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At least 181 records · Page 10

Birkeland currents in the plasma sheet

A search was conducted for the signatures of Birkeland currents in the Earth's magnetic tail, using observed values of B(sub x) and B(sub y) from large sets of spacecraft data. The data were binned by x and y for -10 greater than x(sub GSM) greater than -35 and absolute value of y(sub GSM) less than or equal to 20 R(sub E) (less than or equal to 30 R(sub E) for x(sub GSM) less than or equal to -25 R(sub E)) and in each bin their distribution in the (B(sub x), B(sub y)) plane was fitted by least squares to a piecewise linear function. That gave average x-y distributions of the flaring angle between B(sub xy) and the x direction, as well as that angle's variation across the thickness of the plasma sheet. Angles obtained in the central plasma sheet differed from those derived near the lobe boundary. That is the expected signature if earthward or tailward Birkeland current sheets are embedded in the plasma sheet, and from this dfiference we derived the dawn-dusk profiles of the tail Birkeland currents for several x(sub GSM) intervals. It was found that (1) the Birkeland currents have the sense of region 1 currents, when mapped to the ionosphere; (2) both the linear current density (kiloamperes/R(sub E)) and the net magnitude of the field-aligned currents decrease rapidly down the tail; (3) the total Birkeland current at x approximately equals -10 R(sub E) equals approximately equals 500-700 kA, which is approx. 30% of the net region 1 current observed at ionospheric altitudes, in agreement with model mapping results; and (4) the B(sub z) and B(sub y) components of the interplanetary magnetic field influence the distribution of Birkeland currents in the tail.

Tsyganenko, Nikolai A.↗

Automated Development of Accurate Algorithms and Efficient Codes for Computational Aeroacoustics

The simulation of sound generation and propagation in three space dimensions with realistic aircraft components is a very large time dependent computation with fine details. Simulations in open domains with embedded objects require accurate and robust algorithms for propagation, for artificial inflow and outflow boundaries, and for the definition of geometrically complex objects. The development, implementation, and validation of methods for solving these demanding problems is being done to support the NASA pillar goals for reducing aircraft noise levels. Our goal is to provide algorithms which are sufficiently accurate and efficient to produce usable results rapidly enough to allow design engineers to study the effects on sound levels of design changes in propulsion systems, and in the integration of propulsion systems with airframes. There is a lack of design tools for these purposes at this time. Our technical approach to this problem combines the development of new, algorithms with the use of Mathematica and Unix utilities to automate the algorithm development, code implementation, and validation. We use explicit methods to ensure effective implementation by domain decomposition for SPMD parallel computing. There are several orders of magnitude difference in the computational efficiencies of the algorithms which we have considered. We currently have new artificial inflow and outflow boundary conditions that are stable, accurate, and unobtrusive, with implementations that match the accuracy and efficiency of the propagation methods. The artificial numerical boundary treatments have been proven to have solutions which converge to the full open domain problems, so that the error from the boundary treatments can be driven as low as is required. The purpose of this paper is to briefly present a method for developing highly accurate algorithms for computational aeroacoustics, the use of computer automation in this process, and a brief survey of the algorithms that have resulted from this work. A review of computational aeroacoustics has recently been given by Lele.

Goodrich, John W.↗

Use of Simple Continuum Solutions in Finite Element Alternating Method for Fracture Problems

The performance of the finite element alternating (FEAM) method for two-dimensional crack problems is studied with respect to a polynomial pressure distribution fitted to the crack face stresses. The FEAM alternates between the analytical solution of crack in an infinite plate subjected to arbitrary polynomial distribution and a finite element solution of an uncracked body to satisfy the required boundary conditions in the crack problem. In this paper, the FEAM is applied to embedded crack and edge crack problems. For embedded crack problems, all of the constant, linear, and quadratic ( N=0,1, or 2, respectively) pressure distributions yield very accurate results with this algorithm with 4 to 5 iterations. The edge crack problems, on the other hand, require much higher order polynomials distributions (N=5 to 6) to yield accurate solutions. For slant edge crack problems, the mode-I stress-intensity factors have better accuracy than the mode-II stress-intensity factors for the same convergence tolerance.

