Investigation of the Performance and Internal Flow of a Variable-area, Variable-internal-contraction Inlet at Mach Numbers of 2.00, 2.50, and 2.92
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Scherrer, Richard↗
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Results for “internal variability”
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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↗
An internal variable assisted formulation of moisture sorption models for polymers and composites
The purpose of the paper is to demonstrate that constitutive equations for moisture sorption and swelling can be obtained with an internal variable method which is rooted in the theory of irreversible thermodynamics. Realism is injected into the model through the concept of free volume. The power of the method is illustrated by the solution of the formidable nonlinear boundary value problem for diffusion with swelling-stress dependent diffusivity.
Hiel, C. C.↗
Internal variability of an energy-balance model with delayed albedo effects
A simple, deterministic energy-balance model with possible relevance to climatic variations on the time scale of glaciation cycles, is presented. The lag between ice-sheet extent and zonally-averaged temperature is modeled as a time delay in the ice-albedo feedback. The model exhibits self-sustained oscillations which are quasi-periodic or aperiodic in character. Fourier spectra of solutions have the features of many paleoclimatic records: peaks of variable height and width superimposed on a continuous, red-noise type background.
Bhattacharya, K.↗
Preliminary Experimental Investigation of a Variable-area, Variable-internal-contraction Air Inlet at Mach Numbers Between 1.42 and 2.44
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Scherrer, Richard↗
Static Investigation of a Multiaxis Thrust-Vectoring Nozzle With Variable Internal Contouring Ability
The thrust efficiency and vectoring performance of a convergent-divergent nozzle were investigated at static conditions in the model preparation area of the Langley 16-Foot Transonic Tunnel. The diamond-shaped nozzle was capable of varying the internal contour of each quadrant individually by using cam mechanisms and retractable drawers to produce pitch and yaw thrust vectoring. Pitch thrust vectoring was achieved by either retracting the lower drawers to incline the throat or varying the internal flow-path contours to incline the throat. Yaw thrust vectoring was achieved by reducing flow area left of the nozzle centerline and increasing flow area right of the nozzle centerline; a skewed throat deflected the flow in the lateral direction.
Wing, David J.↗
Bounds on internal state variables in viscoplasticity
A typical viscoplastic model will introduce up to three types of internal state variables in order to properly describe transient material behavior; they are as follows: the back stress, the yield stress, and the drag strength. Different models employ different combinations of these internal variables--their selection and description of evolution being largely dependent on application and material selection. Under steady-state conditions, the internal variables cease to evolve and therefore become related to the external variables (stress and temperature) through simple functional relationships. A physically motivated hypothesis is presented that links the kinetic equation of viscoplasticity with that of creep under steady-state conditions. From this hypothesis one determines how the internal variables relate to one another at steady state, but most importantly, one obtains bounds on the magnitudes of stress and back stress, and on the yield stress and drag strength.
Freed, Alan D.↗
On the use of internal state variables in thermoviscoplastic constitutive equations
The general theory of internal state variables are reviewed to apply it to inelastic metals in use in high temperature environments. In this process, certain constraints and clarifications will be made regarding internal state variables. It is shown that the Helmholtz free energy can be utilized to construct constitutive equations which are appropriate for metallic superalloys. Internal state variables are shown to represent locally averaged measures of dislocation arrangement, dislocation density, and intergranular fracture. The internal state variable model is demonstrated to be a suitable framework for comparison of several currently proposed models for metals and can therefore be used to exhibit history dependence, nonlinearity, and rate as well as temperature sensitivity.
Allen, D. H.↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.
Saleeb, Atef F.↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.
Li, Wei↗
IUE observations of E1405-451 - A new AM Herculis type cataclysmic variable
International Ultraviolet Explorer observations of the recently discovered AM Herculis type cataclysmic variable E1405-451 reveal a UV spectrum (1000-3000 A) similar to the other members of the type. The continuum flux distribution rises steeply at short wavelength and shows the effects of interstellar extinction. Best fit parameters for a blackbody spectrum are T = 25,500 + or - 2300 K with E(B-V) = 0.13 + or - 0.05. Many strong emission lines appear in the spectrum with similar intensities to those in AM Her. C IV 1550 and He II 1640 show some sign of a P Cygni profile. If these profiles are truly P Cygni, they indicate the intriguing possibility of a magnetically confined, radiatively driven wind present in all AM Her systems but only observable in a subset with an orientation like E1405-451.
