Multiscale multiphysics simulation in composite materials

The improvements in terms of computational power provides the capability to analyze with more detail the materials behavior. On one hand, going deeper in the materials to study an increasingly smaller dimension and capture micro- or nano- changes. On the other hand, the increasing computational memory allows to perform finite elements analysis with billions of nodes, that permits to obtain more accurate results. In this sense, the focus of this work is the numerical modeling of the microscale behavior of inhomogeneous materials, with special attention to composite materials under thermo-mechanical loading conditions. This work also proposes and implements optimization tools, at a constitutive law level, as well as the level of both, macro- and micro-structural algorithms. The thesis is proposed as compendium of articles written during the last years and all published in Q1 international journals. In the first publication, a novel damage-mechanics micro-model is presented, able to represent the mechanical behaviors of masonry constituents. The proposed micro-model is based on a tension-compression continuum damage model. The adoption of appropriate failure criteria enables controlling the dilatant behavior of the material, even though this aspect is not generally associated to continuum damage models as it is for plasticity models. The study proposes a simple solution to this issue, consisting in the appropriate definition of the failure surfaces under shear stress states, together with the formulation of proper evolution laws for damage variables. The model keeps the simple and efficient format of classical damage models, where the explicit evaluation of the internal variables avoids nested iterative procedures, thus increasing computational performance and robustness. Another purpose of this research is to carry out a critical comparison of the proposed continuous micro-model with other two well-known discrete micro-modeling strategies. The second publication presents a full thermo-mechanical multiscale methodology, covering the nano-, micro-, and macroscopic scales. In such methodology, direcly deriving from the Classical First-Order Multiscale Method, fundamental material properties are determined by means of molecular dynamics simulations. Afterwards, the material properties obtained are used at the microstructural level by means of finite element analyses. Finally, the macroscale problem is solved while considering the effect of the microstructure using a thermo-mechanical homogenization on a representative volume element (RVE). The publication that close this thesis presents two computationally efficient multiscale procedures able to predict the mechanical non-linear response of composite materials. This is achieved, using an RVE Data Base (DB) calculated a-priori. Through the definitions of an equivalent damage parameter ($d_{eq}$), function of the global stress at the microscale, a series of strain controlled virtual tests of the RVE are performed storing in the DB the homogenized stress and strain state reached at certain levels of d_eq. Afterwards, the solution of the macroscale structure can be solved using the interpolation of the stored data. The first proposed procedure, named Discrete Multiscale Threshold Surface definition (DMTS), stores in the database the tenso-deformational state in which damage starts. Once reaching this state, a non-linear analysis will require the construction of the RVE to analyze the material damage evolution. On the other hand, the second method proposed, named Discrete Multiscale Constitutive Model (DMCM), is completely based on offline data and uses only the stress information stored in the DB to obtain the failure threshold and the non-linear material performance. In the article, special attention has been paid on the construction and validation of the Data Base, as well as on the study of a complete composite structure comparing the speedup obtained with both methods.En las últimas décadas, el avance en términos de poder computacional ofrece la capacidad de analizar más detalladamente el comportamiento de los materiales. Por un lado, profundizar los materiales para estudiar una dimensión cada vez más pequeña y capturar micro o nanocambios. Por otro lado, la capacidad de memoria computacional permite realizar análisis de elementos finitos con miles de millones de nodos, lo que permite obtener resultados lo más exacto posible. El objetivo de este trabajo es la modelización numérica del comportamiento microescala de materiales no homogéneos, con especial atención a los materiales compuestos, en condiciones de carga termo-mecánica, y la aplicación de herramientas de optimización de las leyes constitutivas, así como en a nivel macro y micro estructural. La tesis se propone como un compendio de artículos publicados en revistas internacionales. En la primera publicación, se presenta un micro-modelo basado en el daño mecánico, capaz de representar los comportamientos mecánicos de las estructura de mampostería. El micro-modelo propuesto se basa en un modelo de daño continuo por tensión-compresión. La adopción de criterios de daño apropiados permite al analista controlar la dilatancia del material, aunque este aspecto no está generalmente asociado a los modelos de daño continuo como lo es para los modelos de plasticidad. El estudio propone una solución simple a este problema, que consiste en la definición apropiada de las superficies de daño bajo estados de tensión de cortante junto con la formulación de leyes de evolución apropiadas para las variables de daño. El modelo mantiene el formato simple y eficiente de los modelos de daños clásicos, donde la evaluación explícita de las variables internas evita los procedimientos iterativos anidados, aumentando así el rendimiento computacional. Otro objetivo de esta investigación es realizar una comparación crítica del micro-modelo continuo propuesto con otras dos estrategias bien conocidas de micro-modelado discreto. Posteriormente, se presenta una metodología termomecánica multiescala completa, que cubre las escalas nano, micro y macroscópica. En dicha metodología, derivada directamente del Método Multiescala de Primer Orden, las propiedades fundamentales del material se determinan mediante simulaciones de dinámica molecular que se implementan en consecuencia a nivel microestructural por medio de análisis de elementos finitos. Por otro lado, el problema de macroescala se resuelve considerando el efecto de la microestructura mediante homogeneización termo-mecánica en un elemento de volumen representativo (RVE). Finalmente, se proponen dos procedimientos multiescala computacionalmente eficientes capaces de predecir la respuesta mecánica no lineal de materiales compuestos. Esto se logrará utilizando una base de datos (DB) calculada a priori. A través de las definiciones de un parámetro de daño equivalente (d_eq), funciónes de la tensión global de la microescala, se actuarán una serie de pruebas virtuales de la microescala con deformación controlada para almacenar en el DB el estrés y la tensión homogeneizadas alcanzado en ciertos niveles de d_eq. Posteriormente, la solución de la estructura de macroescala mediante el método multiescala de primer orden se reemplazará por la interpolación de los datos almacenados en el DB. El primer método propuesto, llamado Discrete Multiscale Threshold Surface (DMTS), proporcionará la generación de la RVE en la parte no lineal de la estructura, mientras que el segundo, llamado Discrete Multiscale Constitutive Model (DMCM), es completamente independiente del micromodelo porque solo se utiliza la información de estrés almacenada en el DB. En el articulo se ha prestado especial atención a la creación y validación de la base de datos y al estudio de una estructura compuesta completa comparando la aceleración en terminos de tiempo computationál obtenid

