Multiscale modeling of the plastic behaviour in single crystal tungsten: from atomistic to crystal plasticity simulations

En una planta de fusión, los materiales en contacto con el plasma así como los materiales de primera pared experimentan condiciones particularmente hostiles al estar expuestos a altos flujos de partículas, neutrones y grandes cargas térmicas. Como consecuencia de estas diferentes y complejas condiciones de trabajo, el estudio, desarrollo y diseño de estos materiales es uno de los más importantes retos que ha surgido en los últimos años para la comunidad científica en el campo de los materiales y la energía. Debido a su baja tasa de erosión, alta resistencia al sputtering, alta conductividad térmica, muy alto punto de fusión y baja retención de tritio, el tungsteno (wolframio) es un importante candidato como material de primera pared y como posible material estructural avanzado en fusión por confinamiento magnético e inercial. Sin embargo, el tiempo de vida del tungsteno viene controlado por diversos factores como son su respuesta termo-mecánica en la superficie, la posibilidad de fusión y el fallo por acumulación de helio. Es por ello que el tiempo de vida limitado por la respuesta mecánica del tungsteno (W), y en particular su fragilidad, sean dos importantes aspectos que tienes que ser investigados. El comportamiento plástico en materiales refractarios con estructura cristalina cúbica centrada en las caras (bcc) como el tungsteno está gobernado por las dislocaciones de tipo tornillo a escala atómica y por conjuntos e interacciones de dislocaciones a escalas más grandes. El modelado de este complejo comportamiento requiere la aplicación de métodos capaces de resolver de forma rigurosa cada una de las escalas. El trabajo que se presenta en esta tesis propone un modelado multiescala que es capaz de dar respuestas ingenieriles a las solicitudes técnicas del tungsteno, y que a su vez está apoyado por la rigurosa física subyacente a extensas simulaciones atomísticas. En primer lugar, las propiedades estáticas y dinámicas de las dislocaciones de tipo tornillo en cinco potenciales interatómicos de tungsteno son comparadas, determinando cuáles de ellos garantizan una mayor fidelidad física y eficiencia computacional. Las grandes tasas de deformación asociadas a las técnicas de dinámica molecular hacen que las funciones de movilidad de las dislocaciones obtenidas no puedan ser utilizadas en los siguientes pasos del modelado multiescala. En este trabajo, proponemos dos métodos alternativos para obtener las funciones de movilidad de las dislocaciones: un modelo Monte Cario cinético y expresiones analíticas. El conjunto de parámetros necesarios para formular el modelo de Monte Cario cinético y la ley de movilidad analítica son calculados atomísticamente. Estos parámetros incluyen, pero no se limitan a: la determinación de las entalpias y energías de formación de las parejas de escalones que forman las dislocaciones, la parametrización de los efectos de no Schmid característicos en materiales bcc,etc. Conociendo la ley de movilidad de las dislocaciones en función del esfuerzo aplicado y la temperatura, se introduce esta relación como ecuación de flujo dentro de un modelo de plasticidad cristalina. La predicción del modelo sobre la dependencia del límite de fluencia con la temperatura es validada experimentalmente con ensayos uniaxiales en tungsteno monocristalino. A continuación, se calcula el límite de fluencia al aplicar ensayos uniaxiales de tensión para un conjunto de orientaciones cristalográticas dentro del triángulo estándar variando la tasa de deformación y la temperatura de los ensayos. Finalmente, y con el objetivo de ser capaces de predecir una respuesta más dúctil del tungsteno para una variedad de estados de carga, se realizan ensayos biaxiales de tensión sobre algunas de las orientaciones cristalográficas ya estudiadas en función de la temperatura.-------------------------------------------------------------------------ABSTRACT ----------------------------------------------------------Tungsten and tungsten alloys are being considered as leading candidates for structural and functional materials in future fusion energy devices. The most attractive properties of tungsten for the design of magnetic and inertial fusion energy reactors are its high melting point, high thermal conductivity, low sputtering yield and low longterm disposal radioactive footprint. However, tungsten also presents a very low fracture toughness, mostly associated with inter-granular failure and bulk plasticity, that limits its applications. As a result of these various and complex conditions of work, the study, development and design of these materials is one of the most important challenges that have emerged in recent years to the scientific community in the field of materials for energy applications. The plastic behavior of body-centered cubic (bcc) refractory metals like tungsten is governed by the kink-pair mediated thermally activated motion of h¿ (\1 11)i screw dislocations on the atomistic scale and by ensembles and interactions of dislocations at larger scales. Modeling this complex behavior requires the application of methods capable of resolving rigorously each relevant scale. The work presented in this thesis proposes a multiscale model approach that gives engineering-level responses to the technical specifications required for the use of tungsten in fusion energy reactors, and it is also supported by the rigorous underlying physics of extensive atomistic simulations. First, the static and dynamic properties of screw dislocations in five interatomic potentials for tungsten are compared, determining which of these ensure greater physical fidelity and computational efficiency. The large strain rates associated with molecular dynamics techniques make the dislocation mobility functions obtained not suitable to be used in the next steps of the multiscale model. Therefore, it is necessary to employ mobility laws obtained from a different method. In this work, we suggest two alternative methods to get the dislocation mobility functions: a kinetic Monte Carlo model and analytical expressions. The set of parameters needed to formulate the kinetic Monte Carlo model and the analytical mobility law are calculated atomistically. These parameters include, but are not limited to: enthalpy and energy barriers of kink-pairs as a function of the stress, width of the kink-pairs, non-Schmid effects ( both twinning-antitwinning asymmetry and non-glide stresses), etc. The function relating dislocation velocity with applied stress and temperature is used as the main source of constitutive information into a dislocation-based crystal plasticity framework. We validate the dependence of the yield strength with the temperature predicted by the model against existing experimental data of tensile tests in singlecrystal tungsten, with excellent agreement between the simulations and the measured data. We then extend the model to a number of crystallographic orientations uniformly distributed in the standard triangle and study the effects of temperature and strain rate. Finally, we perform biaxial tensile tests and provide the yield surface as a function of the temperature for some of the crystallographic orientations explored in the uniaxial tensile tests.

