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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

DSS 43 antenna gain analysis for Voyager Uranus encounter: 8.45-GHz radio science data correction

A malfunction of the Deep Space Network (DSN) 64-meter antenna in Australia forced the antenna to operate with a mispositioned subreflector during the Voyager Uranus encounter period (January 24, 1986). Because of changing main reflector shape and quadripod position as a function of elevation angle, the antenna gain and pointing were not as expected, and the 8.45 GHz received signal level changed during the pass. The study described here used the Geometrical Theory of Diffraction (GTD) analysis to determine actual antenna gain and pointing during that period in an attempt to reconstruct the radio science data. It is found that the 1.4 dB of signal variation can be accounted for by antenna geometry changes and pointing error. Suggested modifications to the values measured during the pass are presented. Additionally, an extremely useful tool for the analysis of gravity deformed reflectors was developed for use in future antenna design and analysis projects.

Slobin, S. D.↗
NASA NTRS1989

Generalized mathematical models in design optimization

The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

Papalambros, Panos Y.↗
NASA NTRS2021

Characterizing Deformable Mirrors for the MagAO-X Instrument

The MagAO-X instrument is a new extreme adaptive optics system for high-contrast imaging at visibleand near-infrared wavelengths on the Magellan Clay Telescope. A central component of this system is a 2040-actuatormicroelectromechanical deformable mirror (DM) from Boston Micromachines Corp. that operates at 3.63 kHz forhigh-order wavefront control (the tweeter). Two additional DMs from ALPAO perform the low-order (the woofer)and non-common-path science-arm wavefront correction (the NCPC DM). Prior to integration with the instrument, wecharacterized these devices using a Zygo Verifire Interferometer to measure each DM surface. We present the resultsof the characterization effort here, demonstrating the ability to drive tweeter to a flat of 6.9 nm RMS surface (and 0.56nm RMS surface within its control bandwidth), the woofer to 2.2 nm root mean square (RMS) surface, and the NCPCDM to 2.1 nm RMS surface over the MagAO-X beam footprint on each device. Using focus-diversity phase retrievalon the MagAO-X science cameras to estimate the internal instrument wavefront error (WFE), we further show that theintegrated DMs correct the instrument WFE to 18.7 nm RMS, which, combined with a 11.7% pupil amplitude RMS,produces a Strehl ratio of 0.94 at H↵

Kyle Van Gorkom↗
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 NTRS2025

Erosion Behavior of Ti-hBN Multifunctional Coatings in A Custom-Made Planetary Test Rig at Extreme Lunar Temperatures

Spacecraft landings and takeoffs on the lunar surface, along with extreme temperature variations between day and night (-196 to 150° C), cause high-velocity dust impacts and erosion, resulting in the premature failure of structures. Ti/2 vol% hBN coatings were deposited using atmospheric (APS) and vacuum plasma spray (VPS) using cryo-milled powder feedstock to protect the structural components. The erosion performance of coatings at extreme lunar temperature regimes (-150 to 150° C) was evaluated in a custom-made planetary erosion test rig (PETR) at low (50 mph) and high impact velocities (250 mph). The mass loss of VPS coatings was reduced by 50% compared to the APS coatings and 40% compared to the Ti6Al4V substrate. The cryogenic temperature induces brittleness in the material, rendering it susceptible to extreme conditions of material loss. The particle impact-deformation behavior was captured using a high-speed camera to study the erosion mechanism. This analysis revealed chipping in substrates and brittle APS coatings, while particles rebounding and embedding were observed in VPS coatings. Energy calculations, aided by particle trajectory tracking from the high-speed camera, have conclusively shown that VPS coatings absorb 5–10% more energy than APS coatings during erosion tests. A modified erosion index was developed incorporating the fracture toughness and temperatures. New erosion models for brittle and ductile target materials are proposed for developing erosion-resistant material systems.