Nousek, J. A.↗
Thermodynamic influences on acceleration waves in inhomogeneous isotropic elastic bodies with internal state variables
Thermodynamic properties effects on transverse acceleration wave propagation in inhomogeneous isotropic elastic bodies with internal state variables
Bowen, R. M.↗
The Influence of Internal Model Variability in GEOS-5 on Interhemispheric CO2 Exchange
An ensemble of eight atmospheric CO2 simulations was completed employing the National Aeronautics and Space Administration (NASA) Goddard Earth Observation System, Version 5 (GEOS-5) for the years 2000-2001, each with initial meteorological conditions corresponding to different days in January 2000 to examine internal model variability. Globally, the model runs show similar concentrations of CO2 for the two years, but in regions of high CO2 concentrations due to fossil fuel emissions, large differences among different model simulations appear. The phasing and amplitude of the CO2 cycle at Northern Hemisphere locations in all of the ensemble members is similar to that of surface observations. In several southern hemisphere locations, however, some of the GEOS-5 model CO2 cycles are out of phase by as much as four months, and large variations occur between the ensemble members. This result indicates that there is large sensitivity to transport in these regions. The differences vary by latitude-the most extreme differences in the Tropics and the least at the South Pole. Examples of these differences among the ensemble members with regard to CO2 uptake and respiration of the terrestrial biosphere and CO2 emissions due to fossil fuel emissions are shown at Cape Grim, Tasmania. Integration-based flow analysis of the atmospheric circulation in the model runs shows widely varying paths of flow into the Tasmania region among the models including sources from North America, South America, South Africa, South Asia and Indonesia. These results suggest that interhemispheric transport can be strongly influenced by internal model variability.
Allen, Melissa↗
Internal state variable approach for predicting stiffness reductions in fibrous laminated composites with matrix cracks
A mathematical model utilizing the internal state variable concept is proposed for predicting the upper bound of the reduced axial stiffnesses in cross-ply laminates with matrix cracks. The axial crack opening displacement is explicitly expressed in terms of the observable axial strain and the undamaged material properties. A crack parameter representing the effect of matrix cracks on the observable axial Young's modulus is calculated for glass/epoxy and graphite/epoxy material systems. The results show that the matrix crack opening displacement and the effective Young's modulus depend not on the crack length, but on its ratio to the crack spacing.
Lee, Jong-Won↗
A viscoplastic model with application to LiF-22 percent CaF2 hypereutectic salt
A viscoplastic model for class M (metal-like behavior) materials is presented. One novel feature is its use of internal variables to change the stress exponent of creep (where n is approximately = 5) to that of natural creep (where n = 3), in accordance with experimental observations. Another feature is the introduction of a coupling in the evolution equations of the kinematic and isotropic internal variables, making thermal recovery of the kinematic variable implicit. These features enable the viscoplastic model to reduce to that of steady-state creep in closed form. In addition, the hardening parameters associated with the two internal state variables (one scalar-valued, the other tensor-valued) are considered to be functions of state, instead of being taken as constant-valued. This feature enables each internal variable to represent a much wider spectrum of internal states for the material. The model is applied to a LiF-22 percent CaF2 hypereutectic salt, which is being considered as a thermal energy storage material for space-based solar dynamic power systems.
Freed, A. D.↗
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.↗
Thermodynamically consistent constitutive equations for nonisothermal large strain, elasto-plastic, creep behavior
The paper is concerned with the development of constitutive relations for large nonisothermal elastic-viscoplastic deformations for metals. The kinematics of elastic-plastic deformation, valid for finite strains and rotations, is presented. The resulting elastic-plastic uncoupled equations for the deformation rate combined with use of the incremental elasticity law permits a precise and purely deductive development of elastic-viscoplastic theory. It is shown that a phenomenological thermodynamic theory in which the elastic deformation and the temperature are state variables, including few internal variables, can be utilized to construct elastic-viscoplastic constitutive equations, which are appropriate for metals. The limiting case of inviscid plasticity is examined.
Riff, R.↗
Human and Natural Influences on the Changing Thermal Structure of the Atmosphere
Since the late 1970s, satellite-based instruments have monitored global changes in atmospheric temperature. These measurements reveal multidecadal tropospheric warming and stratospheric cooling, punctuated by short-term volcanic signals of reverse sign. Similar long- and short-term temperature signals occur in model simulations driven by human-caused changes in atmospheric composition and natural variations in volcanic aerosols. Most previous comparisons of modeled and observed atmospheric temperature changes have used results from individual models and individual observational records. In contrast, we rely on a large multimodel archive and multiple observational datasets. We show that a human-caused latitude/altitude pattern of atmospheric temperature change can be identified with high statistical confidence in satellite data. Results are robust to current uncertainties in models and observations. Virtually all previous research in this area has attempted to discriminate an anthropogenic signal from internal variability. Here, we present evidence that a human-caused signal can also be identified relative to the larger "total" natural variability arising from sources internal to the climate system, solar irradiance changes, and volcanic forcing. Consistent signal identification occurs because both internal and total natural variability (as simulated by state-of-the-art models) cannot produce sustained global-scale tropospheric warming and stratospheric cooling. Our results provide clear evidence for a discernible human influence on the thermal structure of the atmosphere.
Santer, Benjamin D.↗