A robust numerical framework for the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Statistical characterization of soft tissue inelastic parameters and application to the material failure of the aortic ach

Caracterización de los procesos de disipación mecánica basándose en la microestructura de los tejidos blandos. We present a continuous damage model with regularized softening (smeared crack models) for fiber reinforced soft tissues. Material parameters of the continuous model derive from the mesoscopic scale. In the mesoscopic scale continuum is considered as a collagenous fibrilreinforced composite. We want to study the continnumlevel response as a function of the nanoscale properties of the collagen and the adherent forces between the tropocollagen molecules.

Experimental and numerical analysis of reinforced concrete elements subjected to blast loading

El hormigón es uno de los materiales de construcción más empleados en la actualidad debido a sus buenas prestaciones mecánicas, moldeabilidad y economía de obtención, entre otras ventajas. Es bien sabido que tiene una buena resistencia a compresión y una baja resistencia a tracción, por lo que se arma con barras de acero para formar el hormigón armado, material que se ha convertido por méritos propios en la solución constructiva más importante de nuestra época. A pesar de ser un material profusamente utilizado, hay aspectos del comportamiento del hormigón que todavía no son completamente conocidos, como es el caso de su respuesta ante los efectos de una explosión. Este es un campo de especial relevancia, debido a que los eventos, tanto intencionados como accidentales, en los que una estructura se ve sometida a una explosión son, por desgracia, relativamente frecuentes. La solicitación de una estructura ante una explosión se produce por el impacto sobre la misma de la onda de presión generada en la detonación. La aplicación de esta carga sobre la estructura es muy rápida y de muy corta duración. Este tipo de acciones se denominan cargas impulsivas, y pueden ser hasta cuatro órdenes de magnitud más rápidas que las cargas dinámicas impuestas por un terremoto. En consecuencia, no es de extrañar que sus efectos sobre las estructuras y sus materiales sean muy distintos que las que producen las cargas habitualmente consideradas en ingeniería. En la presente tesis doctoral se profundiza en el conocimiento del comportamiento material del hormigón sometido a explosiones. Para ello, es crucial contar con resultados experimentales de estructuras de hormigón sometidas a explosiones. Este tipo de resultados es difícil de encontrar en la literatura científica, ya que estos ensayos han sido tradicionalmente llevados a cabo en el ámbito militar y los resultados obtenidos no son de dominio público. Por otra parte, en las campañas experimentales con explosiones llevadas a cabo por instituciones civiles el elevado coste de acceso a explosivos y a campos de prueba adecuados no permite la realización de ensayos con un elevado número de muestras. Por este motivo, la dispersión experimental no es habitualmente controlada. Sin embargo, en elementos de hormigón armado sometidos a explosiones, la dispersión experimental es muy acusada, en primer lugar, por la propia heterogeneidad del hormigón, y en segundo, por la dificultad inherente a la realización de ensayos con explosiones, por motivos tales como dificultades en las condiciones de contorno, variabilidad del explosivo, o incluso cambios en las condiciones atmosféricas. Para paliar estos inconvenientes, en esta tesis doctoral se ha diseñado un novedoso dispositivo que permite ensayar hasta cuatro losas de hormigón bajo la misma detonación, lo que además de proporcionar un número de muestras estadísticamente representativo, supone un importante ahorro de costes. Con este dispositivo se han ensayado 28 losas de hormigón, tanto armadas como en masa, de dos dosificaciones distintas. Pero además de contar con datos experimentales, también es importante disponer de herramientas de cálculo para el análisis y diseño de estructuras sometidas a explosiones. Aunque existen diversos métodos analíticos, hoy por hoy las técnicas de simulación numérica suponen la alternativa más avanzada y versátil para el cálculo de elementos estructurales sometidos a cargas impulsivas. Sin embargo, para obtener resultados fiables es crucial contar con modelos constitutivos de material que tengan en cuenta los parámetros que gobiernan el comportamiento para el caso de carga en estudio. En este sentido, cabe destacar que la mayoría de los modelos constitutivos desarrollados para el hormigón a altas velocidades de deformación proceden del ámbito balístico, donde dominan las grandes tensiones de compresión en el entorno local de la zona afectada por el impacto. En el caso de los elementos de hormigón sometidos a explosiones, las tensiones de compresión son mucho más moderadas, siendo las tensiones de tracción generalmente las causantes de la rotura del material. En esta tesis doctoral se analiza la validez de algunos de los modelos disponibles, confirmando que los parámetros que gobiernan el fallo de las losas de hormigón armado ante explosiones son la resistencia a tracción y su ablandamiento tras rotura. En base a los resultados anteriores se ha desarrollado un modelo constitutivo para el hormigón ante altas velocidades de deformación, que sólo tiene en cuenta la rotura por tracción. Este modelo parte del de fisura cohesiva embebida con discontinuidad fuerte, desarrollado por Planas y Sancho, que ha demostrado su capacidad en la predicción de la rotura a tracción