Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Properties of aluminium nodules foamed with concentrated solar energy

Commercial aluminium foam filled structures and sandwich panels are available for structural applications. As alternative to these materials, small granular foamed pieces are proposed to fill structures as well as sandwich panels. On the present work, foam precursors are obtained by Powder Metallurgy (PM) route, using natural calcium carbonate as foaming agent instead of titanium hydride. Extruded precursor bars were cut into small pieces (around 4.5 mm long and 5mm in diameter). Foaming treatment was carried out on two different ways: electrical preheated furnace and by solar furnace. Foamed nodules presented a low cell size, density e.g. 0.67 g/cm3 to 0.88 g/cm3 and a height/diameter ratio between 0.72 and 0.84 as a function of precursor size. These properties depend on the foaming particle size, foaming cycle and precursor dimensions. Carbonate precursors are easily foamed by concentrated solar energy, due to the lower risk of cell collapse than with hydride precursors, resulting from cell stabilization by oxide skin formation into cells and a low degree of foamed nodules bonding.

Bruise Development and Fruit Response of Pear (cv.'Blanquilla') under Impact Conditions

Pear fruits cv. 'Blanquilla', at various ripening stages, were studied under impact conditions. A 50-6-g spherical steel indentator, with a radius of curvature of 0-94 cm, was dropped on to the fruit from three heights: 4, 6 and 10 cm (0-0199, 0-0299 and 0-0499 J). The variables measured were analyzed. All variables were observed to be related to the impact energy except impact duration, which was related to the fruit firmness. Bruising correlated with impact energy when considering different heights, but not with any specific variable when studying the impact phenomenon at individual heights; however, there was a clear correlation between impact bruising and firmness. Three bruise shapes were observed, corresponding to preclimacteric, climacteric and postclimacteric fruits; a theory for this response is offered. According to the results, the impact response in postclimacteric pear fruits (with firmness values of less than 25 N, and a maturity index above 55) may be explained by the role played by the skin rather than by the pulp.

Impact parameters related to bruising in selected fruits.

Impact testing with an instrumented free-fallingmass (50.4 g) device was applied to three varities of pears and two varieties of apples, forincreasing ripeness stages and impact energy (2 to 20 cm drops). Impact parameters were studied in relation to bruise and to ripeness, establishing relations between them and with the different characteristics of the fruits.

Elastic (stress-strain) halo associated to ion-induced nano-tracks in lithium niobate: role of crystal anisotropy

The elastic strain/stress fields (halo) around a compressed amorphous nano-track (core) caused by a single high-energy ion impact on LiNbO3 are calculated. A method is developed to approximately account for the effects of crystal anisotropy of LiNbO3 (symmetry 3m) on the stress fields for tracks oriented along the crystal axes (X, Y or Z). It only considers the zero-order (axial) harmonic contribution to the displacement field in the perpendicular plane and uses effective Poisson moduli for each particular orientation. The anisotropy is relatively small; however, it accounts for some differential features obtained for irradiations along the crystallographic axes X, Y and Z. In particular, the irradiation-induced disorder (including halo) and the associated surface swelling appear to be higher for irradiations along the X- or Y-axis in comparison with those along the Z-axis. Other irradiation effects can be explained by the model, e.g. fracture patterns or the morphology of pores after chemical etching of tracks. Moreover, it offers interesting predictions on the effect of irradiation on lattice parameters

Flow and fracture behaviour of high performance alloys

Based on our needs, that is to say, through precise simulation of the impact phenomena that may occur inside a jet engine turbine with an explicit non-linear finite element code, four new material models are postulated. Each one of is calibrated for four high-performance alloys that can be encountered in a modern jet engine. A new uncoupled material model for high strain and ballistic is proposed. Based on a Johnson-Cook type model, the proposed formulation introduces the effect of the third deviatoric invariant by means of three different Lode angle dependent functions. The Lode dependent functions are added to both plasticity and failure models. The postulated model is calibrated for a 6061-T651 aluminium alloy with data taken from the literature. The fracture pattern predictability of the JCX material model is shown performing numerical simulations of various quasi-static and dynamic tests. As an extension of the above-mentioned model, a modification in the thermal softening behaviour due to phase transformation temperatures is developed (JCXt). Additionally, a Lode angle dependent flow stress is defined. Analysing the phase diagram and high temperature tests performed, phase transformation temperatures of the FV535 stainless steel are determined. The postulated material model constants for the FV535 stainless steel are calibrated. A coupled elastoplastic-damage material model for high strain and ballistic applications is presented (JCXd). A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson-Cook failure criterion. The weakening in the elastic law and in the Johnson-Cook type constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. A transversely isotropic material model for directionally solidified alloys is presented. The proposed yield function is based a single linear transformation of the stress tensor. The linear operator weighs the degree of anisotropy of the yield function. The elastic behaviour, as well as the hardening, are considered isotropic. To model the hardening, a Johnson-Cook type relation is adopted. A material vector is included in the model implementation. The failure is modelled with the Cockroft-Latham failure criterion. The material vector allows orienting the reference orientation in any other that the user may need. The model is calibrated for the MAR-M 247 directionally solidified nickel-base superalloy.