Krishnamurthy, T.↗

A Two-Axis Direct Fluid Shear Stress Sensor

This innovation is a miniature or micro sized semiconductor sensor design that provides two axis direct non-intrusive measurement of skin friction or wall shear stress in fluid flow. The sensor is fabricated by micro-electro-mechanical system (MEMS) technology, enabling small size and low cost reproductions. The sensors have been fabricated by utilizing MEMS fabrication processes to bond a sensing element wafer to a fluid coupling wafer. This layering technique provides for an out of plane dimension that is on the same order of length as the inplane dimensions. The sensor design has the following characteristics: a shear force collecting plate with dimensions that can be tailored to various application specific requirements such as spatial resolution, temporal resolution and shear force range and resolution. This plate is located coplanar to both the sensor body and flow boundary, and is connected to a dual axis gimbal structure by a connecting column or lever arm. The dual axis gimbal structure has torsional hinges with embedded piezoresistive torsional strain gauges which provide a voltage output that is correlated to the applied shear stress (and excitation current) on force collection plate that is located on the flow boundary surface (hence the transduction method). This combination of design elements create a force concentration and resolution structure that enables the generation of a large stress on the strain gauge from the small shear stress on the flow boundary wall. This design as well as the use of back side electrical contacts establishes a non-intrusive method to quantitatively measure the shear force vector on aerodynamic bodies.

Adcock, Edward E.↗

Analysis of the Harrier forebody/inlet design using computational techniques

Under the support of this Cooperative Agreement, computations of transonic flow past the complex forebody/inlet configuration of the AV-8B Harrier II have been performed. The actual aircraft configuration was measured and its surface and surrounding domain were defined using computational structured grids. The thin-layer Navier-Stokes equations were used to model the flow along with the Chimera embedded multi-grid technique. A fully conservative, alternating direction implicit (ADI), approximately-factored, partially flux-split algorithm was employed to perform the computation. An existing code was altered to conform with the needs of the study, and some special engine face boundary conditions were developed. The algorithm incorporated the Chimera technique and an algebraic turbulence model in order to deal with the embedded multi-grids and viscous governing equations. Comparison with experimental data has yielded good agreement for the simplifications incorporated into the analysis. The aim of the present research was to provide a methodology for the numerical solution of complex, combined external/internal flows. This is the first time-dependent Navier-Stokes solution for a geometry in which the fuselage and inlet share a wall. The results indicate the methodology used here is a viable tool for transonic aircraft modeling.

Chow, Chuen-Yen↗

Characterization of Aerodynamic Performance of Boundary-Layer-Ingesting Inlet Under Crosswind

NASA has been studying future transport concepts, envisioned to be technically realizable in the timeframe of 2020-2030, to meet environmental and performance goals. One concept receiving considerable interest involves a propulsion system embedded into a hybrid wing-body aircraft. While offering significant advantages in fuel savings and noise reduction by this concept, there are several technical challenges that are not encountered in the current fleet and must be overcome so as to deliver target performance and operability. One of these challenges is associated with an inlet system that ingests a significantly thick boundary layer, developing along the wing-body surface, into a serpentine diffuser before the flow meeting fan blades. The flow is subject to considerable total pressure loss and distorted at the fan face, much more significantly than in the inlet system of conventional aircraft. In our previous studies [1, 2], we have shown that through innovative design changes on the airframe surface, it is possible to simultaneously increase total pressure recovery and decrease distortion in the flow, without resorting to conventional penalty-ridden flow control concepts, such as vortex generator or boundary layer bleeding/suction. In the current study, we are interested in understanding the following issues: how the embedded propulsion system performs under a crosswind condition by studying in detail the flow characteristics of two inlets, the baseline and another optimized previously under the cruise condition. With the insight, it is hoped that it can help in the follow-on study by devising effective strategies to minimize flow distortion arising from the integration of an embedded-engine system into an airframe to the level acceptable to the operation and fuel consumption before 2030. To achieve these demanding goals, non-conventional concepts are called for; but technology gap is too big that it requires evolutionary approach by focusing various concepts and technologies needed in the next three generations of aircraft, respectively named as N+1, N+2, and N+3. Noticeably, considerable reduction in each category of 1 is required in N+2 (relative to Boeing 777-200 and GE90 engines) and N+3 (relative to Boeing 737-800 and CFM56-7B engines). In this study, concepts for N+2 is our interest. A concept that has potential to achieve these metrics and has been under intensive study is the hybrid wing body (HWB) airframe with a tightly integrated propulsion system, see Fig. 1. The inlet is non-circular at the entrance and the entering flow, no longer uniform or free of disturbances, and is now carrying with it a boundary layer developing along the fuselage; the inlet is thus known as boundary-layer-ingesting (BLI) inlet.