Abhijith Kunneparambil Sukumaran↗
NASA NTRS1961

A Theoretical Investigation of Vortex-Sheet Deformation Behind a Highly Loaded Wing and Its Effect on Lift

The induced drag polar is developed for wt-ngs capable of attaining extremely high loadings while possessing an elliptical distribution of circulation. This development is accomplished through a theoretical investigation of the vortex-wake deformation process and the deduction of the airfoil forces from the impulse and kinetic energy contents of the ultimate wake form. The investigation shows that the induced velocities of the wake limit the maximum lift coefficient to a value of 1.94 times the wing aspect ratio, for aspect ratios equal to or less than 6.5, and that the section properties of the airfoil limit the lift coefficient to 12.6 for aspect ratios greater than 6.5. Relations are developed for the rate of deformation of the vortex wake. It is also shown that linear wing theory is app1icable up to lift coefficients equal to 1.1 times the aspect ratio.

Cone, Clarence D., Jr.↗
NASA NTRS2017

A View from Above: Earth Observations

Since the 1960s, satellites have been looking down at the Earth to monitor weather patterns and track severe storms, observe how our land surface is changing and responding to hydrometerological extremes, and even to sense how the Earth's crust is deforming from earthquakes and volcanoes. Space and airborne platforms can provide unique views of the disaster lifecycle, informing pre-event mitigation and preparedness, emergency response following an event, and monitoring longer-term recovery. These remotely-sensed data, products and models can provide a global perspective to see beyond administrative boundaries, reach remote places where in situ observations are di cult or non-existent, and provide the necessary context and situational awareness to aid in disaster response. So how do these platforms work? Instruments aboard satellites use different portions of the electromagnetic spectrum to passively or actively observe energy across a range of wavelengths, which can be turned into meaningful data on geophysical, atmospheric, and hydrological variables. e US has had a broad range of Earth observation (EO) platforms delivering open data for scientific research and societal benefits for decades. e Landsat programme, a joint initiative between the US Geological Survey (USGS) and NASA, has the world's longest continuous collection of space-based satellite imagery of the Earth, extending from 1972 to present. e Landsat satellites provide visible, near infrared, and thermal data that are used to support emergency response and disaster relief by mapping changes in water during floods, and dramatic land surface changes, including those resulting from landslides, wild res, severe weather, volcanic plumes, and dust storms.

FEMA↗
NASA NTRS2004

Analytical and Experimental Characterization of Gravity Induced Deformations In Subscale Gossamer Structures

The development of gossamer space structures such as solar sails and sunshields presents many challenges due to their large size and extreme flexibility. The post-deployment structural geometry exhibited during ground testing may significantly depart from the in-space configuration due to the presence of gravity-induced deformations (gravity sag) of lightly preloaded membranes. This paper describes a study carried out to characterize gravity sag in two subscale gossamer structures: a single quadrant from a 2 m, 4 quadrant square solar sail and a 1.7 m membrane layer from a multi-layer sunshield The behavior of the test articles was studied over a range of preloads and in several orientations with respect to gravity. An experimental study was carried out to measure the global surface profiles using photogrammetry, and nonlinear finite element analysis was used to predict the behavior of the test articles. Comparison of measured and predicted surface profiles shows that the finite dement analysis qualitatively predicts deformed shapes comparable to those observed in the laboratory. Quantitatively, finite element analysis predictions for peak gravity-induced deformations in both test articles were within 10% of measured values. Results from this study provide increased insight into gravity sag behavior in gossamer structures, and demonstrates the potential to analytically predict gravity-induced deformations to within reasonable accuracy.

Johnston, John D.↗
NASA NTRS1990

Obliquity histories of Earth and Mars: Influence of inertial and dissipative core-mantle coupling