Desarrollo, análisis y caracterización de procesos de soldeo térmico de espumas de aluminio

Uno de los retos actuales aún pendiente de lograr trabajando con espumas de aluminio, es el desarrollo de métodos de unión fácilmente reproducibles a nivel industrial que permitan la unión de espumas de aluminio entre sí o con otros componentes tipo pletinas, para así poder fabricar piezas de mayor tamaño o con formas complejas, a la vez que se conserven las propiedades y características principales de las espumas de aluminio, tanto en la zona principal de unión o cordón, como en la interfase y zona afectada térmicamente, que se encuentran anexa. Los actuales procesos de unión más utilizados con espumas de aluminio, se basan principalmente en adhesivos y uniones mecánicas. Estas soluciones a priori válidas, añaden problemas técnicos a determinadas aplicaciones de las espumas que frenan la completa integración de estos materiales en un entorno de fabricación flexible y global. Por esta razón, los actuales procesos de producción de las espumas de aluminio se restringen a determinadas ofertas hechas a la medida del cliente, no pudiendo atender por falta de soluciones, a una gran parte del potencial mercado de estos materiales. En el presente trabajo de investigación se han desarrollado y caracterizado diferentes métodos de unión de espumas de aluminio, en configuración a tope y de espumas de aluminio con pletinas en configuración a solape, basados en procesos por soldeo térmico. One of the current challenges even pending of being achieved working with aluminium foams, is the development of easily reproducible methods at industrial level that allow the joint of aluminium foams between them or with other elements as for example aluminium plates for making bigger pieces or with more complex forms, remaining simultaneously in the weld bead the properties and main characteristics of aluminium foam, so much in the joint area or interface, since in the affected closer thermal zone. Currently, the most used joint processes for applying to aluminium foams are based mainly on adhesives and mechanical joins. These solutions initially valid, add technical problems to certain aluminium foams applications, which stop the complete integration of these materials in a more flexible and global manufacture environment. For this reason, current aluminium foam manufacturing processes are restricted to certain offers done to a specific customer requirement, not being able to attend for lack of available solutions, to a great potential market of these materials. In the present work, different joint methods between aluminium foams and between aluminium foams and plates for butt and lap configurations have been developed and characterized based on thermal welding processes.

Estudio del comportamiento mecánico de las espumas pulvimetalúrgicas de aluminio

Con este trabajo se pretende determinar la relación entre las características físicas y mecánicas y la estructura para espumas de aluminio de Al12Si y AA6061 obtenidas por pulvimetalurgia utilizando probetas prismáticas de dimensiones diecisiete por diecisiete por sesenta milímetros. De su estudio mecánico y de análisis de imagen se concluye que las probetas cuyas propiedades físicas y mecánicas están moderadamente por encima de la media poseen mayor número de poros medianos y paredes de poro más gruesas. Por el contrario, las propiedades resultan inferiores cuando se presentan estructuras con un mayor número de poros medianos. Aquellas espumas con estructuras obtenidas por una espumación incompleta presentan una menor porosidad y por ello mayores densidades. En aquellos casos donde la estructura presenta una elevada presencia de poros grandes, sus propiedades mecánicas disminuyen. ABSTRACT With this work we are trying to determine the relation between physical and mechanical characteristics and its structure, for Al12Si and AA6061 aluminium foams, obtained by podwer metallurgy. Aluminium foam samples with dimensions of seventeen per seventeen per sixty millimeters were used. After its mechanical and image analysis study, we conclude that samples whose physical and mechanical properties are moderately over the average, they have a major proportion of medium pores and thicker pore walls. Otherwise, properties result to be inferior when a major number of medium pores structures are presented. Those foam structures obtained with an incomplete foaming process show a lower porosity, and so higher densities. Also, properties decrease in those cases in which the structure presents a high presence of big pores.