SRM Igniter Jet Simulation

The design and development of solid rocket motor (SRM) need to predict the internal gas-dynamic phenomena that happen during the SRM operative life. The operative life of a SRM can be divided in a sequence of different phases: the first phase is the ignition transient during which the solid propellant is ignited; the second phase is the quasi-steady phase during which the SRM reaches the design operative conditions; finally there is the combustion-tail during which the combustion of solid propellant extinguishes. The phenomena happening during ignition transient are often more critical than those occurring in the subsequent phases; within a fraction of a second hot igniter gases flow in the combustion chamber reaching supersonic conditions; pressure jumps of tenths of atmospheres and temperature peaks of thousands of Kelvin degrees can occur. The ignition transient unsteady behaviour can cause net thrust and pressure transients, over-pressure peaks, hang-fires or misfires, propellant grain stresses, dynamic loads on the launch vehicle (and on its payload) and on the ground segment etc... All the above phenomena can compromise the performances of the SRM and often the successful of the launch. The study of the SRM ignition transient is the research background of this Ph.D. dissertation. It is common and well confirmed practice in industry to analyze ignition transient using zero-dimensional, volume-filling or one-dimensional physical models, and only recently two-dimensional approaches can be found. Presently the increasing of the computational capabilities allows to a fully three-dimensional study. The reasons to develop a three-dimensional model are numerous: first of all the combustion chamber of a common SRM has often a three-dimensional geometry; second the igniter nozzles has a three-dimensional configuration with both axial and radial nozzles. Therefore the gas-dynamic phenomena generated by the igniter jets have strong three-dimensional behaviour that is impossible to study by means of a non fully three-dimensional model. The aim of this research is to present and provide suitable three-dimensional model and numerical tools able to describe the SRM ignition transient with particular interest to study the gasdynamical aspects of SRM ignition transient

A Numerical and Experimental Study On the Hydrodynamic of a Catamara Varying the Demihull Separation

