General motion of a variable-mass flexible rocket with internal flow
Dynamical characteristics of variable-mass flexible spinning rocket with internal flow, investigating rigid body motion, elastic displacements and vibrations
Meirovitch, L.↗
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A Three-Dimensional Thermodynamically Based Function for the Progressive Failure of Unidirectional Composites
A thermodynamically-based work potential theory for modeling progressive damage for laminated, unidirectional composites assuming plane stress (2D Schaperystheory) is extended to three dimensioanl (3D). An internal state variable, S, is defined to account for the dissipated energy due to damage evolution in the form of microstructure changes in the matrix. With the stationary of the total work potential with respect to the internal state variable, a thermodynamically-consistent set of evolution equationsis derived. The internal state variable is related to the transverse and shear modulithrough microdamage functions. In the first part of this work, coupon specimensare prepared to conduct experiments to characterize the relations between the internalstate variable and the transverse modulus as well as shear modulus. The informationis subsequent used for the prediction of three point bending test. In the second partof this work, objectivity is studied. Three separate methods utilizing different definitions of a reduced internal state variable or of the order of the polynomials are used to represent the matrix micro-damage functions are employed. The three methods are implemented in a user defined subroutine within a commercial finite element method software package. Results from numerical simulations of a center-notched composites panel are compared. The agreement in the maximum stress predictions among the three methods indicates that objectivity, with respect to the functional form of themicrodamage functions, is satisfied.
carbon fiber reinforced polymer composites↗
A Modeling Investigation of Thermal and Strain Induced Recovery and Nonlinear Hardening in Potential Based Viscoplasticity
Specific forms for both the Gibb's and the complementary dissipation potentials were chosen such that a complete potential based multiaxial, isothermal, viscoplastic model was obtained. This model in general possesses three internal state variables (two scalars associated with dislocation density and one tensor associated with dislocation motion) both thermal and dynamic recovery mechanisms, and nonlinear kinematic hardening. This general model, although possessing associated flow and evolutionary laws, is shown to emulate three distinct classes of theories found in the literature, by modification of the driving threshold function F. A parametric study was performed on a specialized nondimensional multiaxial form containing only a single tensorial internal state variable (i.e., internal stress). The study was conducted with the idea of examining the impact of including a strain-induced recovery mechanism and the compliance operator, derived from the Gibb's potential, on the uniaxial and multiaxial response. One important finding was that inclusion of strain recovery provided the needed flexibility in modeling stress-strain and creep response of metals at low homologous temperatures, without adversely affecting the high temperature response. Furthermore, for nonproportional loading paths, the inclusion of the compliance operator had a significant influence on the multiaxial response, but had no influence on either uniaxial or proportional load histories.
Arnold, S. M.↗
The general motion of a variable-mass flexible rocket with internal flow
Dynamic motion characteristics of variable-mass flexible rocket with internal flow
Meirovitch, L.↗
A continuum damage model of fatigue-induced damage in laminated composites
A model is presented which predicts the stress-strain behavior of continuous fiber reinforced laminated composites in the presence of microstructural damage. The model is based on the concept of continuum damage mechanics and uses internal state variables to characterize the various damage modes. The associated internal state variable growth laws are mathematical models of the loading history induced development of microstructural damage. The model is demonstrated by using it to predict the response of damaged AS-4/3502 graphite/epoxy laminate panels.
Harris, Charles E.↗
Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire
An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
Johnson, Arthur R.↗
A Viscoelastic Hybrid Shell Finite Element
An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
Johnson, Arthur↗
Computational Implementation of a Thermodynamically Based Work Potential Model For Progressive Microdamage and Transverse Cracking in Fiber-Reinforced Laminates
A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.
Pineda, Evan J.↗
Design strategies for the International Space University's variable gravity research facility
A variable gravity research facility named 'Newton' was designed by 58 students from 13 countries at the International Space University's 1989 summer session at the Universite Louis Pasteur, Strasbourge, France. The project was comprehensive in scope, including a political and legal foundation for international cooperation, development and financing; technical, science and engineering issues; architectural design; plausible schedules; and operations, crew issues and maintenance. Since log-term exposure to zero gravity is known to be harmful to the human body, the main goal was to design a unique variable gravity research facility which would find a practical solution to this problem, permitting a manned mission to Mars. The facility would not duplicate other space-based facilities and would provide the flexibility for examining a number of gravity levels, including lunar and Martian gravities. Major design alternatives included a truss versus a tether based system which also involved the question of docking while spinning or despinning to dock. These design issues are described. The relative advantages or disadvantages are discussed, including comments on the necessary research and technology development required for each.