Efficient management of available technologies. Aplication to mining operations for industry supplies

Nowadays, processing Industry Sector is going through a series of changes, including right management and reduction of environmental affections. Any productive process which looks for sustainable management is incomplete if Cycle of Life of mineral resources sustainability is not taken into account. Raw materials for manufacturing are provided by mineral resources extraction processes, such as copper, aluminum, iron, gold, silver, silicon, titanium? Those elements are necessary for Mankind development and are obtained from the Earth through mineral extractive processes. Mineral extraction processes are operations which must take care about the environmental consequences. Extraction of huge volumes of rock for their transformation into raw materials for industry must be optimized to reduce ecological cost of the final product as l was possible. Reducing the ecological balance on a global scale has no sense to design an efficient manufacturing in secondary industry (transformation), if in first steps of the supply chain (extraction) impact exceeds the savings of resources in successive phases. Mining operations size suggests that it is an environmental aggressive activity, but precisely because of its great impact must be the first element to be considered. That idea implies that a new concept born: Reduce economical and environmental cost This work aims to make a reflection on the parameters that can be modified to reduce the energy cost of the process without an increasing in operational costs and always ensuring the same production capacity. That means minimize economic and environmental cost at same time. An efficient design of mining operation which has taken into account that idea does not implies an increasing of the operating cost. To get this objective is necessary to think in global operation view to make that all departments involved have common guidelines which make you think in the optimization of global energy costs. Sometimes a single operational cost must be increased to reduce global cost. This work makes a review through different design parameters of surface mining setting some key performance indicators (KPIs) which are estimated from an efficient point of view. Those KPIs can be included by HQE Policies as global indicators. The new concept developed is that a new criteria has to be applied in company policies: improve management, improving OPERATIONAL efficiency. That means, that is better to use current resources properly (machinery, equipment,?) than to replace them with new things but not used correctly. As a conclusion, through an efficient management of current technologies in each extractive operation an important reduction of the energy can be achieved looking at downstream in the process. That implies a lower energetic cost in the whole cycle of life in manufactured product.

On super free fall.

Villermaux & Pomeau (J. Fluid Mech., vol. 642, 2010, p. 147) analysed the motion of the interface of an inviscid liquid column released from rest in a vertical tube whose area expands gradually downwards, with application to an inverted conical container for which experimental measurements were carried out. An error in the analysis is found and corrected in the present investigation, which provides the new governing equation for the super-accelerated interface motion down gradually varying tubes in general, and integrated results for interface trajectories, velocities and accelerations down a conical tube in particular. Interestingly, the error does not affect any of the conclusions given in the 2010 paper. Further new results are reported here such as the equation governing the centre of mass and proof that the end point acceleration is exactly that of gravity

Sensibilidad a las entallas del acero inoxidable dúplex fuertemente trefilado

En el presente trabajo se estudia la sensibilidad a las entallas suaves de alambres de acero inoxidable dúplex fuertemente trefilado. Las entallas consideradas son reducciones de la sección transversal del alambre no simétricas respecto al eje de revolución. Tras constatar experimentalmente que los alambres con este tipo de daño fallan por agotamiento plástico, se ha determinado numéricamente la carga de agotamiento plástico en función de la profundidad de entalla empleando un mode-lo computacional de elementos finitos. Los resultados numéricos indican que la mayor deformabilidad del alambre debida a la entalla actúa en favor de su tolerancia al daño y permite que ésta alcance el límite superior dado por la carga de agotamiento a tracción simple del ligamento resistente.This research deals with the sensitivity to blunt notches of highly cold-drawn wires made of dúplex stainless steel. The analyzed notches are actually reductions of the wire cross section, asymmetrically mechanized with respect to the longitudinal wire axis. Once experimentally verified that the notched wires fail by plástic collapse, the failure load was found as a function of notch depth by means of a finite element model. The numerical results show that the higher compliance of the wires provided by the notch increases their damage tolerance up to the upper bound given by the tensile plástic failure load of the notch ligament.

