Implementation of a general algorithm for incompressible and compressible flows within the multi-physics code Kratos and preparation of fluid-structure coupling

This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of this environment based on the finite element method (FEM) and an introduction to multidisciplinary problems in general are the starting point of this work and help understanding the following steps more easily. Originating from the basic conservation equations for mass, momentum and energy, the Euler equations for inviscid flow are derived. In this context some approximations are presented that avoid the solution of the energy equation and allow the use of a general approach for the simulation of incompressible, slightly compressible and barotropic flow. The implementation of the incompressible case is outlined step-by-step: Having discretized the continuous problem, a fractional step scheme is presented in order to uncouple pressure and velocity components by a split of the momentum equation. Emphasis is placed on the nodal implementation using an edge-based data structure. Moreover, the orthogonal subscale stabilization - necessary because of the finite element discretization - is explained very briefly. Subsequently, the solver is extended to compressible regime mentioning the respective modifications. For validation purposes numerical examples of incompressible and compressible flows in two and three dimensions round of this first part. In a second step, the implemented flow solver is prepared for the fluid-structure coupling. After presenting solving procedures for multi-disciplinary problems, the arbitrary Lagrangian Eulerian (ALE) formulation is introduced and the conservation equations are modified accordingly. Some preliminary tests are performed, particularly with regard to mesh motion and adjustment of the boundary conditions. Finally, expectations for the envisaged fluid-structure coupling are brought forward

Implementation of a general algorithm for incompressible and compressible flows within the multi-physics code KRATOS and preparation of fluid-structure coupling

This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of this environment based on the finite element method (FEM) and an introduction to multidisciplinary problems in general are the starting point of this work and help understanding the following steps more easily. Originating from the basic conservation equations for mass, momentum and energy, the Euler equations for inviscid flow are derived. In this context some approximations are presented that avoid the solution of the energy equation and allow the use of a general approach for the simulation of incompressible, slightly compressible and barotropic flow. The implementation of the incompressible case is outlined step-by-step: Having discretized the continuous problem, a fractional step scheme is presented in order to uncouple pressure and velocity components by a split of the momentum equation. Emphasis is placed on the nodal implementation using an edge-based data structure. Moreover, the orthogonal subscale stabilization - necessary because of the finite element discretization - is explained very briefly. Subsequently, the solver is extended to compressible regime mentioning the respective modifications. For validation purposes numerical examples of incompressible and compressible flows in two and three dimensions round of this first part. In a second step, the implemented flow solver is prepared for the fluid-structure coupling. After presenting solving procedures for multi-disciplinary problems, the arbitrary Lagrangian Eulerian (ALE) formulation is introduced and the conservation equations are modified accordingly. Some preliminary tests are performed, particularly with regard to mesh motion and adjustment of the boundary conditions. Finally, expectations for the envisaged fluid-structure coupling are brought forward.Preprin

Numerical modelling based on the multiscale homogenization theory. Application in composite materials and structures

A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents. The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs. Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method.En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala

Continuum modelling using the discrete element method. theory and implementation in an object-oriented software platform

The Discrete Element Method is a relatively new technique that has nowadays and intense research in the field of numerical methods. In its first conception, the method was designed for simulations of dynamic system of particles where each element is considered to be an independent and non-deformable entity that interacts with other particles by the laws of the contact mechanics and moves following the second Newton’s law. This first approach for the DEM has obtained excellent results for granular media simulations or another discontinuouslike case. The existing challenge nowadays for the DEM is to be able to simulate the behaviour on a continuous media discretized by a mesh of particles ruled by the equations of the DEM. Although there exist more adequate methods to solve the continuous problem as they are the different variants of the Finite Element Method, the DEM is expected to have a better behaviour when the failure of the media occurs; in terms of tracking the evolution of the fracture locally between the elements of the discretization and also the post-fractural behaviour of the material. Nowadays, there are several DEM codes that try to solve this problem although there is no one which can assure an accurate solution applicable universally to any case. The objective of the present work is to develop calculation software for the Discrete Element Method included in the platform for numerical methods KRATOS, which is developed in CIMNE. One of the goals of the so-called DEM-Application is to be able to reproduce a wide set of engineering problems; not only the discrete ones such as the excavation or agroalimentary applications but also to reproduce the continuous media, simulating compression test for concrete or asphalt samples for instance. In addition it is desired that the application permits the coupling with another methods, particularly the Finite Element Method. In order to do this, the present work includes the study of all the advances and ideas that, globally in the numerical method field and particularly in CIMNE, have been discussed to give other approaches and to keep improving and developing the to the Discrete Element Method