de elementos de hormigón en masa. El modelo ha sido modificado para su implementación en el programa comercial de integración explícita LS-DYNA, utilizando elementos finitos hexaédricos e incorporando la dependencia de la velocidad de deformación para permitir su utilización en el ámbito dinámico. El modelo es estrictamente local y no requiere de remallado ni conocer previamente la trayectoria de la fisura. Este modelo constitutivo ha sido utilizado para simular dos campañas experimentales, probando la hipótesis de que el fallo de elementos de hormigón ante explosiones está gobernado por el comportamiento a tracción, siendo de especial relevancia el ablandamiento del hormigón. Concrete is nowadays one of the most widely used building materials because of its good mechanical properties, moldability and production economy, among other advantages. As it is known, it has high compressive and low tensile strengths and for this reason it is reinforced with steel bars to form reinforced concrete, a material that has become the most important constructive solution of our time. Despite being such a widely used material, there are some aspects of concrete performance that are not yet fully understood, as it is the case of its response to the effects of an explosion. This is a topic of particular relevance because the events, both intentional and accidental, in which a structure is subjected to an explosion are, unfortunately, relatively common. The loading of a structure due to an explosive event occurs due to the impact of the pressure shock wave generated in the detonation. The application of this load on the structure is very fast and of very short duration. Such actions are called impulsive loads, and can be up to four orders of magnitude faster than the dynamic loads imposed by an earthquake. Consequently, it is not surprising that their effects on structures and materials are very different than those that cause the loads usually considered in engineering. This thesis broadens the knowledge about the material behavior of concrete subjected to explosions. To that end, it is crucial to have experimental results of concrete structures subjected to explosions. These types of results are difficult to find in the scientific literature, as these tests have traditionally been carried out by armies of different countries and the results obtained are classified. Moreover, in experimental campaigns with explosives conducted by civil institutions the high cost of accessing explosives and the lack of proper test fields does not allow for the testing of a large number of samples. For this reason, the experimental scatter is usually not controlled. However, in reinforced concrete elements subjected to explosions the experimental dispersion is very pronounced. First, due to the heterogeneity of concrete, and secondly, because of the difficulty inherent to testing with explosions, for reasons such as difficulties in the boundary conditions, variability of the explosive, or even atmospheric changes. To overcome these drawbacks, in this thesis we have designed a novel device that allows for testing up to four concrete slabs under the same detonation, which apart from providing a statistically representative number of samples, represents a significant saving in costs. A number of 28 slabs were tested using this device. The slabs were both reinforced and plain concrete, and two different concrete mixes were used. Besides having experimental data, it is also important to have computational tools for the analysis and design of structures subjected to explosions. Despite the existence of several analytical methods, numerical simulation techniques nowadays represent the most advanced and versatile alternative for the assessment of structural elements subjected to impulsive loading. However, to obtain reliable results it is crucial to have material constitutive models that take into account the parameters that govern the behavior for the load case under study. In this regard it is noteworthy that most of the developed constitutive models for concrete at high strain rates arise from the ballistic field, dominated by large compressive stresses in the local environment of the area affected by the impact. In the case of concrete elements subjected to an explosion, the compressive stresses are much more moderate, while tensile stresses usually cause material failure. This thesis discusses the validity of some of the available models, confirming that the parameters governing the failure of reinforced concrete slabs subjected to blast are the tensile strength and softening behaviour after failure. Based on these results we have developed a constitutive model for concrete at high strain rates, which only takes into account the ultimate tensile strength. This model is based on the embedded Cohesive Crack Model with Strong Discontinuity Approach developed by Planas and Sancho, which has proved its ability in predicting the tensile fracture of plain concrete elements. The model has been modified for its implementation in the commercial explicit integration program LS-DYNA, using hexahedral finite elements and incorporating the dependence of the strain rate, to allow for its use in dynamic domain. The model is strictly local and does not require remeshing nor prior knowledge of the crack path. This constitutive model has been used to simulate two experimental campaigns, confirming the hypothesis that the failure of concrete elements subjected to explosions is governed by their tensile response, being of particular relevance the softening behavior of concrete.