The folded plate model in structural analysis. Elastic, plastic and dynamic formulations for nonprismatic structures

A specific numerical procedure for the analysis of arbitrary nonprismatic folded plate structures is presented. An elastic model is studied and compared with a harmonic solution for a prismatic structure. An extension to the plastic analysis is developed, and the influence of the structural geometry and loading pattern is analyzed. Nonprismatic practical cases, with arbitrary geometry and loading are shown, as well in the elastic range as in the plastic one. Finally, a dynamic formulation is outlined

Effect of misorientation on the compression of highly anisotropic single-crystal micropillars

The effect of crystal misorientation, geometrical tilt, and contact misalignment on the compression of highly anisotropic single crystal micropillars was assessed by means of crystal plasticity finite element simulations. The investigation was focused in single crystals with the NaCl structure, like MgO or LiF, which present a marked plastic anisotropy as a result of the large difference in the critical resolved shear stress between the “soft” {110}〈110〉 and the “hard” {100}〈110〉 active slip systems. It was found that contact misalignment led to a large reduction in the initial stiffness of the micropillar in crystals oriented in the soft and hard direction. The crystallographic tilt did not modify, however, the initial crystal stiffness. From the viewpoint of the plastic response, none of the effects analyzed led to significant differences in the flow stress when the single crystals were oriented along the “soft” [100] direction. Large differences were found, however, if the single crystal was oriented in the “hard” [111] direction as a result of the activation of the soft slip system. Numerical simulations were in very good agreement with experimental literature data.

Effect of the temperature, strain rate and microstructure on flow and fracture characteristics of Ti-45Al-2Nb-2Mn+0.8vol.% TiB2 XD alloy

A series of quasi-static and dynamic tensile tests at varying temperatures were carried out to determine the mechanical behaviour of Ti-45Al-2Nb-2Mn+0.8vol.% TiB2 XD as-HIPed alloy. The temperature for the tests ranged from room temperature to 850  ∘C. The effect of the temperature on the ultimate tensile strength, as expected, was almost negligible within the selected temperature range. Nevertheless, the plastic flow suffered some softening because of the temperature. This alloy presents a relatively low ductility; thus, a low tensile strain to failure. The dynamic tests were performed in a Split Hopkinson Tension Bar, showing an increase of the ultimate tensile strength due to the strain rate hardening effect. Johnson-Cook constitutive relation was used to model the plastic flow. A post-testing microstructural of the specimens revealed an inhomogeneous structure, consisting of lamellar α2 + γ structure and γ phase equiaxed grains in the centre, and a fully lamellar structure on the rest. The assessment of the duplex-fully lamellar area ratio showed a clear relationship between the microstructure and the fracture behaviour.

Monitoring leafy vegetables through packaging films with

Fresh-cut or minimally processed fruit and vegetables have been physically modified from its original form (by peeling, trimming, washing and cutting) to obtain a 100% edible product that is subsequently packaged (usually under modified atmosphere packaging –MAP) and kept in refrigerated storage. In fresh-cut products, physiological activity and microbiological spoilage, determine their deterioration and shelf-life. The major preservation techniques applied to delay spoilage are chilling storage and MAP, combined with chemical treatments antimicrobial solutions antibrowning, acidulants, antioxidants, etc.). The industry looks for safer alternatives. Consequently, the sector is asking for innovative, fast, cheap and objective techniques to evaluate the overall quality and safety of fresh-cut products in order to obtain decision tools for implementing new packaging materials and procedures. In recent years, hyperspectral imaging technique has been regarded as a tool for analyses conducted for quality evaluation of food products in research, control and industries. The hyperspectral imaging system allows integrating spectroscopic and imaging techniques to enable direct identification of different components or quality characteristics and their spatial distribution in the tested sample. The objective of this work is to develop hyperspectral image processing methods for the supervision through plastic films of changes related to quality deterioration in packed readyto-use leafy vegetables during shelf life. The evolutions of ready-to-use spinach and watercress samples covered with three different common transparent plastic films were studied. Samples were stored at 4 ºC during the monitoring period (until 21 days). More than 60 hyperspectral images (from 400 to 1000 nm) per species were analyzed using ad hoc routines and commercial toolboxes of MatLab®. Besides common spectral treatments for removing additive and multiplicative effects, additional correction, previously to any other correction, was performed in the images of leaves in order to avoid the modification in their spectra due to the presence of the plastic transparent film. Findings from this study suggest that the developed images analysis system is able to deal with the effects caused in the images by the presence of plastic films in the supervision of shelf-life in leafy vegetables, in which different stages of quality has been identified.

Resonancias de los paradigmas científicos en las arquitecturas de la Escuela de Madrid

