955 resultados para dynamic elastic modulus
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A sensitivity analysis has been performed to assess the influence of the elastic properties of railway vehicle suspensions on the vehicle dynamic behaviour. To do this, 144 dynamic simulations were performed modifying, one at a time, the stiffness and damping coefficients, of the primary and secondary suspensions. Three values were assigned to each parameter, corresponding to the percentiles 10, 50 and 90 of a data set stored in a database of railway vehicles.After processing the results of these simulations, the analyzed parameters were sorted by increasing influence. It was also found which of these parameters could be estimated with a lesser degree of accuracy in future simulations without appreciably affecting the simulation results. In general terms, it was concluded that the highest influences were found for the longitudinal stiffness and the lateral stiffness of the primary suspension, and the lowest influences for the vertical stiffness and the vertical damping of the primary suspension, with the parameters of the secondary suspension showing intermediate influences between them.
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The book represents a very interesting example of the possibility to combine in a single publication basic theory of structures and quite advanced topics on the same subject. The author fulfills this objective in a reasonable size book, less than 400 pages divided into 15 chapters averaging 20 pages each plus 9 short appendices. A diskette is also included in the book. This diskette contains training as well practical executable programs on different aspects of structural analysis, such as cross-sections properties,general-purpose computer programs for the static, dynamic and stability analysis of simple bar structures, etc. The book figures are didactic and have been carefully drawn.
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The thermal, mechanical, and adhesive properties of nanoclay-modified adhesives were investigated. Two organically modified montmorillonites: Cloisite 93A (C93A) and Nanomer I.30E (I.30E) were used as reinforcement of an epoxy adhesive. C93A and I.30E are modified with tertiary and primary alkyl ammonium cations, respectively. The aim was to study the influence of the organoclays on the curing, and on the mechanical and adhesive properties of the nanocomposites. A specific goal was to compare their behavior with that of Cloisite30B/epoxy and Cloisite15A/ epoxy nanocomposites that we have previously studied. Both C30B and C15A are modified with quaternary alkyl ammonium cations. Differential scanning calorimetry results showed that the clays accelerate the curing reaction, an effect that is related to the chemical structure of the ammonium cations. The three Cloisite/nanocomposites showed intercalated clay structures,the interlayer distance was independent of the clay content. The I.30E/epoxy nanocomposites presented exfoliated structure due to the catalytic effect of the organic modifier. Clay-epoxy nanocompo-sites showed lower glass transition temperature (Tg) and higher values of storage modulus than neat epoxy thermoset, with no significant differences between exfoliated or intercalated nanocom-posites. The shear strength of aluminum joints using clay/epoxy adhesives was lower than with the neat epoxy adhesive. The wáter aging was less damaging for joints with I.30E/epoxy adhesive.
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En esta investigación se ha estudiado el efecto de la variación de la temperatura en la deflexión de firmes flexibles. En primer lugar se han recopilado los criterios existentes de ajuste de la deflexión por efecto de la temperatura. Posteriormente, se ha llevado a cabo un estudio empírico mediante la auscultación de las deflexiones en cinco tramos de carretera con firme flexible y con diferentes espesores de mezclas bituminosas (entre 10 y 30 cm). Las medidas se han efectuado en dos campañas (verano e invierno), tratando de abarcar un amplio rango de temperaturas. En cada campaña, se han llevado a cabo distintas auscultaciones a diferentes temperaturas. Las medidas de cada campaña se han realizado el mismo día. Se han obtenido los coeficientes empíricos de ajuste por temperatura para cada tramo analizado. Además, se ha realizado un estudio teórico mediante la elaboración de diferentes modelos (multicapa elástico lineal, multicapa visco-elástico lineal y elementos finitos) que reproducen la respuesta estructural de los firmes flexibles auscultados. La caracterización mecánica de las mezclas bituminosas se ha realizado mediante ensayos de módulo complejo en laboratorio, a diferentes temperaturas y frecuencias, sobre testigos extraídos en las carreteras estudiadas. Se han calculado los coeficientes teóricos de ajuste por temperatura para cada modelo elaborado y tramo analizado. Finalmente, se ha realizado un estudio comparativo entre los distintos coeficientes de ajuste (existentes, empíricos y teóricos), que ha puesto de manifiesto que, en todos los casos analizados, los coeficientes obtenidos en el modelo de elementos finitos son los que más se aproximan a los coeficientes empíricos (valor de referencia para los tramos analizados). El modelo