crack, implying a strong coupling between chamber pressurization, crack combustion, and propellant deformation, especially when the cracks are narrow and the chamber pressurization rates high. The maximum pressure in the crack cavity is generally higher than that in the chamber. The initial flame-spreading process is not affected by propellant deformation.

Kumar, M.↗

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

Finite elastic-plastic deformation of polycrystalline metals

Applying Hill's self-consistent method to finite elastic-plastic deformations, the overall moduli of polycrystalline solids are estimated. The model predicts a Bauschinger effect, hardening, and formation of vertex or corner on the yield surface for both microscopically non-hardening and hardening crystals. The changes in the instantaneous moduli with deformation are examined, and their asymptotic behavior, especially in relation to possible localization of deformations, is discussed. An interesting conclusion is that small second-order quantities, such as shape changes of grains and residual stresses (measured relative to the crystal elastic moduli), have a first-order effect on the overall response, as they lead to a loss of the overall stability by localized deformation. The predicted incipience of localization for a uniaxial deformation in two dimensions depends on the initial yield strain, but the orientation of localization is slightly less than 45 deg with respect to the tensile direction, although the numerical instability makes it very difficult to estimate this direction accurately.

Iwakuma, T.↗