Los años cincuenta y sesenta son los años de la incorporación definitiva de la arquitectura española al panorama internacional. Entre los arquitectos que protagonizan ese salto sin retorno, se encuentra el grupo de aquellos que unos años más tarde serán denominados por Juan Daniel Fullaondo como Escuela de Madrid. Carlos Flores, en su libro Arquitectura Española Contemporánea 1880-1950, se refiere a esos arquitectos como aquellos que se aplicaban a la difícil tarea de restablecer en España un tipo de arquitectura que conectaba con las teorías, soluciones y lenguajes establecidos por Europa durante las primeras décadas del siglo XX. Sigfried Giedion plantea en Espacio, Tiempo y Arquitectura el origen de una nueva tradición, surgida a partir de la revolución óptica de principios de siglo. Con tradición se refiere a una nueva cultura, que abarca la interrelación de las diferentes actividades del hombre: la similitud de los métodos que se usan en la arquitectura, la construcción, la pintura, el urbanismo o la ciencia. Esa novedad, fundamentada en su independencia y desvinculación con el periodo anterior, se inscribe dentro del esquema evolutivo que Thomas Kuhn plantea en su texto La Estructura de la Revoluciones Científicas, conforme a periodos no acumulativos. Kuhn habla del surgimiento de anomalías en cada periodo, origen de las crisis de pensamiento cuya explicación precisará un necesario cambio paradigmático. En la ciencia, en el campo de la óptica Thomas Young demuestra a principios del siglo XIX la naturaleza ondulatoria de la luz con su experimento de doble rendija; en el electromagnetismo se produce el salto conceptual que supone la postulación de la existencia del campo eléctrico por parte de Michael Faraday, y en termodinámica la consideración apuntada por Planck de que la radiación de la energía de produce de forma discreta, a través de cuantos. En las artes plásticas, paralelamente, Gleizes y Metzinger, en su recopilación de logros cubistas recogida en Sobre el Cubismo, hablan de la evolución sufrida durante el siglo XIX por la pintura: desde el idealismo de principios de siglo, para pasando por el realismo y la representación impresionista de la realidad, concluir prescindiendo de la perspectiva clásica. También la matemática, una vez desarrolladas por Gauss o Lobachevsky y Bolyai geometrías coherentes que incumplen el quinto postulado de Euclides, terminará dando validez a través de Riemann a los espacios ambiente en los que habitan dichas geometrías, desvinculando la relación directa entre espacio geométrico –el espacio ambiente al que da lugar un tipo de geometría- y el espacio físico. Capi Corrales refleja en su libro Contando el Espacio, cómo hasta la teoría de la relatividad y el cubismo, las geometrías no euclídeas no se hicieron notorias también fuera del campo de las matemáticas. El origen de la nueva tradición con la que Giedion se refiere a la nueva cultura de la modernidad coincide con los saltos paradigmáticos que suponen la teoría de la relatividad en las ciencias y el cubismo en las artes plásticas. Ambas se prolongan durante las primeras décadas hasta la teoría cuántica y la abstracción absoluta, barreras que los dos principales precursores de la relatividad y el cubismo, Einstein y Picasso, nunca llegan a franquear. En ese sentido Giedion habla también, además del origen, de su desarrollo, e incorpora las aportaciones periféricas en la arquitectura de Brasil, Japón o Finlandia, incluyendo por tanto la revisión orgánica propugnada por Zevi como parte de esa nueva tradición, quedando abierta a la incorporación tardía de nuevas aportaciones al desarrollo de esa cultura de la modernidad. Eliminado el concepto de la estética trascendental de Kant del tiempo como una referencia absoluta, y asumido el valor constante de la velocidad de la luz, para la teoría de la relatividad no existe una simultaneidad auténtica. Queda así fijada la velocidad de la luz como uno de los límites del universo, y la equivalencia entre masa y energía. En el cubismo la simultaneidad espacial viene motivada por la eliminación del punto de vista preferente, cuyo resultado es la multiplicidad descriptiva de la realidad, que se visualiza en la descomposición en planos, tanto del objeto como del espacio, y la consecuente continuidad entre fondo y figura que en arquitectura se refleja en la continuidad entre edificio y territorio. Sin la consideración de un punto de vista absoluto, no existe una forma auténtica. El cubismo, y su posterior desarrollo por las vanguardias plásticas, hacen uso de la geometría como mecanismo de recomposición de la figura y el espacio, adoptando mecanismos de penetración, superposición y transparencia. Gyorgy Kepes indica en El Lenguaje de la Visión que la descomposición cubista del objeto implica la sucesiva autonomía de los planos, hasta convertirse en elementos constituyentes. Algo que refleja las axonometrías arquitectónicas de Van Doesburg y que culmina con los espacios propuestos por Mies van der Rohe en sus primeros proyectos europeos. Estos mecanismos, encuentran eco en los primeros planteamientos de Javier Carvajal: en la ampliación del Panteón de españoles del cementerio de Campo Verano, un recinto virtual reconstruido mentalmente a partir del uso de tres únicos planos; o en el Pabellón de Nueva York, que organiza su planta baja desde el recorrido, introduciendo el parámetro temporal como una dimensión más. Al uso diferenciado del plano como elemento constituyente, Carvajal incorpora su plegado y su disposición conformando envolventes como mecanismo de cualificación espacial y formal, potenciando la prolongación entre arquitectura y territorio. Una continuidad que quedará culminada en las dos viviendas unifamiliares construidas en Somosaguas. La descomposición volumétrica conduce a unos niveles de abstracción que hace precisa la incorporación de elementos de la memoria -fuentes, patios, celosías…- a modo de red de señales, como las que Picasso y Braque introducen en sus cuadros para permitir su interpretación. Braque insiste en el interés por el espacio que rodea a los objetos. Una búsqueda de la tactilidad del espacio contraria a la perspectiva que aleja el objeto del observador, y que en los jardines de las viviendas de Somosaguas parece emanar de su propia materialidad. Un espacio táctil alejado del espacio geométrico y que Braque identifica con el espacio representativo en el que Poincaré, en La Ciencia y la Hipótesis, ubica nuestras sensaciones. Desdibujar los límites del objeto prolonga el espacio indefinidamente. Con el paso en el arte griego del mito al logos, se abre paso a la matemática como herramienta de comprensión de la naturaleza hasta el siglo XIX. Leon Lederman, en Simetría y la Belleza del Universo, apunta a que una de las mayores contribuciones de la teoría de Einstein es hacer cambiar el modo de pensar la naturaleza, orientándolo hacia la búsqueda de los principios de simetría que subyacen bajo las leyes físicas. Considerando que la simetría es la invariancia de un objeto o un sistema frente a una transformación y que las leyes físicas son las mismas en cualquier punto del espacio, el espacio de nuestro universo posee una simetría traslacional continua. En la ocupación del espacio de las primeras propuestas de Corrales y Molezún aparecen estructuras subyacentes que responden a enlosetados: paralelogramos sometidos a transformaciones continuas, que la naturaleza identifica tridimensionalmente con los grupos cristalográficos. Las plantas del museo de Arte Contemporáneo de la Castellana, la residencia de Miraflores, el pabellón de Bruselas o la torre Peugeot pertenecen a este grupo. La arquitectura como proceso de ocupación continua del territorio y de su trasposición al plano de cubierta, se materializa en líneas estructurales coincidentes con la estructura matemática de sus simetrías de traslación cuya posibilidad de prolongación infinita queda potenciada por el uso de la envolvente transparente. Junto a esta transparencia literal, inherente al material, Colin Rowe y Robert Slutzky nos alertan sobre otra transparencia inherente a la estructura: la transparencia fenomenal, ilustrada por los cuadros de Juan Gris, y cuya intuición aparece reflejada en la casa Huarte en Puerta de Hierro de Madrid. Corrales y Molezún insisten en una lectura de su volumetría alejada de la frontalidad, en la que los contornos de sus cubiertas inclinadas y las visuales tangenciales sugeridas por la organización de sus recorridos introducen una estructura diagonal que se superpone al entendimiento ortogonal de su planta, dibujando una intrincada red de líneas quebradas que permiten al espacio fluctuar entre las secuencia volumétrica propuesta. Los datos relativos al contenido energético de la luz y el concepto de átomo parten de la consideración de la emisión de energía en cuantos realizada por Planck, y concluyen con una circunstancia paradójica: la doble naturaleza de la luz -demostrada por la explicación de Einstein del efecto fotoeléctrico- y la doble naturaleza de la materia -asumida por Bohr y demostrada por el efecto Compton-. Schrödinger y Heisenberg formularán finalmente la ecuación universal del movimiento que rige en las ondas de materia, y cuya representación