A complementary experimental and numerical study of the interference eect for a fast catamaran is presented. Resistance, sinkage and trim are collected by towing tank experiments for Froude number in the range from 0:2 to 0:8 for several separation distances and for the monohull. Resistance coefficient curves reveal the presence of two humps, the second one strongly depending on the separation length; high interference is observed in correspondence of the second hump. To gain a deeper insight into these behaviors, a complementary analysis is carried out by a numerical campaign; simulations are performed by means of an in-house unsteady RANS solver. Verication of numerical results is provided, together with validation, which is made by the comparison with both present and other experimental data. Agreement in terms of resistance coefficient is rather good, comparison error being always smaller than 2.2%

Adaptive and off-line techniques for non-linear multiscale analysis

This paper presents two procedures, based on the numerical multiscale theory, developed to predict the mechanical non-linear response of composite materials under monotonically increasing loads. Such procedures are designed with the objective of reducing the computational cost required in these types of analysis. Starting from virtual tests of the microscale, the solution of the macroscale structure via Classical First-Order Multiscale Method will be replaced by an interpolation of a discrete number of homogenized surfaces previously calculated. These surfaces describe the stress evolution of the microscale at fixed levels of an equivalent damage parameter (). The information required for these surfaces to conduct the analysis is stored in a Data Base using a json format. Of the two methods developed, the first one uses the pre-computed homogenized surface just to obtain the material non-linear threshold, and generates a Representative Volume Element (RVE) once the material point goes into the nonlinear range; the second method is completely off-line and is capable of describing the material linear and non-linear behavior just by using the discrete homogenized surfaces stored in the Data Base. After describing the two procedures developed, this manuscript provides two examples to validate the capabilities of the proposed method

Adaptive and off-line techniques for non-linear multiscale analysis

This paper presents two procedures, based on the numerical multiscale theory, developed to predict the mechanical non-linear response of composite materials under monotonically increasing loads. Such procedures are designed with the objective of reducing the computational cost required in these types of analysis. Starting from virtual tests of the microscale, the solution of the macroscale structure via Classical First-Order Multiscale Method will be replaced by an interpolation of a discrete number of homogenized surfaces previously calculated. These surfaces describe the stress evolution of the microscale at fixed levels of an equivalent damage parameter (). The information required for these surfaces to conduct the analysis is stored in a Data Base using a json format. Of the two methods developed, the first one uses the pre-computed homogenized surface just to obtain the material non-linear threshold, and generates a Representative Volume Element (RVE) once the material point goes into the nonlinear range; the second method is completely off-line and is capable of describing the material linear and non-linear behavior just by using the discrete homogenized surfaces stored in the Data Base. After describing the two procedures developed, this manuscript provides two examples to validate the capabilities of the proposed methods.Postprint (author's final draft

Thermo-mechanical homogenization of composite materials

Postprint (published version

Nuevo Modelo Discreto Multiescala (DM) para análisis no-lineales de materiales compuestos

En los últimos años el estudio del comportamiento de los materiales a nivel microscópico ha aumentado significativamente en términos de diseño de materiales de altas prestaciones. A pesar de los recientes avances de ordenadores de elevado rendimiento, la aplicación de métodos numéricos multiescala para simular grandes estructuras aún requiere costes computacionales prohibitivos. Éste trabajo presenta un procedimiento capaz de predecir la respuesta mecánica no-lineal de los materiales compuestos con el fin de reducir el coste computacional necesario para el análisis numérico de estructuras complejas. La solución de la estructura macroscópica a través del método multiescala de primer orden (FE2) se sustituirá por un modelo discreto obtenido de un análisis del comportamiento de un Volumen Representativo Elemental (RVE) del material. A través de las definiciones de un parámetro de daño equivalente (deq), función del esfuerzo global en la microescala, se realizarán una serie de ensayos virtuales en control de deformación, almacenando el estado de tensión-deformación alcanzado por ciertos niveles de deq en una base de datos. Analizando la evolución de la fractura en los materiales compuestos se puede observar como el régimen no-lineal se alcanza solo en algunos elementos de la estructura. Es por ello que se plantea un procedimiento, el Discrete Multiscale Threshold Surface (DMTS), en el que el análisis del RVE sirve para obtener la superficie en la que empieza el daño (deq >0). Esta ley permite saber si para un determinado estado tenso-deformacional el material ha dañado, sin necesidad de resolver el micro-modelo. Una vez iniciado el daño, se propone de generar de forma adaptiva un RVE con el que obtener el comportamiento dañado del material. Luego, el método FE2 se utilizará solo en los puntos de integración que hayan dañado. Este trabajo demuestra que el método FE2 puede ser remplazado por un Modelo Discreto Multiescala, representativo del material compuesto, obteniendo mejoras computacionales significativas