Estudio de la rotura en barras de acero : aspectos experimentales y numéricos

El acero es, junto con el hormigón, el material más ampliamente empleado en la construcción de obra civil y de edificación. Además de su elevada resistencia, su carácter dúctil resulta un aspecto de particular interés desde el punto de vista de la seguridad estructural, ya que permite redistribuir esfuerzos a elementos adyacentes y, por tanto, almacenar una mayor energía antes del colapso final de la estructura. No obstante, a pesar de su extendida utilización, todavía existen aspectos relacionados con su comportamiento en rotura que necesitan una mayor clarificación y que permitirían un mejor aprovechamiento de sus propiedades. Cuando un elemento de acero es ensayado a tracción y alcanza la carga máxima, sufre la aparición de un cuello de estricción que plantea dificultades para conocer el comportamiento del material desde dicho instante hasta la rotura. La norma ISO 6892-1, que define el método a emplear en un ensayo de tracción con materiales metálicos, establece procedimientos para determinar los parámetros relacionados con este tramo último de la curva F − E. No obstante, la definición de dichos parámetros resulta controvertida, ya que éstos presentan una baja reproducibilidad y una baja repetibilidad que resultan difíciles de explicar. En esta Tesis se busca profundizar en el conocimiento del último tramo de la curva F − E de los aceros de construcción. Para ello se ha realizado una amplia campaña experimental sobre dos aceros representativos en el campo de la construcción civil: el alambrón de partida empleado en la fabricación de alambres de pretensado y un acero empleado como refuerzo en hormigón armado. Los dos materiales analizados presentan formas de rotura diferentes: mientras el primero de ellos presenta una superficie de rotura plana con una región oscura claramente apreciable en su interior, el segundo rompe según la clásica superficie en forma de copa y cono. La rotura en forma de copa y cono ha sido ampliamente estudiada en el pasado y existen modelos de rotura que han logrado reproducirla con éxito, en especial el modelo de Gurson- Tvergaard-Needleman (GTN). En cuanto a la rotura exhibida por el primer material, en principio nada impide abordar su reproducción numérica con un modelo GTN, sin embargo, las diferencias observadas entre ambos materiales en los ensayos experimentales permiten pensar en otro criterio de rotura. En la presente Tesis se realiza una amplia campaña experimental con probetas cilíndricas fabricadas con dos aceros representativos de los empleados en construcción con comportamientos en rotura diferentes. Por un lado se analiza el alambrón de partida empleado en la fabricación de alambres de pretensado, cuyo frente de rotura es plano y perpendicular a la dirección de aplicación de la carga con una región oscura en su interior. Por otro lado, se estudian barras de acero empleadas como armadura pasiva tipo B 500 SD, cuyo frente de rotura presenta la clásica superficie en forma de copa y cono. Estos trabajos experimentales han permitido distinguir dos comportamientos en rotura claramente diferenciados entre ambos materiales y, en el caso del primer material, se ha identificado un comportamiento asemejable al exhibido por materiales frágiles. En este trabajo se plantea la hipótesis de que el primer material, cuya rotura provoca un frente de rotura plano y perpendicular a la dirección de aplicación de la carga, rompe de manera cuasifrágil como consecuencia de un proceso de decohesión, de manera que la región oscura que se observa en el centro del frente de rotura se asemeja a una entalla circular perpendicular a la dirección de aplicación de la carga. Para la reproducción numérica de la rotura exhibida por el primer material, se plantea un criterio de rotura basado en un modelo cohesivo que, como aspecto novedoso, se hace depender de la triaxialidad de tensiones, parámetro determinante en el fallo de este tipo de materiales. Este tipo de modelos presenta varias ventajas respecto a los modelos GTN habitualmente empleados. Mientras los modelos GTN precisan de numerosos parámetros para su calibración, los modelos cohesivos precisan fundamentalmente de dos parámetros para definir su curva de ablandamiento: la tensión de decohesión ft y la energía de fractura GF . Además, los parámetros de los modelos GTN no son medibles de manera experimental, mientras que GF sí lo es. En cuanto a ft, aunque no existe un método para su determinación experimental, sí resulta un parámetro más fácilmente interpretable que los empleados por los modelos GTN, que utilizan valores como el porcentaje de huecos presentes en el material para iniciar el fenómeno de coalescencia o el porcentaje de poros que provoca una pérdida total de la capacidad resistente. Para implementar este criterio de rotura se ha desarrollado un elemento de intercara cohesivo dependiente de la triaxialidad de tensiones. Se han reproducido con éxito los ensayos de tracción llevados a cabo en la campaña experimental empleando dicho elemento de intercara. Además, en estos modelos la rotura se produce fenomenológicamente de la misma manera observada en los ensayos experimentales: produciéndose una decohesión circular en torno al eje de la probeta. En definitiva, los trabajos desarrollados en esta Tesis, tanto experimentales como numéricos, contribuyen a clarificar el comportamiento