matemática es lo que se conoce como función de onda. El objeto es así identificado con su función de onda. Su ondulatoriedad expresará la probabilidad de encontrarse en un lugar determinado. Gyorgy Kepes subraya la necesidad de simplificar el lenguaje para pasar de la objetividad que aún permanece en la pintura cubista a la abstracción total del espacio. Y es así como los artistas plásticos reducen los objetos a simples formas geométricas, haciendo aflorar a la vez, las fuerzas plásticas que los tensionan o equilibran, en un proceso que acaba por eliminar cualquier atisbo de materia. Robert Rosenblum en La Pintura Moderna y la Tradición del Romanticismo Nórdico habla de cómo ese rechazo de la materia en favor de un vacío casi impalpable, campos luminosos de color denso que difunden un sereno resplandor y parecen engendrar las energías elementales de la luz natural, está directamente vinculado a la relación con la naturaleza que establece el romanticismo nórdico. La expresión de la energía de la naturaleza concentrada en un vacío que ya había sido motivo de reflexión para Michael Faraday en su postulación del concepto de campo eléctrico. Sáenz de Oíza incide en la expresión de la condición material de la energía en su propuesta junto a José Luis Romany para la capilla en el Camino de Santiago. La evocación de diferentes fuerzas electromagnéticas, las únicas junto a las gravitatorias susceptibles de ser experimentadas por el hombre, aparecerán visualizadas también en el carácter emergente de algunas de sus obras: el Santuario de Aránzazu o Torres Blancas; pero también en la naturaleza fluyente de sus contornos, la dispersión perimetral de los espacios -el umbral como centro del universoo la configuración del límite como respuesta a las tensiones germinales de la naturaleza. Miguel Fisac, a la vuelta de su viaje a los países nórdicos, aborda una simplificación lingüística orientada hacia la adecuación funcional de los espacios. En el Instituto de Daimiel, el Instituto de formación del profesorado o los complejos para los Padres Dominicos en Valladolid o Alcobendas, organiza progresivamente la arquitectura en diferentes volúmenes funcionales, incidiendo de un modo paralelo en la manifestación de los vínculos que se establecen entre dichos volúmenes como una visualización de las fuerzas que los tensionan y equilibran. En ellos la prolongación de la realidad física más allá de los límites de la envolvente ya es algo más que una simple intuición. Un proceso en el que el tratamiento de la luz como un material de construcción más, tendrá un especial protagonismo. En la iglesia de la Coronación, la iluminación del muro curvo escenifica la condición ondulatoria de la luz, manifestándose como si de un patrón de interferencia se tratara. Frente a la disolución de lo material, el espacio se manifiesta aquí como un medio denso, alejado de la tradicional noción de vacío. Una doble naturaleza, onda y partícula, que será intuido también por Fisac en la materia a través de su uso comprometido del hormigón como único material de construcción. Richard Feynmann nos alerta de la ocupación del espacio por multitud de fuerzas electromagnéticas que, al igual que la luz, precisan de receptores específicos para captar su presencia. Sus célebres diagramas suponen además la visualización definitiva de los procesos subatómicos. Al igual que la abstracción absoluta en las artes plásticas, esas representaciones diagramáticas no son asimilables a imágenes obtenidas de nuestra experiencia. Una intuición plasmada en el uso del diagrama, que irán adquiriendo progresivamente los dibujos de Alejandro de la Sota. La sección del gimnasio Maravillas recoge los trazos de sus principales elementos constructivos: estructura, cerramientos, compartimentaciones…, pero también, y con la misma intensidad, los de las fuerzas que generan su espacio, considerando así su condición de elementos constituyentes. El vacío, nos deja claro Sota, es el lugar donde habitan dichas tensiones. La posterior simplificación de las formas acompañadas de la obsesión por su aligeramiento, la casi desaparición de la envolvente, incide en aquella idea con la que Paul Klee define la actividad del artista en su Teoría del Arte Moderno, y en la que se transmite el distanciamiento hacia lo aparente: No se trata de reproducir lo visible, se trata de volver visible. Así, en Bankunión y Aviaco, como en tantos otros proyectos, frente al objetivo de la forma, Sota plantea el límite como la acotación de un ámbito de actuación. Su propia representación aséptica y diagramática transmite la renuncia a una especificidad espacial. Gilles Deleuze expresa ese posicionamiento en Pintura, el Concepto de Diagrama: el diagrama como la posibilidad de cuadros infinitos, o la posibilidad infinita de cuadros. Aparece así una concepción probabilística del espacio en la que frente a la renuncia por la forma, la tendencia al aligeramiento, y lo difuso de su definición – ideas claras, definición borrosa, en palabras de Llinás referidas al modo de operar de Sota-, la insistente atención a algunos elementos como escaleras, protecciones o miradores parece trasmitir la idea de que la arquitectura queda condensada en aquellos acontecimientos que delatan su condición dinámica, transitoria. Primando la relación frente al objeto, el vínculo frente a lo tangible. English summary. The fifties and sixties were the years of the final incorporation of Spanish architecture to the international scene. Among the architects who star that no return leap, is the group of those who a few years later will be named by Juan Daniel Fullaondo as Escuela de Madrid. Carlos Flores, in his book Arquitectura Española Contemporánea 1880-1950, refers to those architects as those that applied to the difficult task of restoring in Spain an architecture that connected with theories, solutions and established languages in Europe during the first decades of the twentieth century. Sigfried Giedion proposes in Space, Time and Architecture, the origin of a new tradition, arising from the optical revolution at the beginning of the century. With tradition he refers to a new culture, covering the interplay of different human activities: the similarity of the methods used in architecture, building, painting, urban planning or science. This new feature, based on its independence and detachment from the previous period, is part of the evolutionary scheme that Thomas Kuhn proposes in his text The Structure of Scientific Revolutions, according to non-accumulative periods. Kuhn talks about the emergence of anomalies in each period, origin of thought crisis whose explanation will require a paradigm shift needed. In science, in the field of optical Thomas Young demonstrates at the early nineteenth century the wave nature of light with its double-slit experiment , in electromagnetism the postulation of the existence of the electric field by Michael Faraday involves a conceptual leap, and in thermodynamic, the consideration pointed by Planck about quantum energy radiation. In the arts, in a parallel process, Gleizes and Metzinger , in his collection of cubism achievements on their book Du Cubisme, speak of evolution occurring during the nineteenth century by the painting: from the idealism of beginning of the century, going for realism and impressionist representation of reality, and finishing regardless of the classical perspective . Mathematics also, once developed by Gauss and Lobachevsky and Bolyai consistent geometries that violate Euclid's fifth postulate , will end validating Riemann’s ambient spaces in which these geometries inhabit, decoupling the direct relationship between geometric space -the space environment that results in a type of geometry- , and physical space. Capi Corrales reflectes in his book Contando el Espacio, that non-Euclidean geometries were not noticeable outside the field of mathematics until the theory of relativity and cubism. The origin of the new tradition that Giedion relates to the new culture of modernity coincides with paradigmatic leaps pointed by the theory of relativity in science and Cubism in the visual arts. Both are extended during the first decades until quantum theory and absolute abstraction, barriers that the two main precursors of relativity and cubism, Einstein and Picasso never overcome. In that sense Giedion speaks about the origin, but also the development, and incorporates peripheral inputs from Brazil, Japan and Finland architecture, thus including organic revision advocated by Zevi as part of this new tradition, being open to the late addition of new contributions to the development of that culture of modernity. Removed the concept of Kant's transcendental aesthetics, of time as an absolute reference, and assumed the constant value of the speed of light, theory of relativity says there is no authentic concurrency. It is thus fixed the speed of light as one of the limits of the universe, and the equivalence of mass and energy. In cubism, spatial simultaneity results from the elimination of preferential points of view, resulting in the multiplicity descriptive of reality, which is displayed in decomposition levels, both the object and the space, and the resulting continuity between