Effects of traffic loads on reinforced concrete railroad culverts

In the context of the present conference paper culverts are defined as an opening or conduit passing through an embankment usually for the purpose of conveying water or providing safe pedestrian and animal crossings under rail infrastructure. The clear opening of culverts may reach values of up to 12m however, values around 3m are encountered much more frequently. Depending on the topography, the number of culverts is about 10 times that of bridges. In spite of this, their dynamic behavior has received far less attention than that of bridges. The fundamental frequency of culverts is considerably higher than that of bridges even in the case of short span bridges. As the operational speed of modern high-speed passenger rail systems rises, higher frequencies are excited and thus more energy is encountered in frequency bands where the fundamental frequency of box culverts is located. Many research efforts have been spent on the subject of ballast instability due to bridge resonance, since it was first observed when high-speed trains were introduced to the Paris/Lyon rail line. To prevent this phenomenon from occurring, design codes establish a limit value for the vertical deck acceleration. Obviously one needs some sort of numerical model in order to estimate this acceleration level and at that point things get quite complicated. Not only acceleration but also displacement values are of interest e.g. to estimate the impact factor. According to design manuals the structural design should consider the depth of cover, trench width and condition, bedding type, backfill material, and compaction. The same applies to the numerical model however, the question is: What type of model is appropriate for this job? A 3D model including the embankment and an important part of the soil underneath the culvert is computationally very expensive and hard to justify taking into account the associated costs. Consequently, there is a clear need for simplified models and design rules in order to achieve reasonable costs. This paper will describe the results obtained from a 2D finite element model which has been calibrated by means of a 3D model and experimental data obtained at culverts that belong to the high-speed railway line that links the two towns of Segovia and Valladolid in Spain

Repercusión medioambiental del uso de la cerámica estructural en España. Energía embebida y huella de carbono

La producción y el transporte a obra de los productos cerámicos de carácter estructural suponen un importante consumo energético, que conlleva la emisión de gases de efecto invernadero a la atmósfera. El objetivo de la presente Tesis es demostrar la existencia de importantes diferencias en el valor del impacto ambiental asociado a los productos de cerámica estructural fabricados en España, y que estas diferencias podrían quedar cuantificadas y reflejadas mediante un análisis de Huella de Carbono y de la Energía Embebida. Se parte de la inexistencia en España, de base de datos contrastada y consensuada, que establezca las cargas medioambientales en función del tipo de producto cerámico a utilizar. Se realiza en la primera parte del estudio una revisión del estado actual de la Huella de Carbono y la Energía Embebida en el campo de los materiales de construcción, y más concretamente en el sector de la cerámica estructural, que sirve para acotar los límites del estudio y justificar el objeto de la Tesis. La investigación se acota a las etapas de producción y transporte a obra de los productos (estudio cuna a puerta con opciones), al considerar que son éstas, a priori, las que tienen una mayor incidencia en el comportamiento ambiental del producto. Siguiendo los pasos definidos en la normativa aplicable (definición del mapa de procesos – límites y alcance – inventario – cálculo y evaluación), se establece un método específico de identificación y cuantificación de las variables que determinan la Huella de Carbono y Energía Embebida de los productos cerámicos, en función de la tipología de producto. La información necesaria (inventario) se obtiene principalmente con recogida de datos “in situ” de fábricas de productos cerámicos, lo que garantiza que la información tratada en este estudio es de primer nivel. La información se complementa/contrasta con fuentes bibliográficas. Se determinan 6 variables con influencia global en el impacto ambiental, 44 variables principales y 39 secundarias, estableciendo las fórmulas de cálculo a