Liou, Meng-Sing↗

Proton Transport

The transport of protons across membranes is an essential process for both bioenergetics of modern cells and the origins of cellular life. All living systems make use of proton gradients across cell walls to convert environmental energy into a high-energy chemical compound, adenosine triphosphate (ATP), synthesized from adenosine diphosphate. ATP, in turn, is used as a source of energy to drive many cellular reactions. The ubiquity of this process in biology suggests that even the earliest cellular systems were relying on proton gradient for harvesting environmental energy needed to support their survival and growth. In contemporary cells, proton transfer is assisted by large, complex proteins embedded in membranes. The issue addressed in this Study was: how the same process can be accomplished with the aid of similar but much simpler molecules that could have existed in the protobiological milieu? The model system used in the study contained a bilayer membrane made of phospholipid, dimyristoylphosphatidylcholine (DMPC) which is a good model of the biological membranes forming cellular boundaries. Both sides of the bilayer were surrounded by water which simulated the environment inside and outside the cell. Embedded in the membrane was a fragment of the Influenza-A M$_2$ protein and enough sodium counterions to maintain system neutrality. This protein has been shown to exhibit remarkably high rates of proton transport and, therefore, is an excellent model to study the formation of proton gradients across membranes. The Influenza M$_2$ protein is 97 amino acids in length, but a fragment 25 amino acids long. which contains a transmembrane domain of 19 amino acids flanked by three amino acids on each side. is sufficient to transport protons. Four identical protein fragments, each folded into a helix, aggregate to form small channels spanning the membrane. Protons are conducted through a narrow pore in the middle of the channel in response to applied voltage. This channel is large enough to contain water molecules. and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small ions, such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel with the histidine residues in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel loses its structural integrity and one helix moves away from the remaining three. Additional information is contained within the original extended abstract.

Pohorille, Andrew↗

The M2 Proton Channel of Influenza Virus: How Does It Work?

The transport of protons across membranes is an essential process for both bioenergetics of modem cells and the origins of cellular life. All living systems make use of proton gradients across cell walls to convert environmental energy into a high-energy chemical compound, adenosine triphosphate (ATR), synthesized from adenosine diphosphate. ATR, in turn, is used as a source of energy to drive many cellular reactions. The ubiquity of this process in biology suggests that even the earliest cellular systems were relying on proton gradient for harvesting environmental energy needed to support their survival and growth. In contemporary cells, proton transfer is assisted by large, complex proteins embedded in membranes. The issue addressed in this study was: how the same process can be accomplished with the aid of similar, but much simpler molecules that could have existed in the protobiological milieu? The model system used in the study contained a bilayer membrane made of phospholipid, dimyristoylphosphatidylcholine (DMPC), which is a good model of the biological membranes focusing cellular boundaries. Both sides of the bilayer were surrounded by water which simulated the environment inside and outside the cell. Embedded in the membrane was a fragment of the Influenza-A M2 protein and enough sodium counterions to maintain system neutrality. This protein has been shown to exhibit remarkably high rates of proton transport and, therefore, is an excellent model to study the formation of proton gradients across membranes. The Influenza M2 protein is 97 amino acids in length, but a fragment 25 amino acids long, which contains a transmembrane domain of 19 amino acids flanked by 3 amino acids on each side, is sufficient to transport protons. Four identical protein fragments, each folded into a helix, aggregate to form small channels spanning the membrane. Protons are conducted through a narrow pore in the middle of the channel in response to applied voltage. This channel is large enough to contain water molecules, and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional, important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel, in which the histidine residues were in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel looses its structural integrity and one helix moves away from the remaining three. This result indicates that such a mechanism of proton transport is unlikely. The simulations revealed that translocation along a network of water molecules in the channel and tautomerization of the histidine residues in the M2 proteins in the most likely mechanism of proton transport. The results not only explain how a remarkably simple protein system can efficiently aid in the formation of proton gradients across cell walls, but also suggest how this system can be genetically re-engineered to become a directional, reversible proton pump. Such a pump can provide energy to laboratory-built models of simple cellular systems. If they were successfully constructed it would greatly advance our understanding of the beginnings of life and find important applications in medicine and pharmacology.