Bailey, Sheila G.↗
Thermoviscoplastic model with application to copper
A viscoplastic model is developed which is applicable to anisothermal, cyclic, and multiaxial loading conditions. Three internal state variables are used in the model; one to account for kinematic effects, and the other two to account for isotropic effects. One of the isotropic variables is a measure of yield strength, while the other is a measure of limit strength. Each internal state variable evolves through a process of competition between strain hardening and recovery. There is no explicit coupling between dynamic and thermal recovery in any evolutionary equation, which is a useful simplification in the development of the model. The thermodynamic condition of intrinsic dissipation constrains the thermal recovery function of the model. Application of the model is made to copper, and cyclic experiments under isothermal, thermomechanical, and nonproportional loading conditions are considered. Correlations and predictions of the model are representative of observed material behavior.
Freed, Alan D.↗
On the Temporal Variability of Low-Mode Internal Tides in the Deep Ocean
In situ measurements of internal tides are typically characterized by high temporal variability, with strong dependence on stratification, mesoscale eddies, and background currents commonly observed. Thus, it is surprising to find phase-locked internal tides detectable by satellite altimetry. An important question is how much tidal variability is missed by altimetry. We address this question in several ways. We subset the altimetry by season and find only very small changes -- an important exception being internal tides in the South China Sea where we observe strong seasonal dependence. A wavenumber-domain analysis confirms that throughout most of the global ocean there is little temporal variability in altimetric internal-tide signals, at least in the first baroclinic mode, which is the mode that dominates surface elevation. The analysis shows higher order modes to be significantly more variable. The results of this study have important practical implications for the anticipated SWOT wide-swath altimeter mission, for which removal of internal tide signals is critical for observing non-tidal submesoscale phenomena.
Ray, Richard D.↗
The International Space University's variable gravity research facility design
A manned mission to Mars will require long travel times between Earth and Mars. However, exposure to long-duration zero gravity is known to be harmful to the human body. Some of the harmful effects are loss of heart and lung capacity, inability to stand upright, muscular weakness and loss of bone calcium. A variable gravity research facility (VGRF) that would be placed in low Earth orbit (LEO) was designed by students of the International Space University 1989 Summer Session held in Strasbourg, France, to provide a testbed for conducting experiments in the life and physical sciences in preparation for a mission to Mars. This design exercise was unique because it addressed all aspects concerning a large space project. The VGRF design was described which was developed by international participants specializing in the following areas: the politics of international cooperation, engineering, architecture, in-space physiology, material and life science experimentation, data communications, business, and management.
Bailey, Sheila G.↗
Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow
A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.
Meirovitch, L.↗
Summary of nonaxisymmetric nozzle internal performance from the NASA Langley Static Test Facility
Early experimental work on multifunction nozzles (prior to 1978) concentrated on quantifying the isolated and installed performance of specific nozzle designs at various power settings during cruise, vectored thrust, and reverse thrust operating modes. Since 1978, however, significant effort has been expended on developing a parametric data base on nozzle internal design variables which could lead to improved internal performance and/or lower structural weight. Much of this work has been conducted in the Static Test Facility of the NASA/Langley 16-Foot Transonic Tunnel using subscale models and high pressure air to simulate jet exhaust. A review of the research effort on nonaxisymmetric multifunction nozzles along with a summary of many of the results is presented. In addition, internal performance results from subscale models tested in the Static Test Facility and from full-scale engine/nozzle tests are compared.
Leavitt, L. D.↗
Plasticity and Damage Modeling of Stress Asymmetry and Dynamic Behavior of AFS Additive Manufactured Aluminum Alloy 2219
The Solid State Additive Manufacturing (AM) process referred as MELD that fabricated the samples in this study, provides a new path for repairing, coating, joining and additive manufacturing metals and metal matrix composites. This research will be the first application of a physics-based microstructure dependent internal state variable (ISV) plasticity and damage material model to capture the mechanical response of an AM Aluminum Alloy (AA) 2219 via the MELD process. In this research, a microstructure-based internal state variable (ISV) plasticity-damage model was used to capture the mechanical behavior of AFS 2219 aluminum alloy. Aeroprobe Corporation, creator and patent holder for the MELD process, fabricated the material by pushing a solid filler rod of AA2219-T861 material through a hollow rotating tool onto an AA2219 T851 plate substrate. As feedstock, solid or powder precursor metals are pushed through a nonconsumable rotating cylindrical tool. Herein, added layers are deposited and metallurgically bonded to substrate material or previously deposited layers by the heat generated from the rotating tool through plastic deformation of the filler material. Once a layer has been added, the tool height increases, and starts the deposition of the next layer. This process results in beneficial properties such as grain refinement, homogenization and reduced porosity (fully dense). This process will experience temperatures similar to those in the weld nugget zone (WNZ) in