desarrollado de elementos finitos permite reproducir el comportamiento visco-elástico de las mezclas bituminosas y el carácter dinámico de las cargas aplicadas. Se han utilizado elementos tipo tetraedro isoparamétrico lineal (C3D8R) para el firme y la parte superior del cimiento, mientras que para la parte inferior se han empleado elementos infinitos (CIN3D8). In this research the effect produced by the temperature change on flexible pavements deflection is analysed. First, the existing criteria of deflection adjustment by temperature were collected. Additionally, an empirical analysis was carried out, consisting on deflection tests in five flexible-pavement road sections with different asphalt mix thickness (from 10 to 30 cm). The measures were taken in two seasons (summer and winter) in an effort to register a wide range of temperatures. Different surveys were carried out at different temperatures in each season. The tests of each season were done at the same day. The empirical temperature adjustment factors for every analysed section were obtained. A theoretical study was carried out by developing different models (linear elastic multilayer, linear visco-elastic multilayer and finite elements) that reproduce the structural response of the tested flexible pavements. The mechanical characterization of the asphalt mixes was achieved through laboratory complex-modulus tests at different temperatures and frequencies, using pavement cores from the surveyed roads. The theoretical temperature adjustment factors for each model developed and each section analysed were calculated. Finally, a comparative study among the different adjustment factors (existing, empirical and theoretical) was carried out. It has shown that, in all analysed cases, the factors obtained with the finite elements model are the closest to the empirical factors (reference value for the analysed sections). The finite elements model developed makes it possible to reproduce the visco-elastic behavior of the asphalt mixes and the dynamic nature of the applied loads. Linear isoparametric tetrahedral elements (C3D8R) have been used for the pavement and the subgrade, while infinite elements (CIN3D8) have been used for the foundations.
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La industria de la energía eólica marina ha crecido de forma significativa durante los últimos 15 años, y se espera que siga creciendo durante los siguientes. La construcción de torres en aguas cada vez más profundas y el aumento en potencia y tamaño de las turbinas han creado la necesidad de diseñar estructuras de soporte cada vez más fiables y optimizadas, lo que requiere un profundo conocimiento de su comportamiento. Este trabajo se centra en la respuesta dinámica de una turbina marina con cimentación tipo monopilote y sobre la que actúa la fuerza del viento. Se han realizado cálculos con distintas propiedades del suelo para cubrir un rango de rigideces que va desde una arena muy suelta a una muy densa. De este modo se ha analizado la influencia que tiene la rigidez del suelo en el comportamiento de la estructura. Se han llevado a cabo análisis estáticos y dinámicos en un modelo de elementos finitos implementado en Abaqus. El desplazamiento en la cabeza de la torre y la tensión en su base se han obtenido en función de la rigidez del suelo, y con ellos se ha calculado la amplificación dinámica producida cuando la frecuencia natural del sistema suelo‐cimentación torre se aproxima a la frecuencia de la carga. Dos diferentes enfoques a la hora de modelizar el suelo se han comparado: uno utilizando elementos continuos y otro utilizando muelles elásticos no lineales. Por último, un análisis de fiabilidad se ha llevado a cabo con un modelo analítico para calcular la probabilidad de resonancia del sistema, en el que se han considerado las propiedades de rigidez del suelo como variables aleatorias. Offshore wind energy industry has experienced a significant growth over the past 15 years, and it is expected to continue its growth in the coming years. The expansion to increasingly deep waters and the rise in power and size of the turbines have led to a need for more reliable and optimized support designs, which requires an extensive knowledge of the behaviour of these structures. This work focuses on the dynamic response of an offshore wind turbine founded on a monopile and subjected to wind loading. Different soil properties have been considered in order to cover the range of stiffness from a very loose to a very dense sand. In this way, the influence of stiffness on the structure behaviour has been assessed. Static and dynamic analyses have been carried out by means of a finite element model implemented in Abaqus. Head displacement and stress at the tower base have been obtained as functions of soil stiffness, and they have been used to calculate the dynamic amplification that is produced when the natural frequency of the system soil‐foundation‐tower approaches the load frequency. Two different approaches of soil modelling have been compared: soil modelled as a continuum and soil simulated with non linear elastic springs. Finally, a reliability analysis to assess the probability of resonance has been performed with an analytical model, in which soil stiffness properties are considered as stochastic variables.