Kratos Dem, a paralel code for concrete testing simulations using the discrete element method

This dissertation is the result of the implementation of a Discrete Element Method code in an open source object-oriented software platform called Kratos developed in CIMNE (Barcelona). After the introduccion and the objectives, a brief review on the Discrete Element Method in its basic conception is presented in the third chapter of the document while the theoretical developments and discussions for the application of the method to continous media, specially to conctrete testing simulation, can be found in the fourth chapter. Also here, special attention is paid to the capabilities of this method when it is applied to continuous media; several numerical analisis are performed here to show the possibilities and limitations of the method in the fifth chapter. In the sixth chapter, the Kratos framework is introduced and the basic structure of the developed application is explained. The implementation of the utilities that permit, from a user-friendly interface, perform concrete test simulations can be found here. Furthermore, the possibilities and advatages that the Kratos framework provides the DEM-Application are shown as well as examples of how the code behaves in terms of High Performance Computing. Additionally, examples of coupling of this application with other codes and work done by other researchers in the institution are here presented. In the seventh chapter, the results of the different concrete simulation tests can be found as a verification of the code comparing with the results obained by Dempack. Finally, in the last chapter some conclusions and future work is presented. The objective of the KDEM, in its conception, was to have a base program for the DEM coded in a very powerful and versatile platform, the open-source multiphysics code Kratos. This permits different researchers extending and improving the code as well as using as a closed package for projects and simulation by advanced users and engineers. Previous to this, in CIMNE, another code based on the Discrete Element Method has been used for engineering projects, Dempack. When the KDEM code started the purpose was to provide CIMNE a general DEM application able to be parallelized and to be combined with other fluid or structure applications. At the same time, a lot of implementation has been done in order to substitute, and improve if possible, the existing code Dempack; part of this thesis focuses on the concrete test simulation, a field where CIMNE has currently projects ongoing. The result of this work accomplishes the objective of providing Kratos a general purpose paralelizable Discrete Element Method application which is the of the interest of CIMNE. In a second term, it presents the first promising results in the field of Concrete Test Simulation, following the objective of substituing in the future, the existing application, Dempack