de los aceros de construcción en el último tramo de la curva F − E y los mecanismos desencadenantes de la rotura final del material, aspecto que puede contribuir a un mejor aprovechamiento de las propiedades de estos aceros en el futuro y a mejorar la seguridad de las estructuras construidas con ellos. Steel is, together with concrete, the most widely used material in civil engineering works. Not only its high strength, but also its ductility is of special interest from the point of view of the structural safety, since it enables stress distribution with adjacent elements and, therefore, more energy can be stored before reaching the structural failure. However, despite of being extensively used, there are still some aspects related to its fracture behaviour that need to be clarified and that will allow for a better use of its properties. When a steel item is tested under tension and reaches the maximum load point, necking process begins, which makes difficult to define the material behaviour from that moment onward. The ISO standard 6892-1, which defines the tensile testing method for metallic materials, describes the procedures to obtain some parameters related to this last section of the F − E curve. Nevertheless, these parameters have proved to be controversial, since they have low reproducibility and repeatibility rates that are difficult to explain. This Thesis tries to deepen the knowledge of the last section of the F − E curve for construction steels. An extensive experimental campaign has been carried out with two representative steels used in civil engineering works: a steel rod used for manufacturing prestressing steel wires, before the cold-drawing process is applied, and steel bars used in reinforced concrete structures. Both materials have different fracture surfaces: while the first of them shows a flat fracture surface, perpendicular to the loading direction with a dark region in the centre of it, the second one shows the classical cup-cone fracture surface. The cup-cone fracture surface has been deeply studied in the past and different numerical models have been able to reproduce it with success, with a special mention to the Gurson-Tvergaard-Needleman model (GTN). Regarding the failure surface shown by the first material, in principle it can be numerically reproduced by a GTN model, but the differences observed between both materials in the experimental campaign suggest thinking of a different failure criterium. In the present Thesis, an extensive experimental campaign has been carried out using cylindrical specimens made of two representative construction steels with different fracture behaviours. On one hand, the initial eutectoid steel rod used for manufacturing prestressing steel wires is analysed, which presents a flat fracture surface, perpendicular to the loading direction, and with a dark region in the centre of it. On the other hand, B 500 SD steel bars, typically used in reinforced concrete structures and with the typical cup-cone fracture surface, are studied. These experimental works have allowed distinguishing two clearly different fracture behaviours between both materials and, in the case of the first one, a fragile-like behaviour has been identified. For the first material, which shows a flat fracture surface perpendicular to the loading direction, the following hypothesis is proposed in this study: a quasi-brittle fracture is developed as a consequence of a decohesion process, with the dark region acting as a circular crack perpendicular to the loading direction. To reproduce numerically the fracture behaviour shown by the first material, a failure criterium based on a cohesive model is proposed in this Thesis. As an innovative contribution, this failure criterium depends on the stress triaxiality state of the material, which is a key parameter when studying fracture in this kind of materials. This type of models have some advantages when compared to the widely used GTN models. While GTN models need a high number of parameters to be defined, cohesive models need basically two parameters to define the softening curve: the decohesion stress ft and the fracture energy GF . In addition to this, GTN models parameters cannot be measured experimentally, while GF is indeed. Regarding ft, although no experimental procedure is defined for its obtention, it has an easier interpretation than the parameters used by the GTN models like, for instance, the void volume needed for the coalescence process to start or the void volume that leads to a total loss of the bearing capacity. In order to implement this failure criterium, a triaxiality-dependent cohesive interface element has been developed. The experimental results obtained in the experimental campaign have been successfully reproduced by using this interface element. Furthermore, in these models the failure mechanism is developed in the same way as observed experimentally: with a circular decohesive process taking place around the longitudinal axis of the specimen. In summary, the works developed in this Thesis, both experimental and numerical, contribute to clarify the behaviour of construction steels in the last section of the F − E curve and the mechanisms responsible for the eventual material failure, an aspect that can lead to a better use of the properties of these steels in the future and a safety improvement in the structures built with them.