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Una Red de Procesadores Evolutivos o NEP (por sus siglas en ingles), es un modelo computacional inspirado por el modelo evolutivo de las celulas, específicamente por las reglas de multiplicación de las mismas. Esta inspiración hace que el modelo sea una abstracción sintactica de la manipulation de information de las celulas. En particu¬lar, una NEP define una maquina de cómputo teorica capaz de resolver problemas NP completos de manera eficiente en tóerminos de tiempo. En la praóctica, se espera que las NEP simuladas en móaquinas computacionales convencionales puedan resolver prob¬lemas reales complejos (que requieran ser altamente escalables) a cambio de una alta complejidad espacial. En el modelo NEP, las cóelulas estóan representadas por palabras que codifican sus secuencias de ADN. Informalmente, en cualquier momento de cómputo del sistema, su estado evolutivo se describe como un coleccion de palabras, donde cada una de ellas representa una celula. Estos momentos fijos de evolucion se denominan configuraciones. De manera similar al modelo biologico, las palabras (celulas) mutan y se dividen en base a bio-operaciones sencillas, pero solo aquellas palabras aptas (como ocurre de forma parecida en proceso de selection natural) seran conservadas para la siguiente configuracióon. Una NEP como herramienta de computation, define una arquitectura paralela y distribuida de procesamiento simbolico, en otras palabras, una red de procesadores de lenguajes. Desde el momento en que el modelo fue propuesto a la comunidad científica en el año 2001, múltiples variantes se han desarrollado y sus propiedades respecto a la completitud computacional, eficiencia y universalidad han sido ampliamente estudiadas y demostradas. En la actualidad, por tanto, podemos considerar que el modelo teórico NEP se encuentra en el estadio de la madurez. La motivación principal de este Proyecto de Fin de Grado, es proponer una aproxi-mación práctica que permita dar un salto del modelo teórico NEP a una implantación real que permita su ejecucion en plataformas computacionales de alto rendimiento, con el fin de solucionar problemas complejos que demanda la sociedad actual. Hasta el momento, las herramientas desarrolladas para la simulation del modelo NEP, si bien correctas y con resultados satisfactorios, normalmente estón atadas a su entorno de ejecucion, ya sea el uso de hardware específico o implementaciones particulares de un problema. En este contexto, el propósito fundamental de este trabajo es el desarrollo de Nepfix, una herramienta generica y extensible para la ejecucion de cualquier algo¬ritmo de un modelo NEP (o alguna de sus variantes), ya sea de forma local, como una aplicación tradicional, o distribuida utilizando los servicios de la nube. Nepfix es una aplicacion software desarrollada durante 7 meses y que actualmente se encuentra en su segunda iteration, una vez abandonada la fase de prototipo. Nepfix ha sido disenada como una aplicacion modular escrita en Java 8 y autocontenida, es decir, no requiere de un entorno de ejecucion específico (cualquier maquina virtual de Java es un contenedor vólido). Nepfix contiene dos componentes o móodulos. El primer móodulo corresponde a la ejecución de una NEP y es por lo tanto, el simulador. Para su desarrollo, se ha tenido en cuenta el estado actual del modelo, es decir, las definiciones de los procesadores y filtros mas comunes que conforman la familia del modelo NEP. Adicionalmente, este componente ofrece flexibilidad en la ejecucion, pudiendo ampliar las capacidades del simulador sin modificar Nepfix, usando para ello un lenguaje de scripting. Dentro del desarrollo de este componente, tambióen se ha definido un estóandar de representacióon del modelo NEP basado en el formato JSON y se propone una forma de representation y codificación de las palabras, necesaria para la comunicación entre servidores. Adicional-mente, una característica importante de este componente, es que se puede considerar una aplicacion aislada y por tanto, la estrategia de distribution y ejecución son total-mente independientes. El segundo moódulo, corresponde a la distribucióon de Nepfix en la nube. Este de-sarrollo es el resultado de un proceso de i+D, que tiene una componente científica considerable. Vale la pena resaltar el desarrollo de este modulo no solo por los resul-tados