partir de dichas variables. Los resultados de cálculo y evaluación determinan que, para unas mismas condiciones de fabricación, las diferencias entre productos cerámicos llegan hasta un 27% para la Huella de Carbono y un 35% para Energía Embebida. La relevancia que alcanza el impacto asociado al transporte del producto a obra puede llegar hasta un 40% del total. El método de cálculo y las fórmulas desarrolladas se integran en una hoja de cálculo, para el cálculo de Huella de Carbono y Energía Embebida de los productos cerámicos, que permite, a su vez, conocer la repercusión medioambiental que tiene la introducción de modificaciones o innovaciones en el proceso de producción o transporte a obra. Así mismo, el trabajo desarrollado ha servido para poner en relieve una serie de problemas y falta de información en el campo de la cerámica estructural y el medioambiente que pueden ser objeto de futuras líneas de investigación, tanto para el sector de la edificación como para la comunidad científica, pudiendo implementar la metodología desarrollada en otras investigaciones. Se considera que la investigación realizada y sus resultados suponen una aportación importante para conocer y reducir el impacto ambiental de los edificios, desde la perspectiva del ciclo de vida y considerando que el impacto ambiental de un edificio comienza desde el momento en que se extraen las materias primas para la fabricación de los materiales con los que se construyen los edificios. ABSTRACT The production and transport of structural ceramic products involves an important energy consumption, which leads to the emission of greenhouse gases into the atmosphere. The objective of the research is to demonstrate the existence of significant differences in the value of the environmental impact of structural ceramic products manufactured in Spain, and these differences could be quantified by the Carbon Footprint and Embodied Energy. It starts from the absence in Spain, of contrasted and agreed databases that establish the environmental loads depending on the type of ceramic product. In the first part of the study reviews the current state of the Carbon Footprint and Embedded Energy in the field of building materials, and more specifically in the field of structural ceramics, which serves to limit the scope of the study and justify the purpose of this Thesis. The Research is bounded to production and transportation stages of (cradle to gate with options), considering they are the stages that have a greater impact on the environmental performance of the product. Following the steps defined in applicable rules (definition of process map - boundaries and scope – inventory analysis- calculation and impact assessment), it sets a specific method for the identification and quantification of the variables that determine the Carbon Footprint and Embedded Energy of structural ceramic products, depending on the type of product. The information (inventory) is given mainly with a data collection in ceramic factories (and in a consultation with the manufactures of the products), ensuring that the information handled in this Thesis is a first rate data. It is established 6 variables with a global influence in the environmental impact, 44 primary and 39 secondary variables, establishing calculation formula from these variables. The results of calculation and assessment determined that, for same manufacturing conditions, the differences between ceramic products reach 27% for Carbon Footprint and 35% for Embodied Energy. The relevance that reaches the impact of transport can reach 40% of the total. The method of calculation and formulas developed are integrated into a simple calculation tool, excel base, to calculate the Carbon Footprint and Embodied Energy of structural ceramic products, which allows, know the environmental impact of changes or innovations in the production process or transport to work. The work also has served to find a problems and gaps in the field of structural ceramics and the environment that may well be the subject of future research, both for the building sector to the scientific community, implementing the methodology developed in other research. It is considered that the research and its results represent an important contribution to understand and reduce the environmental impact of buildings from the perspective of the life cycle, considering that the environmental impact of a building starts from the time that the raw materials are extracted for the manufacture of building materials.