Thermodynamics of zinc insertion in CuGaS2:Ti, used as a modulator agent in an intermediate-band photovoltaic material

An intermediate-bandphotovoltaicmaterial, which has an isolated metallic band located between the top of the valence band and bottom of the conduction band of some semiconductors, has been proposed as third generation solar cell to be used in photovoltaic applications. Density functional theory calculations of Zn in CuGaS2:Ti have previously shown that, the intermediate-band position can be modulated in proportion of Zn insertion in such a way that increasing Zn concentration can lead to aband-gap reduction, and an adjustment of the intermediate-band position. This could be interesting in the formation of an intermediate-bandmaterial, that has the maximum efficiency theoretically predicted for the intermediate-band solar cell. In this work, the energetics of several reaction schemes that could lead to the decomposition of the modulated intermediate-bandphotovoltaicmaterial, CuGaS2:Ti:Zn, is studied in order to assess the thermodynamic stability of this material. Calculations of the total free energy and disorder entropy have been taken into account, to get the reaction energy and free energy of the compound decomposition, which is found to be thermodynamically favorable

Impact And Explosive Loads On Concrete Buildings Using Shell And Beam Type Elements

The threat of impact or explosive loads is regrettably a scenario to be taken into account in the design of lifeline or critical civilian buildings. These are often made of concrete and not specifically designed for military threats. Numerical simulation of such cases may be undertaken with the aid of state of the art explicit dynamic codes, however several difficult challenges are inherent to such models: the material modeling for the concrete anisotropic failure, consideration of reinforcement bars and important structural details, adequate modeling of pressure waves from explosions in complex geometries, and efficient solution to models of complete buildings which can realistically assess failure modes. In this work we employ LS-Dyna for calculation, with Lagrangian finite elements and explicit time integration. Reinforced concrete may be represented in a fairly accurate fashion with recent models such as CSCM model [1] and segregated rebars constrained within the continuum mesh. However, such models cannot be realistically employed for complete models of large buildings, due to limitations of time and computer resources. The use of structural beam and shell elements for this purpose would be the obvious solution, with much lower computational cost. However, this modeling requires careful calibration in order to reproduce adequately the highly nonlinear response of structural concrete members, including bending with and without compression, cracking or plastic crushing, plastic deformation of reinforcement, erosion of vanished elements etc. The main objective of this work is to provide a strategy for modeling such scenarios based on structural elements, using available material models for structural elements [2] and techniques to include the reinforcement in a realistic way. These models are calibrated against fully three-dimensional models and shown to be accurate enough. At the same time they provide the basis for realistic simulation of impact and explosion on full-scale buildings

Failure and impact behavior of facade panels made of glass fiber reinforced cement(GRC)

GRC is a cementitious composite material made up of a cement mortar matrix and chopped glass fibers. Due to its outstanding mechanical properties, GRC has been widely used to produce cladding panels and some civil engineering elements. Impact failure of cladding panels made of GRC may occur during production if some tool falls onto the panel, due to stone or other objects impacting at low velocities or caused by debris projected after a blast. Impact failure of a front panel of a building may have not only an important economic value but also human lives may be at risk if broken pieces of the panel fall from the building to the pavement. Therefore, knowing GRC impact strength is necessary to prevent economic costs and putting human lives at risk. One-stage light gas gun is an impact test machine capable of testing different materials subjected to impact loads. An experimental program was carried out, testing GRC samples of five different formulations, commonly used in building industry. Steel spheres were shot at different velocities on square GRC samples. The residual velocity of the projectiles was obtained both using a high speed camera with multiframe exposure and measuring the projectile’s penetration depth in molding clay blocks. Tests were performed on young and artificially aged GRC samples to compare GRC’s behavior when subjected to high strain rates. Numerical simulations using a hydrocode were made to analyze which parameters are most important during an impact event. GRC impact strength was obtained from test results. Also, GRC’s embrittlement, caused by GRC aging, has no influence on GRC impact behavior due to the small size of the projectile. Also, glass fibers used in GRC production only maintain GRC panels’ integrity but have no influence on GRC’s impact strength. Numerical models have reproduced accurately impact tests.

Multivariant non-failure analysis via standard abstract interpretation

Non-failure analysis aims at inferring that predicate calis in a program will never fail. This type of information has many applications in functional/logic programming. It is essential for determining lower bounds on the computational cost of calis, useful in the context of program parallelization, instrumental in partial evaluation and other program transformations, and has also been used in query optimization. In this paper, we re-cast the non-failure analysis proposed by Debray et al. as an abstract interpretation, which not only allows to investígate it from a standard and well understood theoretical framework, but has also several practical advantages. It allows us to incorpórate non-failure analysis into a standard, generic abstract interpretation engine. The analysis thus benefits from the fixpoint propagation algorithm, which leads to improved information propagation. Also, the analysis takes advantage of the multi-variance of the generic engine, so that it is now able to infer sepárate non-failure information for different cali patterns. Moreover, the implementation is simpler, and allows to perform non-failure and covering analyses alongside other analyses, such as those for modes and types, in the same framework. Finally, besides the precisión improvements and the additional simplicity, our implementation (in the Ciao/CiaoPP multiparadigm programming system) also shows better efRciency.