friction stir welding (FSW), ranging from 0.6-0.9 Tm, with Tm being the melting point of the material. MELD is highly scalable with AA deposition rates reaching over 1000 cm3/hr, which allows for MELD being used for repairs, coatings, and building components. A motivating factor driving the research for physics-based history dependent material modeling of MELD components is the ability to accurately capture the stress-state and strain rate dependence in the material caused by variations in material microstructure from the MELD processing of new or repaired components. The ISV model incorporates microstructural content and is consistent with continuum level kinematics, kinetics, and thermodynamics. These features allow the ISV model to capture large deformations at the structural scale using the kinematic and isotropic hardening, while microscale damage is obtained from the microstructural features. The benefits of the ISV model arise from the inclusion of structure-property relationships identified from microstructural characterization and experimentation. The Bauschinger effect (BE) is an important concept, vital in the accurate prediction of cyclic stress-strain response of ductile materials such as metals. The ISV model has been successfully used to capture the behavior and damage, and the BE of different aluminum alloys and steels. The ISV model uses kinematic and isotropic hardening to help capture deformations of the material at the macro scale. To understand this hardening relationship, calculating the kinematic and isotropic hardening relationship in the material is warranted for a high-fidelity model. Electron Backscattered Diffraction (EBSD) was used to characterize the as-fabricated microstructure, where a fully-dense equiaxed grain morphology with average grain size of 2.5 μm was observed. Microhardness mapping of the as-built structures, monotonic tension and compression experiments at both quasi-static (0.001/s) strain rates, tension-followed-by-compression and compression-followed-by-tension experiments were performed to obtain the set of plasticity and damage constants necessary to capture strain rate and stress state behavior of this additive material. To calibrate the plasticity-damage model, a single set of constants were determined to capture the different stress states the MELD AA2219. One set of the constants was determined from experimental true stress-strain curves for the tension and compression data. Additionally, microstructural information and data from the open literature were used as the other model constants. This research is a first of its kind for AFS AA2219, includes correlating the ISV model to the monotonic experimental results that capture the isotropic and kinematic plasticity mechanical response.
Rivera, O. G.↗
The Potential for Snow to Supply Human Water Demand in the Present and Future
Runoff from snowmelt is regarded as a vital water source for people and ecosystems throughout the Northern Hemisphere (NH). Numerous studies point to the threat global warming poses to the timing and magnitude of snow accumulation and melt. But analyses focused on snow supply do not show where changes to snowmelt runoff are likely to present the most pressing adaptation challenges, given sub-annual patterns of human water consumption and water availability from rainfall. We identify the NH basins where present spring and summer snowmelt has the greatest potential to supply the human water demand that would otherwise be unmet by instantaneous rainfall runoff. Using a multi-model ensemble of climate change projections, we find that these basins - which together have a present population of approx. 2 billion people - are exposed to a 67% risk of decreased snow supply this coming century. Further, in the multi-model mean, 68 basins (with a present population of more than 300 million people) transition from having sufficient rainfall runoff to meet all present human water demand to having insufficient rainfall runoff. However, internal climate variability creates irreducible uncertainty in the projected future trends in snow resource potential, with about 90% of snow-sensitive basins showing potential for either increases or decreases over the near-term decades. Our results emphasize the importance of snow for fulfilling human water demand in many NH basins, and highlight the need to account for the full range of internal climate variability in developing robust climate risk management decisions.
Mankin, Justin S.↗
Diagnosing Changes In Earth's Top-Of-Atmosphere Radiation Budget Since 2000
Earth’s radiation budget (ERB) is a key indicator of the climate system as it describes the delicate balance between how much of the sun’s energy reaching Earth is absorbed and how much thermal infrared radiation is emitted back to space. It is now well established that there is a positive net imbalance in ERB of 0.5-1 Wm-2. This imbalance, referred to as Earth’s Energy Imbalance (EEI), is shaped by natural and anthropogenic climate forcings and the climate system’s response to the forcing.When averaged over a long period, a positive EEI leads to an increase in surface temperature, sea levelrise, ocean heat content, melting of snow and sea-ice, and an acceleration of the hydrological cycle.EEI is also influenced by internal climate variability at interannual (e.g., El Niño/Southern Oscillation(ENSO)) and longer timescales (e.g., Pacific Decadal Oscillation (PDO)). Here we use CERES data toshow that since 2000, EEI has been increasing at a rate of 0.04+-0.03 Wm-2 per yr, corresponding to 0.8 Wm-1 over the 20-year CERES record. To understand the underlying causes for this increase, we analyze the CERES data in the context of internal climate variability indices and regional pattern changes. We also perform a partial radiative perturbation analysis that decomposes the TOA SW and LW radiation variations in terms of contributions by clouds, aerosols, surface albedo, temperature,water vapor and other gases (e.g., ozone, carbon dioxide, methane, etc.).
Norman G Loeb↗
Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models
A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.
Klein, Vladislav↗