prócticos esperados, sino por el proceso de investigation que se se debe abordar con esta nueva perspectiva para la ejecución de sistemas de computación natural. La principal característica de las aplicaciones que se ejecutan en la nube es que son gestionadas por la plataforma y normalmente se encapsulan en un contenedor. En el caso de Nepfix, este contenedor es una aplicacion Spring que utiliza el protocolo HTTP o AMQP para comunicarse con el resto de instancias. Como valor añadido, Nepfix aborda dos perspectivas de implementation distintas (que han sido desarrolladas en dos iteraciones diferentes) del modelo de distribution y ejecucion, que tienen un impacto muy significativo en las capacidades y restricciones del simulador. En concreto, la primera iteration utiliza un modelo de ejecucion asincrono. En esta perspectiva asincrona, los componentes de la red NEP (procesadores y filtros) son considerados como elementos reactivos a la necesidad de procesar una palabra. Esta implementation es una optimization de una topologia comun en el modelo NEP que permite utilizar herramientas de la nube para lograr un escalado transparente (en lo ref¬erente al balance de carga entre procesadores) pero produce efectos no deseados como indeterminacion en el orden de los resultados o imposibilidad de distribuir eficiente-mente redes fuertemente interconectadas. Por otro lado, la segunda iteration corresponde al modelo de ejecucion sincrono. Los elementos de una red NEP siguen un ciclo inicio-computo-sincronizacion hasta que el problema se ha resuelto. Esta perspectiva sincrona representa fielmente al modelo teórico NEP pero el proceso de sincronizacion es costoso y requiere de infraestructura adicional. En concreto, se requiere un servidor de colas de mensajes RabbitMQ. Sin embargo, en esta perspectiva los beneficios para problemas suficientemente grandes superan a los inconvenientes, ya que la distribuciín es inmediata (no hay restricciones), aunque el proceso de escalado no es trivial. En definitiva, el concepto de Nepfix como marco computacional se puede considerar satisfactorio: la tecnología es viable y los primeros resultados confirman que las carac-terísticas que se buscaban originalmente se han conseguido. Muchos frentes quedan abiertos para futuras investigaciones. En este documento se proponen algunas aproxi-maciones a la solucion de los problemas identificados como la recuperacion de errores y la division dinamica de una NEP en diferentes subdominios. Por otra parte, otros prob-lemas, lejos del alcance de este proyecto, quedan abiertos a un futuro desarrollo como por ejemplo, la estandarización de la representación de las palabras y optimizaciones en la ejecucion del modelo síncrono. Finalmente, algunos resultados preliminares de este Proyecto de Fin de Grado han sido presentados recientemente en formato de artículo científico en la "International Work-Conference on Artificial Neural Networks (IWANN)-2015" y publicados en "Ad-vances in Computational Intelligence" volumen 9094 de "Lecture Notes in Computer Science" de Springer International Publishing. Lo anterior, es una confirmation de que este trabajo mas que un Proyecto de Fin de Grado, es solo el inicio de un trabajo que puede tener mayor repercusion en la comunidad científica. Abstract Network of Evolutionary Processors -NEP is a computational model inspired by the evolution of cell populations, which might model some properties of evolving cell communities at the syntactical level. NEP defines theoretical computing devices able to solve NP complete problems in an efficient manner. In this model, cells are represented by words which encode their DNA sequences. Informally, at any moment of time, the evolutionary system is described by a collection of words, where each word represents one cell. Cells belong to species and their community evolves according to mutations and division which are defined by operations on words. Only those cells are accepted as surviving (correct) ones which are represented by a word in a given set of words, called the genotype space of the species. This feature is analogous with the natural process of evolution. Formally, NEP is based on an architecture for parallel and distributed processing, in other words, a network of language processors. Since the date when NEP was pro¬posed, several extensions and variants have appeared engendering a new set of models