figure and background that architecture is reflected in the continuity between building and land. Without the consideration of an absolute point of view, there isn’t an authentic shape. Cubism, and its subsequent development by the vanguard arts, make use of geometry as a means of rebuilding the figure and space, taking penetration mechanisms, overlapping and transparency. Gyorgy Kepes suggest in Languaje of Vision, that cubist decomposition of the object involves successive planes autonomy, to become constituent elements. Something that reflects the Van Doesburg’s architectural axonometrics and culminates with the spaces proposed by Mies van der Rohe in his first European projects. These mechanisms are reflected in the first approaches by Javier Carvajal: the extension of Spanish Pantheon in Campo Verano Cemetery, virtual enclosure mentally reconstructed from 24 the use of only three planes, or in the Spanish Pavilion of New York, which organizes its ground floor from the tour, introducing the time parameter as an additional dimension. Carvajal adds to the differential use of the plane as a constituent, Carvajal incorporates its folding and forming enclosures available as a mechanism for spatial and formal qualification, promoting the extension between architecture and territory. A continuity that will be completed in the two houses built in Somosaguas. Volumetric decomposition, as the fragmentation achieved in the last cubist experiences, needs the incorporation of elements of memory - fountains, patios, shutters...- as a network of signals, such as those introduced by Picasso and Braque in their paintings to allow their interpretation. Braque insists in his interest in the space surrounding the objects. A search of the tactility of space contrary to the perspective, which moves the observer away from the object, and that in the gardens of Somosaguas seems to emanate from its own materiality. A tactile space away from the geometric space and Braque identified with the representative space in which Poincaré in La Science et l´hypothèse, located our feelings. To blur those boundaries of the object extends the space indefinitely. With the passage in Greek art from myth to logos, it opens up to mathematics as a tool for understanding the nature until the nineteenth century. Leon Lederman, in Symmetry and beautiful Universe, suggests that one of the greatest contributions of Einstein's theory is to change the mindset of nature, namely the search for symmetry principles that underlie physical laws. Considering that symmetry is the invariance of an object or system from a transformation and that physical laws are the same at any point in space, the space of our universe has a continuous translational symmetry. In the space occupation of the first proposals by Corrales and Molezún underlying structures appear that match enlosetados: parallelograms under continuous transformations, which nature identifies tridimensionally with the crystallographic groups. Plants in the Contemporary Art Museum in La Castellana, the residence in Miraflores, the Brussels pavilion or the Peugeot tower belong to this group. The architecture as a process of continuous occupation of the territory and of its transposition to the deck, embodied in structural lines coincide with the mathematical structure of the translational symmetry and infinite extension whose possibility is enhanced by the use of the transparent cover. Alongside this literal transparency inherent to the material, Colin Rowe and Robert Slutzky alert us another transparency inherent in the structure: phenomenal transparency, illustrated by the Juan Gris’ works, and whose intuition is reflected in the Huarte’s house in Puerta de Hierro in Madrid. Corrales and Molezún insist on a reading of its volume away from the frontal, in which the outline of their inclined roofs and tangential visual suggested by the organization of his circulations introduce a diagonal structure which overlaps the orthogonal understanding of its plant, drawing an intricate web of broken lines that allow the space fluctuate between the volumetric sequence proposal. Information concerning to the energy mean of light and the concept of atom start from the consideration by Plank about the energy emission, and conclude with a paradoxical situation: the dual nature of light - demonstrated by the explanation of Einstein's photoelectric effect-, and the dual nature of matter -assumed by Bohr and demonstrated by the Compton effect-. Finally, Schrödinger and Heisenberg will formulate the universal movement equation governing in undulatory matter, whose mathematical representation is what is known as a wave function. The object is thus identified with its wave function. Its undulatory expression speaks about the probability of being found in a certain place. Gyorgy Kepes emphasizess the need to simplify the language to move from the objectivity that still remains in the cubist painting to the total abstraction of the space. And this is how artists reduced the objects to simple geometric shapes, making emerge at a time, the plastic forces that tense or balance them, in a process that eventually eliminate any trace of matter. Robert Rosenblum in Modern Painting and the Northern Romantic Tradition. Friedrich to Rothko talks about how this rejection of matter in an almost impalpable vacuum: dense color light fields that broadcast a serene glow and seem to generate the elemental energies of natural light is directly linked to the relationship with nature that sets the northern romanticism. An expression of the power of nature concentrated in a vacuum which had been reason for thought by Michael Faraday in his application of the concept of electric field. Saenz de Oíza touches upon the material expression of the energy in its proposal with Jose Luis Romany to the chapel on the Camino de Santiago. The presence of electromagnetic forces, the only ones with the gravitational one capable of being experienced by the man will also visualize in the emerging nature of some of his works: the sanctuary of Aránzazu or Torres Blancas, but also in the flowing nature of its contours, and the inclusion of interest in the realization of space fluctuating boundary: the threshold as the center of the universe. Miguel Fisac, back from his trip to the Northern Countries, starts on a linguistic simplification oriented to the functional adequacy of spaces. In the Daimiel Institute, in the Institute to Teacher Formation or in the complex to the Dominican Fathers in Valladolid or Alcobendas, progressively organized into different functional volumes architecture, focusing in a parallel way in the manifestation of the links established between these volumes as a visualization of the forces that tense and balance them. The prolongation of the physical reality beyond the limits of the envelope is already something more than a simple intuition. A process in which the treatment of light as a construction material, have a special role. In the Coronation church, curved wall lighting dramatizes the undulatory condition of the light, manifesting as if an interference pattern is involved. Versus the dissolution of the material, the space is expressed here as a dense atmosphere, away from the traditional notion of the vacuum. A dual nature, wave and particle, which is also sensed by Fisac in his committed use of concrete as a unique construction material. Richard Feynman alerts us to the occupation of space by many electromagnetic forces, which like the light, require specific receptors to capture their presence. His famous diagrams also involve the final visualization of atomic processes. As absolute abstraction in the visual arts, these representations are not assimilated to images obtained from our experience. A diagrammatic nature, abstracted from figuration, which will obtein the pictures of Alejandro de la Sota. The section of Maravillas gym collects traces of its main building blocks: structure, enclosures... but also, and with the same intensity, of the forces that generate their space as constituent elements. Sota makes it clear: the vacuum is where inhabit these tensions. The subsequent simplification of forms, accompanied by the obsession with his lightening, the near disappearance of the envelope, touches upon that idea which Paul Klee defines the activity of the artist in his Modern Art Theory, the spacing out to the apparent: it is not to reproduce the visible, it is to turn visible. Thus, in Bankunión and Aviaco, as in many other projects, against the shape, raises the limit as the dimension of a scope. His own aseptic and diagrammatic representation transmits waiver to a spatial specificity that Gilles Deleuze clearly expressed in Painting. The Concept Diagram: The diagram as the possibility of infinite pictures, or infinite possibility of the picture. Thus appears the probabilistic concept of space in which, opposite to the diffuse of its definition -clear ideas, diffuse definition, as Llinas said- the insistent attention to some elements like stairs, guards or lookouts seems to concentrate the architecture in its dynamic condition, transitional. The relationship opposite the object, the link opposite the tangible.