Non-failure analysis for logic programs

We provide a method whereby, given mode and (upper approximation) type information, we can detect procedures and goals that can be guaranteed to not fail (i.e., to produce at least one solution or not termínate). The technique is based on an intuitively very simple notion, that of a (set of) tests "covering" the type of a set of variables. We show that the problem of determining a covering is undecidable in general, and give decidability and complexity results for the Herbrand and linear arithmetic constraint systems. We give sound algorithms for determining covering that are precise and efiicient in practice. Based on this information, we show how to identify goals and procedures that can be guaranteed to not fail at runtime. Applications of such non-failure information include programming error detection, program transiormations and parallel execution optimization, avoiding speculative parallelism and estimating lower bounds on the computational costs of goals, which can be used for granularity control. Finally, we report on an implementation of our method and show that better results are obtained than with previously proposed approaches.

Estimating the computational cost of logic programs

Information about the computational cost of programs is potentially useful for a variety of purposes, including selecting among different algorithms, guiding program transformations, in granularity control and mapping decisions in parallelizing compilers, and query optimization in deductive databases. Cost analysis of logic programs is complicated by nondeterminism: on the one hand, procedures can return múltiple Solutions, making it necessary to estímate the number of solutions in order to give nontrivial upper bound cost estimates; on the other hand, the possibility of failure has to be taken into account while estimating lower bounds. Here we discuss techniques to address these problems to some extent.

