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Finite element models of varying complexities were used to solve problems in solid mechanics. Particular emphasis was given to concrete which is nonisotropic at any level of deformation and is also nonlinear in terms of stress-strain relationships.
The characteristic trace element signature that each mineral in the source region imparts on the magma constitutes the conceptual basis for trace element modeling. It is shown that abundances of trace elements in extrusive igneous rocks may be used as petrological and geochemical probes of the source regions of the rocks if differentiation processes, partition coefficients, phase equilibria, and initial concentrations in the source region are known. Although compatible and incompatible trace elements are useful in modeling, the present review focuses primarily on examples involving the rare-earth elements.
The full text of a paper presented at the Whither Turbulence Workshop (Cornell University, March 22-24, 1989) on past and future trends in turbulence modeling is provided. It is argued that Reynolds stress models are likely to remain the preferred approach for technological applications for at least the next few decades. In general agreement with the Launder position paper, it is further argued that among the variety of Reynolds stress models in use, second-order closures constitute by far the most promising approach. However, some needed improvements in the specification of the turbulent length scale are emphasized. The central points of the paper are illustrated by examples from homogeneous turbulence.
Increases in the concentration of water vapor constitute the single largest positive feedback in models of global climate warming caused by greenhouse gases. It has been suggested that sinking air in the regions surrounding deep cumulus clouds will dry the upper troposphere and eliminate or reverse the direction of water vapor feedback. This hypothesis has been tested by performing an idealized simulation of climate change with two different versions of a climate model which both incorporate drying due to subsidence of clear air but differ in their parameterization of moist convection and stratiform clouds. Despite increased drying of the upper troposphere by cumulus clouds, upper-level humidity increases in the warmer climate because of enhanced upward moisture transport by the general circulation and increased accumulation of water vapor and ice at cumulus cloud tops.
High by-pass turbofan engines have fewer fan blades and lower rotation speeds than their predecessors. Consequently, the noise suppression at the low frequency end of the noise spectra has become an increasing concern. This has led to a renewed emphasis on improving noise suppression efficiency of passive, duct liner treatments at the lower frequencies. For a variety of reasons, passive liners are comprised of locally-reacting, resonant absorbers. One reason for this design choice is to satisfy operational and economic requirements. The simplest liner design consists of a single layer of honeycomb core sandwiched between a porous facesheet and an impervious backing plate. These resonant absorbing structures are integrated into the nacelle wall and are very ef- ficient over a limited bandwidth centered on their resonance frequency. Increased noise suppression bandwidth and greater suppression at lower frequencies is typically achieved for conventional liners by increasing the liner depth and incorporating thin porous septa into the honeycomb core. However, constraints on liner depth in modern high by-pass engine nacelles severely limit the suppression bandwidth extension to lower frequencies. Also, current honeycomb core liners may not be suitable for irregular geometric volumes heretofore not considered. It is of interest, therefore, to find ways to circumvent liner depth restrictions and resonator cavity shape constraints. One way to increase effective liner depth is to skew the honeycomb core axis relative to the porous facesheet surface. Other possibilities are to alter resonator cavity shape, e.g. high aspect ratio, narrow channels that possibly include right angle bends, 180. channel fold-backs, and splayed channel walls to conform to irregular geometric constraints. These possibilities constitute the practical motivation for expanding impedance modeling capability to include unconventional resonator orientations and shapes. The work reported in this paper is in the nature of a progress report and is limited to examining the implications of resonator axis skew on the composite normal incidence impedance of an array of resonator channels. Specifically, experimental results are compared with a modified impedance prediction model for highaspect- ratio, rectangular, resonator channels with varying amounts of skew relative to the incident particle velocity. It is shown that for resonator channel widths of 1 to 2 mm, aspect ratios of 25 to 50, and skew angles of zero to sixty degrees, the surface impedance of test models can be predicted with good accuracy. Predicted resistances and reactances are particularly well correlated through the first resonance and first anti-resonance for all six test models investigated. Beyond the first anti-resonance, the impedance prediction model loses the ability to predict details of resistance and reactance but still predicts the mean trends very well.
The SRP believes strongly that regularly performed in-flight crew assessments are needed in order to identify a change in health status before a medical condition becomes clinically apparent. It is this early recognition in change that constitutes the foundation of the "occupational health model" expounded in the HRP Requirements Document as a key component of the HRP risk mitigation strategy that will enable its objective of "prevention and mitigation of human health and performance risks". A regular crew status examination of physiological and clinical performance is needed. This can be accomplished through instrumented monitoring of routine embedded tasks. The SRP recommends addition of a new gap to address this action under Category 3.0 Mitigate the Risk. This new gap is closely associated with Task 4.19 which addresses the lack of adequate biomedical monitoring capabilities for performing periodic clinical status evaluations and contingency medical monitoring. A corollary to these gaps is the critical emphasis on preventive medicine, not only during pre- and post-flight phases of a mission as is the current practice, but continued into the in-flight phases of exploration class missions.
It is noted that electrochemically based cell models can advance state-of-the-art battery prediction by allowing variations in the parameters that constitute wear-out and predict end-of-life performance. This modeling method is used as the foundation for the simulation of Ni-Cd battery performance. This simulation tool consists of a comprehensive computer model to be developed which would predict the voltage behavior of a battery under mission conditions.