On the Controversy About the Presence of Grain Boundary Sliding in Mg AZ31

Highly-textured, rolled AZ31 sheet material shows a significant drop in the plastic anisotropy (r-value; r=εw/εt) in tension between 25°C and 200°C. This behavior was initially explained as a result of the increased activity of non-basal slip with increased temperature. Other authors suggested, however, that the mechanism resp onsible for this phenomenon was the activation of grain boundary sliding (GBS). Here, in-situ ten sile tests have been carried out in an SEM at various temperatures in order to obtain further evi dence of the role of GBS during moderate to high temperature deformation of Mg alloys, which remains highly controversial.

Effect of layer thickness on the high temperature mechanical properties of Al/SiC nanolaminates

Composite laminates on the nanoscale have shown superior hardness and toughness, but little is known about their high temperature behavior. The mechanical properties (elastic modulus and hardness) were measured as a function of temperature by means of nanoindentation in Al/SiC nanolaminates, a model metal–ceramic nanolaminate fabricated by physical vapor deposition. The influence of the Al and SiC volume fraction and layer thicknesses was determined between room temperature and 150 °C and, the deformation modes were analyzed by transmission electron microscopy, using a focused ion beam to prepare cross-sections through selected indents. It was found that ambient temperature deformation was controlled by the plastic flow of the Al layers, constrained by the SiC, and the elastic bending of the SiC layers. The reduction in hardness with temperature showed evidence of the development of interface-mediated deformation mechanisms, which led to a clear influence of layer thickness on the hardness.

A plastic analysis of nonprismatic folded plate structures

A computer method for the plastic analysis of folded plate structures is presented. The method considers the specific characteristics of the folded plate structural model using a simplified one-dimensional theory. and it can be applied to the analysis of any type of folded pIates, either prismatic or nonprismatic, with arbitrary cross-section. A simple example is analyzed in order to show the possibilities of the procedure and some results of interest are presented

Written on the threshold

One of the most productive discoveries of art and architectural criticism is the comparative reading between different situations. It is an approach that does away with all conventions and destroys any attempt to codifing the future. It also reveals the futility of established styles or movements. In the early 20th century, the Russian Formalists spoke of the dissimilarity of the similar in literature and more than a few studies on the visual arts have used the comparative method, from Heinrich Wolfflin to Robert Venturi. But something more has to be added, personal biography. The involvement of the individual, their name and their life, in the history of art bursts in with all the force of what is real, with no need for credibility, because it merely is what it is. The histories of architecture and art tell things in a believable, perfectly connected manner, without the fits and starts of personal biography - when this appears we find ourselves in a different sort of situation.

Analysis and design of a thrombectomy device by using simulation techniques

Purpose: In this work, we present the analysis, design and optimization of one experimental device recently developed in the UK, called the 'GP' Thrombus Aspiration Device (GPTAD). This device has been designed to remove blood clots without the need to make contact with the clot itself thereby potentially reducing the risk of problems such as downstream embolisation. Method: To obtain the minimum pressure necessary to extract the clot and to optimize the device, we have simulated the performance of the GPTAD analysing the resistances, compliances and inertances effects. We model a range of diameters for the GPTAD considering different forces of adhesion of the blood clot to the artery wall, and different lengths of blood clot. In each case we determine the optimum pressure required to extract the blood clot from the artery using the GPTAD, which is attached at its proximal end to a suction pump. Result: We then compare the results of our mathematical modelling to measurements made in laboratory using plastic tube models of arteries of comparable diameter. We use abattoir porcine blood clots that are extracted using the GPTAD. The suction pressures required for such clot extraction in the plastic tube models compare favourably with those predicted by the mathematical modelling. Discussion & Conclusion: We conclude therefore that the mathematical modelling is a useful technique in predicting the performance of the GPTAD and may potentially be used in optimising the design of the device.