An experimental and numerical study of ductile failure under quasi-static and impact loadings of Inconel 718 nickel-base superalloy

A numerical and experimental study of ballistic impacts at various temperatures on precipitation hardened Inconel 718 nickel-base superalloy plates has been performed. A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion has been implemented in LS-DYNA non-linear finite element code to model the mechanical behaviour of such an alloy. The ballistic impact tests have been carried out at three temperatures: room temperature (25 °C), 400 °C and 700 °C. The numerical study showed that the mesh size is crucial to predict correctly the shear bands detected in the tested plates. Moreover, the mesh size convergence has been achieved for element sizes on the same order that the shear bands. The residual velocity as well as the ballistic limit prediction has been considered excellent for high temperature ballistic tests. Nevertheless, the model has been less accurate for the numerical simulations performed at room temperature, being though in reasonable agreement with the experimental data. Additionally, the influence that the Lode angle had on quasi-static failure patterns such as cup-cone and slanted failure has been studied numerically. The study has revealed that the combined action of weakened constitutive equations and Lode angle dependent failure criterion has been necessary to predict the previously-mentioned failure patterns

Low Work-Function Thermionic Emission and Orbital-Motion-Limited Ion Collection at Bare-Tether Cathodic Contact

Una amarra electrodinámica (electrodynamic tether) opera sobre principios electromagnéticos intercambiando momento con la magnetosfera planetaria e interactuando con su ionosfera. Es un subsistema pasivo fiable para desorbitar etapas de cohetes agotadas y satélites al final de su misión, mitigando el crecimiento de la basura espacial. Una amarra sin aislamiento captura electrones del plasma ambiente a lo largo de su segmento polarizado positivamente, el cual puede alcanzar varios kilómetros de longitud, mientras que emite electrones de vuelta al plasma mediante un contactor de plasma activo de baja impedancia en su extremo catódico, tal como un cátodo hueco (hollow cathode). En ausencia de un contactor catódico activo, la corriente que circula por una amarra desnuda en órbita es nula en ambos extremos de la amarra y se dice que ésta está flotando eléctricamente. Para emisión termoiónica despreciable y captura de corriente en condiciones limitadas por movimiento orbital (orbital-motion-limited, OML), el cociente entre las longitudes de los segmentos anódico y catódico es muy pequeño debido a la disparidad de masas entre iones y electrones. Tal modo de operación resulta en una corriente media y fuerza de Lorentz bajas en la amarra, la cual es poco eficiente como dispositivo para desorbitar. El electride C12A7 : e−, que podría presentar una función de trabajo (work function) tan baja como W = 0.6 eV y un comportamiento estable a temperaturas relativamente altas, ha sido propuesto como recubrimiento para amarras desnudas. La emisión termoiónica a lo largo de un segmento así recubierto y bajo el calentamiento de la operación espacial, puede ser más eficiente que la captura iónica. En el modo más simple de fuerza de frenado, podría eliminar la necesidad de un contactor catódico activo y su correspondientes requisitos de alimentación de gas y subsistema de potencia, lo que resultaría en un sistema real de amarra “sin combustible”. Con este recubrimiento de bajo W, cada segmento elemental del segmento catódico de una amarra desnuda de kilómetros de longitud emitiría corriente como si fuese parte de una sonda cilíndrica, caliente y uniformemente polarizada al potencial local de la amarra. La operación es similar a la de una sonda de Langmuir 2D tanto en los segmentos catódico como anódico. Sin embargo, en presencia de emisión, los electrones emitidos resultan en carga espacial (space charge) negativa, la cual reduce el campo eléctrico que los acelera hacia fuera, o incluso puede desacelerarlos y hacerlos volver a la sonda. Se forma una doble vainas (double sheath) estable con electrones emitidos desde la sonda e iones provenientes del plasma ambiente. La densidad de corriente termoiónica, variando a lo largo del segmento catódico, podría seguir dos leyes distintas bajo diferentes condiciones: (i) la ley de corriente limitada por la carga espacial (space-charge-limited, SCL) o (ii) la ley de Richardson-Dushman (RDS). Se presenta un estudio preliminar sobre la corriente SCL frente a una sonda emisora usando la teoría de vainas (sheath) formada por la captura iónica en condiciones OML, y la corriente electrónica SCL entre los electrodos cilíndricos según Langmuir. El modelo, que incluye efectos óhmicos y el efecto de transición de emisión SCL a emisión RDS, proporciona los perfiles de corriente y potencial a lo largo de la longitud completa de la amarra. El análisis muestra que en el modo más simple de fuerza de frenado, bajo condiciones orbitales y de amarras típicas, la emisión termoiónica proporciona un contacto catódico eficiente y resulta en una sección catódica pequeña. En el análisis anterior, tanto la transición de emisión SCL a RD como la propia ley de emisión SCL consiste en un modelo muy simplificado. Por ello, a continuación se ha estudiado con detalle la solución de vaina estacionaria de una sonda con emisión termoiónica polarizada negativamente respecto a un plasma isotrópico, no colisional y sin campo magnético. La existencia de posibles partículas atrapadas ha sido ignorada y el estudio incluye tanto un estudio semi-analítico mediante técnica asintóticas como soluciones numéricas completas del problema. Bajo las tres condiciones (i) alto potencial, (ii) R = Rmax para la validez de la captura iónica OML, y (iii) potencial monotónico, se desarrolla un análisis asintótico auto-consistente para la estructura de plasma compleja que contiene las tres especies de cargas (electrones e iones del plasma, electrones emitidos), y cuatro regiones espaciales distintas, utilizando teorías de movimiento orbital y modelos cinéticos de las especies. Aunque los electrones emitidos