Modelización de costas rocosas acantiladas

El retroceso de las costas acantiladas es un fenómeno muy extendido sobre los litorales rocosos expuestos a la incidencia combinada de los procesos marinos y meteorológicos que se dan en la franja costera. Este fenómeno se revela violentamente como movimientos gravitacionales del terreno esporádicos, pudiendo causar pérdidas materiales y/o humanas. Aunque el conocimiento de estos riesgos de erosión resulta de vital importancia para la correcta gestión de la costa, el desarrollo de modelos predictivos se encuentra limitado desde el punto de vista geomorfológico debido a la complejidad e interacción de los procesos de desarrollo espacio-temporal que tienen lugar en la zona costera. Los modelos de predicción publicados son escasos y con importantes inconvenientes: a) extrapolación, extienden la información de registros históricos; b) empíricos, sobre registros históricos estudian la respuesta al cambio de un parámetro; c) estocásticos, determinan la cadencia y magnitud de los eventos futuros extrapolando las distribuciones de probabilidad extraídas de catálogos históricos; d) proceso-respuesta, de estabilidad y propagación del error inexplorada; e) en Ecuaciones en Derivadas Parciales, computacionalmente costosos y poco exactos. La primera parte de esta tesis detalla las principales características de los modelos más recientes de cada tipo y, para los más habitualmente utilizados, se indican sus rangos de aplicación, ventajas e inconvenientes. Finalmente como síntesis de los procesos más relevantes que contemplan los modelos revisados, se presenta un diagrama conceptual de la recesión costera, donde se recogen los procesos más influyentes que deben ser tenidos en cuenta, a la hora de utilizar o crear un modelo de recesión costera con el objetivo de evaluar la peligrosidad (tiempo/frecuencia) del fenómeno a medio-corto plazo. En esta tesis se desarrolla un modelo de proceso-respuesta de retroceso de acantilados costeros que incorpora el comportamiento geomecánico de materiales cuya resistencia a compresión no supere los 5 MPa. El modelo simula la evolución espaciotemporal de un perfil-2D del acantilado que puede estar formado por materiales heterogéneos. Para ello, se acoplan la dinámica marina: nivel medio del mar, cambios en el nivel medio del lago, mareas y oleaje; con la evolución del terreno: erosión, desprendimiento rocoso y formación de talud de derrubios. El modelo en sus diferentes variantes es capaz de incluir el análisis de la estabilidad geomecánica de los materiales, el efecto de los derrubios presentes al pie del acantilado, el efecto del agua subterránea, la playa, el run-up, cambios en el nivel medio del mar o cambios (estacionales o interanuales) en el nivel medio de la masa de agua (lagos). Se ha estudiado el error de discretización del modelo y su propagación en el tiempo a partir de las soluciones exactas para los dos primeros periodos de marea para diferentes aproximaciones numéricas tanto en tiempo como en espacio. Los resultados obtenidos han permitido justificar las elecciones que minimizan el error y los métodos de aproximación más adecuados para su posterior uso en la modelización. El modelo ha sido validado frente a datos reales en la costa de Holderness, Yorkshire, Reino Unido; y en la costa norte del lago Erie, Ontario, Canadá. Los resultados obtenidos presentan un importante avance en los modelos de recesión costera, especialmente en su relación con las condiciones geomecánicas del medio, la influencia del agua subterránea, la verticalización de los perfiles rocosos y su respuesta ante condiciones variables producidas por el cambio climático (por ejemplo, nivel medio del mar, cambios en los niveles de lago, etc.). The recession of coastal cliffs is a widespread phenomenon on the rocky shores that are exposed to the combined incidence of marine and meteorological processes that occur in the shoreline. This phenomenon is revealed violently and occasionally, as gravitational movements of the ground and can cause material or human losses. Although knowledge of the risks of erosion is vital for the proper management of the coast, the development of cliff erosion predictive models is limited by