An Experimental and Numerical Study of Ballistic Impacts on a Turbine Casing Material at Varying Temperatures

An experimental and numerical study of ballistic impacts on steel plates at various temperatures (700ºC, 400ºC and room temperature) has been carried out. The motivation for this work is the blade‐off event that may occur inside a jet engine turbine. However, as a first attempt to understand this complex loading process, a somewhat simpler approach is carried out in the present work. The material used in this study is the FV535 martensitic stainless steel, which is one of the most commonly used materials for turbine casings. Based on material test data, a Modified Johnson‐Cook (MJC) model was calibrated for numerical simulations using the LS‐DYNA explicit finite element code (see Figure 1). To check the mesh size sensitivity, 2D axisymmetric finite element models with three different mesh sizes and configurations were used for the various temperatures. Two fixed meshes with 64 and 128 elements over the 2mm thick plate and one mesh with 32 elements over the thickness with adaptive remeshing were used in the simulations. The formation of adiabatic shear bands in the perforation process has been found critical in order to achieve good results. Adiabatic shear bands are formed by the temperature rise due to the accumulation of plastic strain during impact (see Figure 2). The influence of the thermal softening in the plastic model has hence been analyzed for the room temperature impact tests, where the temperature gradient is highest

Multi-criteria selection of structural adhesives to bond ABS parts obtained by rapid prototyping

One of the most used methods in rapidprototyping is Fused Deposition Modeling (FDM), which provides components with a reasonable strength in plastic materials such as ABS and has a low environmental impact. However, the FDM process exhibits low levels of surface finishing, difficulty in getting complex and/or small geometries and low consistency in “slim” elements of the parts. Furthermore, “cantilever” elements need large material structures to be supported. The solution of these deficiencies requires a comprehensive review of the three-dimensional part design to enhance advantages and performances of FDM and reduce their constraints. As a key feature of this redesign a novel method of construction by assembling parts with structuraladhesive joints is proposed. These adhesive joints should be designed specifically to fit the plastic substrate and the FDM manufacturing technology. To achieve this, the most suitable structuraladhesiveselection is firstly required. Therefore, the present work analyzes five different families of adhesives (cyanoacrylate, polyurethane, epoxy, acrylic and silicone), and, by means of the application of technical multi-criteria decision analysis based on the analytic hierarchy process (AHP), to select the structuraladhesive that better conjugates mechanical benefits and adaptation to the FDM manufacturing process

Inmovilización de TiO2 sobre polímeros transparentes en el UV-A para la eliminación fotocatalítica de tricloroetileno en aire