A new, widely applicable model for local interfacial debonding in composite materials is presented. Unlike its direct predecessors, the new model allows debonding to progress via unloading of interfacial stresses even as global loading of the composite continues. Previous debonding models employed for analysis of titanium matrix composites are surpassed by the accuracy, simplicity, and efficiency demonstrated by the new model. The new model was designed to operate seamlessly within NASA Glenn's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), which was employed to simulate the time- and rate-dependent (viscoplastic) transverse tensile and creep behavior of SiC/Ti composites. MAC/GMC's ability to simulate the transverse behavior of titanium matrix composites has been significantly improved by the new debonding model. Further, results indicate the need for a more accurate constitutive representation of the titanium matrix behavior in order to enable predictions of the composite transverse response, without resorting to recalibration of the debonding model parameters.
This paper evaluates the simulation of snow by the Community Land Model, version 4 (CLM4), the land model component of the Community Earth System Model, version 1.0.4 (CESM1.0.4). CLM4 was run in an offline mode forced with the corrected land-only replay of the Modern-Era Retrospective Analysis for Research and Applications (MERRA-Land) and the output was evaluated for the period from January 2001 to January 2011 over the Northern Hemisphere poleward of 30 deg N. Simulated snow-cover fraction (SCF), snow depth, and snow water equivalent (SWE) were compared against a set of observations including the Moderate Resolution Imaging Spectroradiometer (MODIS) SCF, the Interactive Multisensor Snow and Ice Mapping System (IMS) snow cover, the Canadian Meteorological Centre (CMC) daily snow analysis products, snow depth from the National Weather Service Cooperative Observer (COOP) program, and Snowpack Telemetry (SNOTEL) SWE observations. CLM4 SCF was converted into snow-cover extent (SCE) to compare with MODIS SCE. It showed good agreement, with a correlation coefficient of 0.91 and an average bias of -1.54 x 10(exp 2) sq km. Overall, CLM4 agreed well with IMS snow cover, with the percentage of correctly modeled snow-no snow being 94%. CLM4 snow depth and SWE agreed reasonably well with the CMC product, with the average bias (RMSE) of snow depth and SWE being 0.044m (0.19 m) and -0.010m (0.04 m), respectively. CLM4 underestimated SNOTEL SWE and COOP snow depth. This study demonstrates the need to improve the CLM4 snow estimates and constitutes a benchmark against which improvement of the model through data assimilation can be measured.
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. A micromechanics approach is employed in this work, in which state variable constitutive equations originally developed for metals have been modified to model the deformation of the polymer matrix, and a strength of materials based micromechanics method is used to predict the effective response of the composite. In the analysis of the inelastic deformation of the polymer matrix, the definitions of the effective stress and effective inelastic strain have been modified in order to account for the effect of hydrostatic stresses, which are significant in polymers. Two representative polymers, a toughened epoxy and a brittle epoxy, are characterized through the use of data from tensile and shear tests across a variety of strain rates. Results computed by using the developed constitutive equations correlate well with data generated via experiments. The procedure used to incorporate the constitutive equations within a micromechanics method is presented, and sample calculations of the deformation response of a composite for various fiber orientations and strain rates are discussed.
The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.
A numerical procedure has been developed to investigate the nonlinear and strain rate dependent deformation response of polymer matrix composite laminated plates under high strain rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain rate dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated in order to improve the developed strain rate dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher order laminated plate theory which is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain rate loadings. Results show the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.
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.
Galactic cosmic rays (GCR) are a constant source of radiation that constitutes one of the major hazards during deep space exploration missions for both astronauts and hardware. In this work, GCR models commonly used by the space radiation protection community are compared with recently published high-precision, high- resolution measurements of cosmic ray lithium, beryllium, boron, carbon, nitrogen, and oxygen fluxes along with their ratios (Li/B, Li/C, Li/O, Be/B, Be/C, Be/O, B/C, B/O, C/O, N/B, N/O) from the Alpha Magnetic Spectrometer (AMS). All of the models were developed and calibrated prior to the publication of this AMS data, therefore this is an opportunity to validate the models against an independent data set. This paper is a compliment to the previously published comparison of GCR models with AMS hydrogen, helium, and the boron-to-carbon ratio.
The ionospheric configuration of the vertical Birkeland currents associated with an auroral arc is calculated from a model based on the assumption that the auroral electrons constitute a net current into the ionosphere. It is further assumed that the return vertical current out of the ionosphere is impeded along the field lines which connect the arc to the magnetosphere. The magnitude, location, and structure of the return Birkeland current calculated from the model agree well with measurements of these parameters by a rocket-borne experiment.
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.
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
The lack of agreement between our previously computed values and those measured by Viking of the N-15:N-14 isotope enhancement ratio has led us to reevaluate our model of the Martian ionosphere. In previous models, we were unable to reproduce the ion profiles measured by the RPA on Viking using electron temperatures that were higher that the ion temperatures. When we increased the electron temperatures to 2500-3000 K and with a zero flux upper boundary condition, the ion densities at high altitudes exceeded the measured values by a large factor. We found that we can better fit the observed profiles if we impose a loss process at the upper boundary of our model. If the horizontal fluxes of ions do not constitute a net loss of ions, then the escape of N due to dissociative recombination is also inhibited and better agreement with the measured isotope ratio is found. The production of escaping nitrogen atoms is closely related to the production of thermospheric odd nitrogen; therefore, the densities of NO measured by Viking provide a convenient check on our nitrogen escape model. Our standard model NO densities are less that the measured values by a factor of 2-3, as are those of previous models. We find that reasonable agreement can be obtained by assuming that the rate coefficient for loss of odd nitrogen in the reaction of N with NO is smaller at temperatures that prevail in the lower Martian thermosphere than the standard value, which applies to temperatures of 200-400 K. Other aspects of this investigation are presented.