the complex interactions between environmental processes and material properties over a range of temporal and spatial scales. Published prediction models are scarce and present important drawbacks: extrapolation, that extend historical records to the future; empirical, that based on historical records studies the system response against the change in one parameter; stochastic, that represent of cliff behaviour based on assumptions regarding the magnitude and frequency of events in a probabilistic framework based on historical records; process-response, stability and error propagation unexplored; PDE´s, highly computationally expensive and not very accurate. The first part of this thesis describes the main features of the latest models of each type and, for the most commonly used, their ranges of application, advantages and disadvantages are given. Finally as a synthesis of the most relevant processes that include the revised models, a conceptual diagram of coastal recession is presented. This conceptual model includes the most influential processes that must be taken into account when using or creating a model of coastal recession to evaluate the dangerousness (time/frequency) of the phenomenon to medium-short term. A new process-response coastal recession model developed in this thesis has been designed to incorporate the behavioural and mechanical characteristics of coastal cliffs which are composed of with materials whose compressive strength is less than 5 MPa. The model simulates the spatial and temporal evolution of a cliff-2D profile that can consist of heterogeneous materials. To do so, marine dynamics: mean sea level, waves, tides, lake seasonal changes; is coupled with the evolution of land recession: erosion, cliff face failure and associated protective colluvial wedge. The model in its different variants can include analysis of material geomechanical stability, the effect of debris present at the cliff foot, groundwater effects, beach and run-up effects, changes in the mean sea level or changes (seasonal or inter-annual) in the mean lake level. Computational implementation and study of different numerical resolution techniques, in both time and space approximations, and the produced errors are exposed and analysed for the first two tidal periods. The results obtained in the errors analysis allow us to operate the model with a configuration that minimizes the error of the approximation methods. The model is validated through profile evolution assessment at various locations of coastline retreat on the Holderness Coast, Yorkshire, UK and on the north coast of Lake Erie, Ontario, Canada. The results represent an important stepforward in linking material properties to the processes of cliff recession, in considering the effect of groundwater charge and the slope oversteeping and their response to changing conditions caused by climate change (i.e. sea level, changes in lakes levels, etc.).

Damage localization and failure locus under biaxial loading in glass-fiber nonwoven felts

The pattern of damage localization and fracture under uniaxial and biaxial tension was studied in glass–fiber nonwoven felts. The analyses were carried out within the framework of the finite-element simulation of plain and notched specimens in which the microstructure of the felt, made up of fiber bundles connected at the cross point through an organic binder, was explicitly represented. Following previous experimental observations, fracture by interbundle decohesion and energy dissipation by frictional sliding between the bundles were included in the model. It was found that the failure path in these materials was controlled by the maximum applied normal stress, regardless of the loading path, and that the failure locus under biaxial tension was well represented by the von Mises failure criteria. The notch sensitivity of the nonwoven felts was limited and the presence of a notch did not modify the failure path.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Crack mechanical failure in ceramic materials under ion irradiation: case of lithium niobate crystal

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion- generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.