El gran desarrollo industrial y demográfico de las últimas décadas ha dado lugar a un consumo crecientemente insostenible de energía y materias primas, que influye negativamente en el ambiente por la gran cantidad de contaminantes generados. Entre las emisiones tienen gran importancia los compuestos orgánicos volátiles (COV), y entre ellos los compuestos halogenados como el tricloroetileno, debido a su elevada toxicidad y resistencia a la degradación. Las tecnologías generalmente empleadas para la degradación de estos compuestos presentan inconvenientes derivados de la generación de productos tóxicos intermedios o su elevado coste. Dentro de los procesos avanzados de oxidación (Advanced Oxidation Processes AOP), la fotocatálisis resulta una técnica atractiva e innovadora de interés creciente en su aplicación para la eliminación de multitud de compuestos orgánicos e inorgánicos, y se ha revelado como una tecnología efectiva en la eliminación de compuestos orgánicos volátiles clorados como el tricloroetileno. Además, al poder aprovechar la luz solar como fuente de radiación UV permite una reducción significativa de costes energéticos y de operación. Los semiconductores más adecuados para su empleo como fotocatalizadores con aprovechamiento de la luz solar son aquellos que tienen una banda de energía comparable a la de los fotones de luz visible o, en su defecto, de luz ultravioleta A (Eg < 3,5 eV), siendo el más empleado el dióxido de titanio (TiO2). El objetivo principal de este trabajo es el estudio de polímeros orgánicos comerciales como soporte para el TiO2 en fotocatálisis heterogénea y su ensayo para la eliminación de tricloroetileno en aire. Para ello, se han evaluado sus propiedades ópticas y su resistencia a la fotodegradación, y se ha optimizado la fijación del fotocatalizador para conseguir un recubrimiento homogéneo, duradero y con elevada actividad fotocatalítica en diversas condiciones de operación. Los materiales plásticos ensayados fueron el polietileno (PE), copolímero de etil vinil acetato con distintos aditivos (EVA, EVA-H y EVA-SH), polipropileno (PP), polimetil (metacrilato) fabricado en colada y extrusión (PMMA-C y PMMA-E), policarbonato compacto y celular (PC-C y PC-Ce), polivinilo rígido y flexible (PVC-R y PVC-F), poliestireno (PS) y poliésteres (PET y PETG). En base a sus propiedades ópticas se seleccionaron el PP, PS, PMMA-C, EVA-SH y PVC-R, los cuales mostraron un valor de transmitancia superior al 80% en el entorno de la región estudiada (λ=365nm). Para la síntesis del fotocatalizador se empleó la tecnología sol-gel y la impregnación multicapa de los polímeros seleccionados por el método de dip-coating con secado intermedio a temperaturas moderadas. Con el fin de evaluar el envejecimiento de los polímeros bajo la radiación UV, y el efecto sobre éste del recubrimiento fotoactivo, se realizó un estudio en una cámara de exposición a la luz solar durante 150 días, evaluándose la resistencia química y la resistencia mecánica. Los resultados de espectroscopía infrarroja y del test de tracción tras el envejecimiento revelaron una mayor resistencia del PMMA y una degradación mayor en el PS, PVC-R y EVA SH, con una apreciable pérdida del recubrimiento en todos los polímeros. Los fotocatalizadores preparados sobre soportes sin tratamiento y con tres capas de óxido de titanio mostraron mejores resultados de actividad con PMMA-C, PET y PS, con buenos resultados de mineralización. Para conseguir una mayor y mejor fijación de la película al soporte se realizaron tratamientos químicos abrasivos con H2SO4 y NaOH y tratamientos de funcionalización superficial por tecnología de plasma a presión atmosférica (APP) y a baja presión (LPP). Con los tratamientos de plasma se consiguió una excelente mojabilidad de los soportes, que dio lugar a una distribución uniforme y más abundante del fotocatalizador, mientras que con los tratamientos químicos no se obtuvo una mejora significativa. Asimismo, se prepararon fotocatalizadores con una capa previa de dióxido de silicio con la intervención de surfactantes (PDDA-SiO2-3TiO2 y SiO2FC-3TiO2), consiguiéndose buenas propiedades de la película en todos los casos. Los mejores resultados de actividad con tratamiento LPP y tres capas de TiO2 se lograron con PMMA-C (91% de conversión a 30 ppm de TCE y caudal 200 ml·min-1) mejorando significativamente también la actividad fotocatalítica en PVC-R y PS. Sin embargo, el material más activo de todos los ensayados fue el PMMA-C con el recubrimiento SiO2FC-3TiO2, logrando el mejor grado de mineralización, del 45%, y una velocidad de 1,89 x 10-6 mol· m-2 · s-1, que dio lugar a la eliminación del 100 % del tricloroetileno en las condiciones anteriormente descritas. A modo comparativo se realizaron ensayos de actividad con otro contaminante orgánico tipo, el formaldehído, cuya degradación fotocatalítica fue también excelente (100% de conversión y 80% de mineralización con 24 ppm de HCHO en un caudal de aire seco de 200 ml·min-1). Los buenos resultados de actividad obtenidos confirman las enormes posibilidades que ofrecen los polímeros transparentes en el UV-A como soportes del dióxido de titanio para la eliminación fotocatalítica de contaminantes en aire. ABSTRACT The great industrial and demographic development of recent decades has led to an unsustainable increase of energy and raw materials consumption that negatively affects the environment due to the large amount of waste and pollutants generated. Between emissions generated organic compounds (VOCs), specially the halogenated ones such as trichloroethylene, are particularly important due to its high toxicity and resistance to degradation. The technologies generally used for the degradation of these compounds have serious inconveniences due to the generation of toxic intermediates turn creating the problem of disposal besides the high cost. Among the advanced oxidation processes (AOP), photocatalysis is an attractive and innovative technique with growing interest in its application for the removal of many organic and inorganic compounds, and has emerged as an effective technology in eliminating chlorinated organic compounds such as trichloroethylene. In addition, as it allows the use of sunlight as a source of UV radiation there is a significant reduction of energy costs and operation. Semiconductors suitable to be used as photocatalyst activated by sunlight are those having an energy band comparable to that of the visible or UV-A light (Eg <3,5 eV), being titanium dioxide (TiO2), the most widely used. The main objective of this study is the test of commercial organic polymers as supports for TiO2 to be applied in heterogeneous photocatalysis and its assay for removing trichloroethylene in air. To accomplish that, its optical properties and resistance to photooxidation have been evaluated, and different operating conditions have been tested in order to optimize the fixation of the photocatalyst to obtain a homogeneous coating, with durable and high photocatalytic activity. The plastic materials tested were: polyethylene (PE), ethyl vinyl acetace copolymers with different additives (EVA, EVA-H and EVA -SH), polypropylene (PP), poly methyl (methacrylate) manufactured by sheet moulding and extrusion (PMMA-C and PMMA-E), compact and cellular polycarbonates (PC-C PC-Ce), rigid and flexible polyvinyl chloride (PVC-R and PVC-F), polystyrene (PS) and polyesters (PET and PETG). On the basis of their optical properties PP, PS, PMMA-C, EVA-SH and PVC-R were selected, as they showed a transmittance value greater than 80% in the range of the studied region (λ = 365nm). For the synthesis of the photocatalyst sol-gel technology was employed with multilayers impregnation of the polymers selected by dip-coating, with intermediate TiO2 drying at moderate temperatures. To evaluate the polymers aging due to UV radiation, and the effect of photoactive coating thereon, a study in an sunlight exposure chamber for 150 days was performed, evaluating the chemical resistance and the mechanical strength. The results of infrared spectroscopy and tensile stress test after aging showed the PMMA is the most resistant sample, but a greater degradation in PS, PVC-R and EVA SH, with a visible loss of the coating in all the polymers tested. The photocatalysts prepared on the untreated substrates with three layers of TiO2 showed better activity results when PMMA-C, PET and PS where used. To achieve greater and better fixation of the film to the support, chemical abrasive treatments, with H2SO4 and NaOH, as well as surface functionalization treatments with atmospheric pressure plasma (APP) and low pressure plasma (LPP) technologies were performed. The plasma treatment showed the best results, with an excellent wettability of the substrates that lead to a better and uniform distribution of the photocatalyst compared to the chemical treatments tested, in which no significant improvement was obtained. Also photocatalysts were prepared with the a silicon dioxide previous layer with the help of surfactants (SiO2- 3TiO2 PDDA-and-3TiO2 SiO2FC), obtaining good properties of the film in all cases. The best activity results for LPP-treated samples with three layers of TiO2 were achieved with PMMA-C (91% conversion, in conditions of 30 ppm of TCE and 200 ml·min-1 air flow rate), with a significant improvement of the photocatalytic activity in PVC-R and PS samples too. However, among all the materials assayed, PMMA-C with SiO2FC-3TiO2 coating was the most active one, achieving the highest mineralization grade (45%) and a reaction rate of 1,89 x 10-6 mol· m-2 · s-1, with total trichloroethylene elimination in the same conditions. As a comparative assay, an activity test was also performed with another typical organic contaminant, formaldehyde, also with good results (100% conversion with 24 ppm of HCHO and 200 ml·min-1 gas flow rate). The good activity results obtained in this study confirm the great potential of organic polymers which are transparent in the UV-A as supports for titanium dioxide for photocatalytic removal of air organic pollutants.

Boundary element formulation for elastoplastic analysis of axisymmetric bodies

The complete formulation of B.E.M. applied to the analysis of axisymmetric bodies acting in the plastic range is presented in this paper. The concept of derivative of a singular integral given by Mikhlin has been used in order to calculate the stresses in internal points. Also a semianalytical approach is proposed to compute the matrix coefficients, presenting the way in which it can be done and the results obtained.