presentan carga espacial despreciable muy lejos de la sonda, su efecto no se puede despreciar en el análisis global de la estructura de la vaina y de dos capas finas entre la vaina y la región cuasi-neutra. El análisis proporciona las condiciones paramétricas para que la corriente sea SCL. También muestra que la emisión termoiónica aumenta el radio máximo de la sonda para operar dentro del régimen OML y que la emisión de electrones es mucho más eficiente que la captura iónica para el segmento catódico de la amarra. En el código numérico, los movimientos orbitales de las tres especies son modelados para potenciales tanto monotónico como no-monotónico, y sonda de radio R arbitrario (dentro o más allá del régimen de OML para la captura iónica). Aprovechando la existencia de dos invariante, el sistema de ecuaciones Poisson-Vlasov se escribe como una ecuación integro-diferencial, la cual se discretiza mediante un método de diferencias finitas. El sistema de ecuaciones algebraicas no lineal resultante se ha resuelto de con un método Newton-Raphson paralelizado. Los resultados, comparados satisfactoriamente con el análisis analítico, proporcionan la emisión de corriente y la estructura del plasma y del potencial electrostático. ABSTRACT An electrodynamic tether operates on electromagnetic principles and exchanges momentum through the planetary magnetosphere, by continuously interacting with the ionosphere. It is a reliable passive subsystem to deorbit spent rocket stages and satellites at its end of mission, mitigating the growth of orbital debris. A tether left bare of insulation collects electrons by its own uninsulated and positively biased segment with kilometer range, while electrons are emitted by a low-impedance active device at the cathodic end, such as a hollow cathode, to emit the full electron current. In the absence of an active cathodic device, the current flowing along an orbiting bare tether vanishes at both ends and the tether is said to be electrically floating. For negligible thermionic emission and orbital-motion-limited (OML) collection throughout the entire tether (electron/ion collection at anodic/cathodic segment, respectively), the anodic-to-cathodic length ratio is very small due to ions being much heavier, which results in low average current and Lorentz drag. The electride C12A7 : e−, which might present a possible work function as low as W = 0.6 eV and moderately high temperature stability, has been proposed as coating for floating bare tethers. Thermionic emission along a thus coated cathodic segment, under heating in space operation, can be more efficient than ion collection and, in the simplest drag mode, may eliminate the need for an active cathodic device and its corresponding gas-feed requirements and power subsystem, which would result in a truly “propellant-less” tether system. With this low-W coating, each elemental segment on the cathodic segment of a kilometers-long floating bare-tether would emit current as if it were part of a hot cylindrical probe uniformly polarized at the local tether bias, under 2D probe conditions that are also applied to the anodic-segment analysis. In the presence of emission, emitted electrons result in negative space charge, which decreases the electric field that accelerates them outwards, or even reverses it, decelerating electrons near the emitting probe. A double sheath would be established with electrons being emitted from the probe and ions coming from the ambient plasma. The thermionic current density, varying along the cathodic segment, might follow two distinct laws under different con ditions: i) space-charge-limited (SCL) emission or ii) full Richardson-Dushman (RDS) emission. A preliminary study on the SCL current in front of an emissive probe is presented using the orbital-motion-limited (OML) ion-collection sheath and Langmuir’s SCL electron current between cylindrical electrodes. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects considered and the transition from SCL to full RDS emission is included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission provides efficient cathodic contact and leads to a short cathodic section. In the previous analysis, both the transition between SCL and RDS emission and the current law for SCL condition have used a very simple model. To continue, considering an isotropic, unmagnetized, colissionless plasma and a stationary sheath, the probe-plasma contact is studied in detail for a negatively biased probe with thermionic emission. The possible trapped particles are ignored and this study includes both semianalytical solutions using asymptotic analysis and complete numerical solutions. Under conditions of i) high bias, ii) R = Rmax for ion OML collection validity, and iii) monotonic potential, a self-consistent asymptotic analysis is carried out for the complex plasma structure involving all three charge species (plasma electrons and ions, and emitted electrons) and four distinct spatial regions using orbital motion theories and kinetic modeling of the species. Although emitted electrons present negligible space charge far away from the probe, their effect cannot be neglected in the global analysis for the sheath structure and two thin layers in between the sheath and the quasineutral region. The parametric conditions for the current to be space-chargelimited are obtained. It is found that thermionic emission increases the range of probe radius for OML validity and is greatly more effective than ion collection for cathodic contact of tethers. In the numerical code, the orbital motions of all three species are modeled for both monotonic and non-monotonic potential, and for any probe radius R (within or beyond OML regime for ion collection). Taking advantage of two constants of motion (energy and angular momentum), the Poisson-Vlasov equation is described by an integro differential equation, which is discretized using finite difference method. The non-linear algebraic equations are solved using a parallel implementation of the Newton-Raphson method. The results, which show good agreement with the analytical results, provide the results for thermionic current, the sheath structure, and the electrostatic potential.