For both the Earth and Mars, secular variations in the angular separation of the spin axis from the orbit normal are suspected of driving major climatic changes. There is considerable interest in determining the amplitude and timing of these obliquity variations. If the orientation of the orbital plane were inertially fixed, and the planet were to act as a rigid body in it response to precessional torques, the spin axis would simply precess around the orbit at a fixed obliquity and at a uniform angular rate. The precession rate parameter depends on the principal moments of inertia and rotation rate of the perturbed body, and on the gravitational masses and semiminor axes of the perturbing bodies. For Mars, the precession rate is not well known, but probably lies in the interval 8 to 10 arcsec/year. Gravitational interactions between the planets lead to secular motions of the orbit planes. In the rigid body case, the spin axis still attempts to precess about the instantaneous orbit normal, but now the obliquity varies. The hydrostatic figure of a planet represents a compromise between gravitation, which attempts to attain spherical symmetry, and rotation, which prefers cylindrical symmetry. Due to their higher mean densities the cores of the Earth and Mars will be more nearly spherical than the outer layers of these planets. On short time scales it is appropriate to consider the core to be an inviscid fluid constrained to move with the ellipsoidal region bounded by the rigid mantle. The inertial coupling provided by this mechanism is effective whenever the ellipticicy of the container exceeds the ratio of precessional to rotational rates. If the mantle were actually rigid, this would be an extremely effective type of coupling. However, on sufficiently long time scales, the mantle will deform viscously and can accommodate the motions of the core fluid. A fundamentally different type of coupling is provided by electromagnetic or viscous torques. This type of coupling is likely to be most important on longer time scales. In each case, the mantle exerts an equal and opposite torque on the core.

Bills, Bruce G.↗
NASA NTRSDate not supplied

Utilizing 3D-DIC on Mars 2020 Rover Wheel Assembly: Test-Analysis Correlation

Following the successful implementation of full-field photogrammetry, more specifically three-dimensional Digital Image Correlation (3D-DIC), on the Mars 2020 Heat Shield Structural Failure Review assessment, 3D-DIC was selected as one of the primary measurement techniques for the Mars 2020 Rover wheel assembly qualification test at the NASA Jet Propulsion Laboratory (JPL). To validate the Rover wheel landing loads simulations, it was extremely important to have high confidence in the wheel models. Due to the large deformations and strains that the wheel would be subject to during landing, traditional instrumentation such as linear variable displacement transducers (LVDTs), electrical-resistance strain gages and string potentiometers, would not be sufficient on their own to provide all the necessary validation data. Therefore, the NASA Engineering and Safety Center (NESC) provided the 3D-DIC expertise and support to measure the high deformation and strain in the wheel flexures and qualify the overall structural response of the Mars 2020 rover wheel assembly. There were two key objectives for the photogrammetry technique: (1) monitor the wheel response in real-time, guarding against anomalous behavior and failure, and (2) provide test data for test-analysis correlation to validate and/or improve the high-fidelity computational model. The contents of this paper will focus on the challenges of applying 3D-DIC to the Mars 2020 Rover wheel assembly and how these challenges were overcome. Examples of test-analysis correlation during the stiffness characterization and structural qualification will be presented and discussed in detail. Experimental results were compared with the analysis and showed excellent agreement between the predicted behavior and helped validate the high-fidelity models.

Mars 2020 Rover Wheel↗
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 NTRS1998

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Composite Micromechanical Model - Part 2

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 second paper of a two part report, a three-dimensional composite micromechanical model is described which allows for the analysis of the rate dependent, nonlinear deformation response of a polymer matrix composite. Strain rate dependent inelastic constitutive equations utilized to model the deformation response of a polymer are implemented within the micromechanics method. The deformation response of two representative laminated carbon fiber reinforced composite materials with varying fiber orientation has been predicted using the described technique. The predicted results compare favorably to both experimental values and the response predicted by the Generalized Method of Cells, a well-established micromechanics analysis method.

Goldberg, Robert K.↗
NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗
NASA NTRS1998

Analysis and Design of Variable Stiffness Composite Cylinders

An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.

Tatting, Brian F.↗
NASA NTRS1986

The low cycle fatigue behavior of a plasma-sprayed coating material

Single crystal nickel-base superalloys employed in turbine blade applications are often used with a plasma spray coating for oxidation and hot corrosion resistance. These coatings may also affect fatigue life of the superalloy substrate. As part of a large program to understand the fatigue behavior of coated single crystals, fully reversed, total strain controlled fatigue tests were run on a free standing NiCoCrAlY coating alloy, PWA 276, at 0.1 Hz. Fatigue tests were conducted at 650 C, where the NiCoCrAlY alloy has modest ductility, and at 1050 C, where it is extremely ductile, showing tensile elongation in excess of 100 percent. At the lower test temperature, deformation induced disordering softened the NiCoCrAlY alloy, while at the higher test temperature cyclic hardening was observed which was linked to gradual coarsening of the two phase microstructure. Fatigue life of the NiCoCrAlY alloy was significantly longer at the higher temperature. Further, the life of the NiCoCrAlY alloy exceeds that of coated, /001/-oriented PWA 1480 single crystals at 1050 C, but at 650 C the life of the coated crystal is greater than that of the NiCoCrAlY alloy on a total strain basis.