named Networks of Bio-inspired Processors (NBP). During this time, several works have proved the computational power of NBP. Specifically, their efficiency, universality, and computational completeness have been thoroughly investigated. Therefore, we can say that the NEP model has reached its maturity. The main motivation for this End of Grade project (EOG project in short) is to propose a practical approximation that allows to close the gap between theoretical NEP model and a practical implementation in high performing computational platforms in order to solve some of high the high complexity problems society requires today. Up until now tools developed to simulate NEPs, while correct and successful, are usu¬ally tightly coupled to the execution environment, using specific software frameworks (Hadoop) or direct hardware usage (GPUs). Within this context the main purpose of this work is the development of Nepfix, a generic and extensible tool that aims to execute algorithms based on NEP model and compatible variants in a local way, similar to a traditional application or in a distributed cloud environment. Nepfix as an application was developed during a 7 month cycle and is undergoing its second iteration once the prototype period was abandoned. Nepfix is designed as a modular self-contained application written in Java 8, that is, no additional external dependencies are required and it does not rely on an specific execution environment, any JVM is a valid container. Nepfix is made of two components or modules. The first module corresponds to the NEP execution and therefore simulation. During the development the current state of the theoretical model was used as a reference including most common filters and processors. Additionally extensibility is provided by the use of Python as a scripting language to run custom logic. Along with the simulation a definition language for NEP has been defined based on JSON as well as a mechanisms to represent words and their possible manipulations. NEP simulator is isolated from distribution and as mentioned before different applications that include it as a dependency are possible, the distribution of NEPs is an example of this. The second module corresponds to executing Nepfix in the cloud. The development carried a heavy R&D process since this front was not explored by other research groups until now. It's important to point out that the development of this module is not focused on results at this point in time, instead we focus on feasibility and discovery of this new perspective to execute natural computing systems and NEPs specifically. The main properties of cloud applications is that they are managed by the platform and are encapsulated in a container. For Nepfix a Spring application becomes the container and the HTTP or AMQP protocols are used for communication with the rest of the instances. Different execution perspectives were studied, namely asynchronous and synchronous models were developed for solving different kind of problems using NEPs. Different limitations and restrictions manifest in both models and are explored in detail in the respective chapters. In conclusion we can consider that Nepfix as a computational framework is suc-cessful: Cloud technology is ready for the challenge and the first results reassure that the properties Nepfix project pursued were met. Many investigation branches are left open for future investigations. In this EOG implementation guidelines are proposed for some of them like error recovery or dynamic NEP splitting. On the other hand other interesting problems that were not in the scope of this project were identified during development like word representation standardization or NEP model optimizations. As a confirmation that the results of this work can be useful to the scientific com-munity a preliminary version of this project was published in The International Work- Conference on Artificial Neural Networks (IWANN) in May 2015. Development has not stopped since that point and while Nepfix in it's current state can not be consid¬ered a final product the most relevant ideas, possible problems and solutions that were produced during the seven months development cycle are worthy to be gathered and presented giving a meaning to this EOG work.
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We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.