Pohorille, Andrew↗

Thriving in the Carbon-Aware Market: How to Account for Emissions in the Era of Carbon-Centered Trade Policies

Emerging global policies, such as the European Union's enacted Carbon Border Adjustment Mechanism and similar policies under development in Canada, Australia and the United Kingdom, will place a premium on goods traded into their territories with higher embedded emissions than those produced domestically. U.S. manufacturers could stand to benefit from such policies; given the investments U.S. industry has made to reduce the energy and emission intensities of its operations. For example, the overall GHG intensity of U.S. steel production in 2019 was ~0.96 t CO2/t steel, less than half that of China (~1.97 t CO2/t steel), and bested only by Italy. To realize these benefits, transparent, accurate, interoperable and accepted embedded emissions accounting and calculation methods are required. Achieving this requires overcoming challenges related to data availability, boundary definitions, and product definitions among others, both at individual facilities as well as through value chains. We will present technical findings on methodology considerations and data-availability constraints for determining the emissions of traded goods, using steel as a pilot and leveraging publicly available data. Issues such as determining the appropriate scope for emissions accounting, implications of the specificity of product chosen, emissions allocation in multi-product facilities, and enumeration of emissions for products manufactured across multiple facilities will be discussed. By sharing the results of our efforts, we aim to inform the development and execution of embedded emissions accounting methods from a technical perspective such that U.S. manufacturers can thrive in emerging global markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Bentz, Daniel N.↗

Inlet Flow Control and Prediction Technologies for Embedded Propulsion Systems

Fail-safe, hybrid, flow control (HFC) is a promising technology for meeting high-speed cruise efficiency, low-noise signature, and reduced fuel-burn goals for future, Hybrid-Wing-Body (HWB) aircraft with embedded engines. This report details the development of HFC technology that enables improved inlet performance in HWB vehicles with highly integrated inlets and embedded engines without adversely affecting vehicle performance. In addition, new test techniques for evaluating Boundary-Layer-Ingesting (BLI)-inlet flow-control technologies developed and demonstrated through this program are documented, including the ability to generate a BLI-like inlet-entrance flow in a direct-connect, wind-tunnel facility, as well as, the use of D-optimal, statistically designed experiments to optimize test efficiency and enable interpretation of results. Validated improvements in numerical analysis tools and methods accomplished through this program are also documented, including Reynolds-Averaged Navier-Stokes CFD simulations of steady-state flow physics for baseline, BLI-inlet diffuser flow, as well as, that created by flow-control devices. Finally, numerical methods were employed in a ground-breaking attempt to directly simulate dynamic distortion. The advances in inlet technologies and prediction tools will help to meet and exceed "N+2" project goals for future HWB aircraft.

McMillan, Michelle L.↗

Aerodynamic Design and Optimization of Fan Stage for Boundary Layer Ingestion Propulsion System

The present paper addresses the process of preliminary design of a low-pressure fan and outlet guide vane (OGV) of a boundary layer ingestion (BLI) propulsion system. The tail-cone thruster systems of NASA's STARC_ABL (Single-aisle Turboelectric Aircraft with an Aft Boundary-Layer propulsor) adopts an axi-symmetric BLI type inlet as opposed to other embedded engine systems. Thus, the focus of the present work is placed on maximizing the efficiency of the fan and OGV stages under a significant radial distortion. A parameterization with B-spline function for camber line angles, metal chord, thickness distribution and stacking axis of blades is presented. The flowpath lines are also parameterized by B-spline function and aggregated in the design system of blades. The design optimization with evolutionary algorithm is performed with constraints of fan pressure ratio, OGV exit swirl angle and nozzle exit properties. The inlet conditions for the turbo-machinery CFD (Computational Fluid Dynamics) domain and the design goal of the fan stage are driven by a propulsion airframe integration (PAI) model that uses a 3-D unstructured RANS (Reynolds Average Navier Stokes) solver and actuator disk model. The expected power saving of the BLI propulsor is quantified via PAI analysis and the resulting preliminary design of the fan stages is compared with a clean-inlet flow propulsor.