Gayda, J.↗
NASA NTRS1986

Low cycle fatigue behaviour of a plasma-sprayed coating material

Single crystal nickel-base superalloys employed in turbine blade applications are often used with a plasma spray coating for oxidation and hot corrosion resistance. These coatings may also affect fatigue life of the superalloy substrate. As part of a large program to understand the fatigue behavior of coated single crystals, fully reversed, total strain controlled fatigue tests were run on a free standing NiCoCrAlY coating alloy, PWA 276, at 0.1 Hz. Fatigue tests were conducted at 650 C, where the NiCoCrAlY alloy has modest ductility, and at 1050 C, where it is extremely ductile, showing tensile elongation in excess of 100 percent. At the lower test temperature, deformation induced disordering softened the NiCoCrAlY alloy, while at the higher test temperature cyclic hardening was observed which was linked to gradual coarsening of the two phase microstructure. Fatigue life of the NiCoCrAlY alloy was significantly longer at the higher temperature. Further, the life of the NiCoCrAlY alloy exceeds that of coated, /001/-oriented PWA 1480 single crystals at 1050 C but at 650 C the life of the coated crystal is greater than that of the NiCoCrAlY alloy on a total strain basis.

Gayda, J.↗
NASA NTRS2003

Coronagraphic Amplitude and Phase Correction for Detecting Planets

Detection of earth-like planets around other stars using coronagraphy requires the optical beam into the coronagraph to be extremely uniform in both phase and amplitude. Errors in phase can be corrected using a deformable mirror, and error in amplitude can be corrected using a spatial light modulator, both in the pupil plan,a. These corrections can be combined using a Michelson interferometer. If amplitude corrections of only a few percent range are needed, the required accuracy of 10 (circumflex) -4 can be obtained with spatial light modulators with the modest dynamic range of 8 bits.

Woodgate, Bruce E.↗
NASA NTRS1999

Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach

Potential gas turbine applications will expose polymer matrix composites to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under extreme conditions. Specifically, analytical methods designed for these applications must have the capability of properly capturing the strain rate sensitivities and nonlinearities that are present in the material response. The Ramaswamy-Stouffer constitutive equations, originally developed to analyze the viscoplastic deformation of metals, have been modified to simulate the nonlinear deformation response of ductile, crystalline polymers. The constitutive model is characterized and correlated for two representative ductile polymers. Fiberite 977-2 and PEEK, and the computed results correlate well with experimental values. The polymer constitutive equations are implemented in a mechanics of materials based composite micromechanics model to predict the nonlinear, rate dependent deformation response of a composite ply. Uniform stress and uniform strain assumptions are applied to compute the effective stresses of a composite unit cell from the applied strains. The micromechanics equations are successfully verified for two polymer matrix composites. IM7/977-2 and AS4/PEEK. The ultimate strength of a composite ply is predicted with the Hashin failure criteria that were implemented in the composite micromechanics model. The failure stresses of the two composite material systems are accurately predicted for a variety of fiber orientations and strain rates. The composite deformation model is implemented in LS-DYNA, a commercially available transient dynamic explicit finite element code. The matrix constitutive equations are converted into an incremental form, and the model is implemented into LS-DYNA through the use of a user defined material subroutine. The deformation response of a bulk polymer and a polymer matrix composite are predicted by finite element analyses. The results compare reasonably well to experimental values, with some discrepancies. The discrepancies are at least partially caused by the method used to integrate the rate equations in the polymer constitutive model.

Goldberg, Robert K.↗