Micro-scale continuous and discrete numerical models for nonlinear analysis of masonry shear walls

A novel damage mechanics-based continuous micro-model for the analysis of masonry-walls is presented and compared with other two well-known discrete micro-models. The discrete micro-models discretize masonry micro-structure with nonlinear interfaces for mortar-joints, and continuum elements for units. The proposed continuous micro-model discretizes both units and mortar-joints with continuum elements, making use of a tension/compression damage model, here refined to properly reproduce the nonlinear response under shear and to control the dilatancy. The three investigated models are validated against experimental results. They all prove to be similarly effective, with the proposed model being less time-consuming, due to the efficient format of the damage model. Critical issues for these types of micro-models are analysed carefully, such as the accuracy in predicting the failure load and collapse mechanism, the computational efficiency and the level of approximation given by a 2D plane-stress assumption.Peer ReviewedPostprint (author's final draft

Nuevo modelo discreto multiescala (DM) para análisis no-lineales de materiales compuestos

En los últimos años el estudio del comportamiento de los materiales a nivel microscópico ha aumentado significativamente en términos de diseño de materiales de altas prestaciones. A pesar de los recientes avances de ordenadores de elevado rendimiento, la aplicación de métodos numéricos multiescala para simular grandes estructuras aún requiere costes computacionales prohibitivos. Éste trabajo presenta un procedimiento capaz de predecir la respuesta mecánica no-lineal de los materiales compuestos con el fin de reducir el coste computacional necesario para el análisis numérico de estructuras complejas. La solución de la estructura macroscópica a través del método multiescala de primer orden (FE2) se sustituirá por un modelo discreto obtenido de un análisis del comportamiento de un Volumen Representativo Elemental (RVE) del material. A través de las definiciones de un parámetro de daño equivalente función del esfuerzo global en la microescala, se realizarán una serie de ensayos virtuales en control de deformación, almacenando el estado de tensión-deformación alcanzado por ciertos niveles de daño equivalente en una base de datos. Analizando la evolución de la fractura en los materiales compuestos se puede observar como el régimen no-lineal se alcanza solo en algunos elementos de la estructura. Es por ello que se plantea un procedimiento, el Discrete Multiscale Threshold Surface (DMTS), en el que el análisis del RVE sirve para obtener la superficie en la que empieza el daño. Esta ley permite saber si para un determinado estado tenso-deformacional el material ha dañado, sin necesidad de resolver el micro-modelo. Una vez iniciado el daño, se propone de generar de forma adaptiva un RVE con el que obtener el comportamiento dañado del material. Luego, el método FE2 se utilizará solo en los puntos de integración que hayan dañado. Este trabajo demuestra que el método FE2 puede ser remplazado por un Modelo Discreto Multiescala, representativo del material compuesto, obteniendo mejoras computacionales significativasPostprint (published version

Multiscale thermo-mechanical analysis of multi-layered coatings in solar thermal applications

Solar selective coatings can be multi-layered materials that optimize the solar absorption while reducing thermal radiation losses, granting the material long-term stability. These layers are deposited on structural materials (e.g., stainless steel, Inconel) in order to enhance the optical and thermal properties of the heat transfer system. However, interesting questions regarding their mechanical stability arise when operating at high temperatures. In this work, a full thermo-mechanical multiscale methodology is presented, covering the nano-, micro-, and macroscopic scales. In such methodology, fundamental material properties are determined by means of molecular dynamics simulations that are consequently implemented at the microstructural level by means of finite element analyses. On the other hand, the macroscale problem is solved while taking into account the effect of the microstructure via thermo-mechanical homogenization on a representative volume element (RVE). The methodology presented herein has been successfully implemented in a reference problem in concentrating solar power plants, namely the characterization of a carbon-based nanocomposite and the obtained results are in agreement with the expected theoretical values, demonstrating that it is now possible to apply successfully the concepts behind Integrated Computational Materials Engineering to design new coatings for complex realistic thermo-mechanical applications.Peer ReviewedPostprint (author's final draft