Turbo-machinery↗

Computational Micromechanics Model for the Analysis of Fiber Kinking in Unidirectional FRP

A computational micromechanics (CMM) model is developed to analyze fiber kinking, which is a failure mechanism that takes place in fiber-reinforced composites when they are loaded under longitudinal compression. The CMM model consists of a single AS4 carbon fiber with an initial misalignment embedded in an 8552 polymer matrix. The deformation of the model is governed by periodic boundary conditions (PBC). The relatively simple CMM model enables the evaluation of the role played by initial misalignment of the fiber, shear yielding of the matrix and fiber-matrix debonding. A novel microscale experimental technique devoted to the characterization of the longitudinal compressive strength of the fibers, X(sup f)(sub c) , was developed. By exercising the model and comparing it with several existing models in the literature, the nonlinear shear response of the composite lamina was shown to play a fundamental role not only in the prediction of the compressive strength X(sub c), but also during the post-peak regime in terms of residual stress σ(sub r) and fiber rotation φ. Finally, the influence of the fiber-matrix interface damage (not considered in most other fiber kinking models) on the fiber kinking phenomenon was assessed through a parametric study.

Polymer-matrix composites (PMC)↗

Physical properties of Saturn's rings

Spaceborne astronomy data on Saturn's rings is summarized. The main rings are composed primarily of ice, possibly of low density and including small amounts of reddish material; particle radii are primarily centimeter-to-several meters, but significant amounts of micron-sized dust exists in certain regions including regions of resonance-induced collisions. The particle surface albedo and size distribution varies globally and locally. Evidence suggests several embedded moonlets of 10 km radius within Encke's division. The cause of the abrupt regional boundaries and associated differences in particle properties, especially the cause of the very abrupt and qualitatively similar inner A and B ring boundaries; the gap-ringlet structure and broad plateau features observed in the C and Cassini regions; the F and G rings (assuming that Enceladus is responsible for the E ring); and the cause of spokes and the SED are not understood.

Cuzzi, J. N.↗

Interactive algebraic grid-generation technique

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Smith, R. E.↗

The morphology of strike-slip faults - Examples from the San Andreas Fault, California

The dilatational strains associated with vertical faults embedded in a horizontal plate are examined in the framework of fault kinematics and simple displacement boundary conditions. Using boundary element methods, a sequence of examples of dilatational strain fields associated with commonly occurring strike-slip fault zone features (bends, offsets, finite rupture lengths, and nonuniform slip distributions) is derived. The combinations of these strain fields are then used to examine the Parkfield region of the San Andreas fault system in central California.

Bilham, Roger↗

Local grid refinement for transonic flow problems

The present use of locally refined Cartesian grids to solve transonic flow problems about three-dimensional aircraft configurations obviates surface-conforming grid generation through an embedding of surface-geometry paneling in the grid. Accurate resolution of flow close to the boundary, and in regions with strong velocity gradients, is achieved via hierarchical local refinement which subdivides a given grid cell into eight cells. Fast and reliable convergence is obtained by combining several preconditioners and damping strategies. Methods are suggested for preclusion of global convergence problems.

Melvin, Robin G.↗

Modeling the growth and interaction of fractures

The research objectives are to develop accurate, efficient numerical tool for fracture mechanics analysis with the capabilities of the method including the modeling of multiple site damage and the simulation of crack propagation. The fracture is modeled using a distribution of edge dislocations. Fundamental solutions for dislocations in an infinite medium, in the neighborhood of a circular inhomogeneity, and near a bi-material interface are incorporated into the procedure to allow exceptionally accurate modeling of fracture geometries involving these types of inhomogeneities. To model arbitrary (finite) domains under general boundary conditions, a combination of the dislocation methodology and boundary element techniques is used. The dislocation scheme is a natural means to model the crack(s), and the boundary element method is an effective way to model the region in which the crack is embedded. The hybrid scheme is relatively easy to use and is very accurate. The research accomplishments are presented.

Mear, Mark E.↗