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Neste trabalho foi estudada a influência da adição de quitosana e sílica a monômeros dimetacrílicos, BisEMA e TEGDMA, por meio das técnicas de fotocalorimetria, termogravimetria e análise dinâmico mecânica. Os resultados dos experimentos de fotocalorimetria demonstraram que a quitosana pode aumentar a velocidade de polimerização e o máximo de conversão para alguns sistemas em determinadas concentrações da mesma, já a sílica tem pouco efeito nas reações de fotopolimerização das amostras. Para os experimentos de termogravimetria, a quitosana tem pouca influência na degradação das amostras não alterando significativamente as curvas TGA/DTG, por outro lado a sílica acelerou a degradação térmica das amostras. A avaliação das propriedades mecânicas demonstrou que a quitosana diminui a temperatura de transição vítrea e a resposta elástica dos sistemas não afetando os valores dos módulos de armazenamento e módulos de perda. A sílica apresentou a tendência de aumento de temperatura de transição vítrea e não alteração da resposta elástica das amostras.
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The effect of foundation embedment on settlement calculation is a widely researched topic in which there is no scientific consensus regarding the magnitude of settlement reduction. In this paper, a non-linear three dimensional Finite Element analysis has been performed with the aim of evaluating the aforementioned effect. For this purpose, 1800 models were run considering different variables, such as the depth and dimensions of the foundation and the Young’s modulus and Poisson’s ratio of the soil. The settlements from models with foundations at surface level and at depth were then compared and the relationship between them established. The statistical analysis of this data allowed two new expressions, with a mean maximum error of 1.80%, for the embedment influence factor of a foundation to be proposed and these to be compared with commonly used corrections. The proposed equations were validated by comparing the settlements calculated with the proposed influence factors and the true settlements measured in several real foundations. From the comprehensive study of all modelled cases, an improved approach, when compared to those proposed by other authors, for the calculation of the true elastic settlements of an embedded foundation is proposed.
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The conductance across an atomically narrow metallic contact can be measured by using scanning tunneling microscopy. In certain situations, a jump in the conductance is observed right at the point of contact between the tip and the surface, which is known as “jump to contact” (JC). Such behavior provides a way to explore, at a fundamental level, how bonding between metallic atoms occurs dynamically. This phenomenon depends not only on the type of metal but also on the geometry of the two electrodes. For example, while some authors always find JC when approaching two atomically sharp tips of Cu, others find that a smooth transition occurs when approaching a Cu tip to an adatom on a flat surface of Cu. In an attempt to show that all these results are consistent, we make use of atomistic simulations; in particular, classical molecular dynamics together with density functional theory transport calculations to explore a number of possible scenarios. Simulations are performed for two different materials: Cu and Au in a [100] crystal orientation and at a temperature of 4.2 K. These simulations allow us to study the contribution of short- and long-range interactions to the process of bonding between metallic atoms, as well as to compare directly with experimental measurements of conductance, giving a plausible explanation for the different experimental observations. Moreover, we show a correlation between the cohesive energy of the metal, its Young's modulus, and the frequency of occurrence of a jump to contact.
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"Project no. 9782. Contract AF 49 (638)-430 ... CU-11-60-AF-430-CE."
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Thesis (Ph.D.)--University of Washington, 2016-06
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Dynamic rheological behaviour of starch-honey systems was studied using a strain-controlled rheometer. A dynamic temperature (30-130 degreesC) ramp test was used at 10 rad s(-1) frequency, 1% strain, 2 degreesC min(-1) ramp rate, 25 mm parallel plate, and 1.5 min gap, using Wheaten cornflour(TM) and five honeys to generate 25 formulations (0.34-0.80 g water/g dry starch). G', G, and eta* increased upon gelatinisation, and they reduced as the honey content was increased. For all the formulations, G' was higher than G, and tan 6 was generally less than 1.0. Key gelatinisation characterising temperatures (onset, peak and end) ranged from 96.0 to 122.3 degreesC, but did not vary much (CV < 5%) for each honey irrespective of the concentration. The influence of water, fructose and glucose, singly and in combination, on gelatinisation indices (temperature and rheological parameters) was investigated. An exponential equation was employed to describe the relationship, and relevant parameters were obtained. The consequences of the observations in the study are discussed particularly as they relate to extrusion of such systems, and possible interactions between fructose and glucose in the starch-honey systems. (C) 2003 Elsevier Ltd. All rights reserved.
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The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.
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An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particle-based numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.