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

Multiscale computational modeling of single cell migration in 3D

La migración celular es un proceso complejo, orquestado por factores químicos y biológicos, por la microestructura y por las propiedades mecánicas de la matriz extracelular. Este fenómeno es fundamental para el desarrollo de tejidos en los organismos pluricelulares, y como seres humanos, nos acompaña durante toda la vida, desde el mismo momento de la concepción hasta la muerte. Juega un papel fundamental durante el desarrollo embrionario determinando la formación de los diferentes órganos (morfogénesis) y es clave en todos los procesos regenerativos como la renovación de la piel, la respuesta inflamatoria o la cicatrización de heridas. Sin embargo, también contribuye al desarrollo de procesos patológicos como la metástasis, el retraso mental, la osteoporosis o enfermedades vasculares entre otros. Es por ello de vital importancia el conocer los mecanismos fundamentales que controlan la migración celular con el fin de tratar de manera efectiva las diferentes patologías, así como avanzar en el trasplante de órganos y el desarrollo de tejidos artificiales. Así pues, el objetivo de esta Tesis es el desarrollo de modelos a distintas escalas y centrados en diversos aspectos de la migración, de manera que faciliten la compresión de fenómenos específicos y sirvan como guía para el diseño de experimentos. Dada la complejidad y las grandes diferencias respecto a la migración colectiva, todos los modelos y análisis de esta Tesis se centran en células individuales. En primer lugar se ha estudiado la migración tridimensional de una célula individual embebida en una matriz extracelular donde su velocidad y orientación se consideran reguladas por estímulos mecánicos. Para ello se ha desarrollado un modelo mecanosensor basado en elementos finitos y se ha analizado el comportamiento celular en función de diferentes rigideces y condiciones de contorno a escala celular. A medida que el trabajo ha progresado, los resultados del modelo unidos a nuevos avances científicos publicados en este ámbito, han reforzado la idea de que el mecansimo mecanosensor juega un papel crítico en los procesos que dirigen la migración celular. Por ello, se ha necesitado un estudio más profundo de este fenómeno para lo que se ha utilizado un modelo mucho más detallado a escala intracelular. Así pues, se ha explorado la estructura interna del citoesqueleto y su comportamiento ante cambios mecánicos en la matriz extracelular, utilizando un modelo discreto de partículas basado en dinámica Browniana con el que se ha simulado la formación de una red de actina (polimerización) entrecruzada con proteínas y motores moleculares. En concreto, se ha estudiado el comportamiento activo de estos motores y su papel como sensores de estímulos mecánicos externos (mecanosensores) de manera que los resultados obtenidos con este modelo “micro” han permitido validar las hipótesis del modelo previo. Consecuentemente, se ha revisado el modelo mecánico y se le ha añadido dependencia temporal, obteniendo un modelo continuo capaz de predecir respuestas celulares macroscópicas basadas en el comportamiento de los componentes microestructurales. En otras palabras, esta simplificación ha permitido la introducción de la respuesta macroscópica emergente obtenida del comportamiento dinámico de la microestructura, disminuyendo enormemente el coste computacional y por tanto permitiendo simulaciones a mayores escalas espacio-temporales. A continuación se han introducido las nuevas hipótesis en un modelo probabilístico de migración a escala celular basado en elementos finitos que permite al mismo tiempo el estudio de factores tanto a escala macroscópica (velocidades, trayectorias) como a escala celular (orientación, área de adhesión, tensiones celulares, desplazamientos de la matriz etc.). Adicionalmente, este modelo es sensible no sólo a la mecánica sino a las condiciones fluido-químicas del entorno, las cuales han sido analizadas igualmente mediante simulaciones por elementos finitos. Con todo esto, los modelos desarrollados todavía no incluyen una descripción detallada de procesos importantes envueltos en la migración celular como la protrusión de la membrana, la polimerización de actina en el frente celular o la formación de adhesiones focales. Por lo tanto, para completar la Tesis, se ha desarrollado un modelo continuo basado en diferencias finitas que permite el estudio del comportamiento dinámico del lamelipodio y el papel fundamental que juegan la polimerización de actina, los motores moleculares y las adhesiones focales (FAs) en el frente celular durante la migración. Cell migration is a complex process, orchestrated by biological and chemical factors, and by the microstructure and extracellular matrix (ECM) mechanical properties among others. It is essential for tissue development in multicellular organisms, and as human beings, it accompanies us throughout life, from conception to death. It plays a major role during embryonic development, defining organ formation (morphogenesis) and being crucial in all the regenerative processes such as skin renewal, inflammatory response or wound healing. However, it is also involved in several pathological processes e.g. metastasis, mental retardation, osteoporosis or vascular diseases. Therefore, understanding the fundamental mechanisms controling cell migration is vitally important to effectively treat different pathologies and to make progress in organ transplantation and tissue development. Thus, the main scope of this Thesis is the development of mathematical models at different scales and focused on different aspects of cell migration so that specific phenomena can be better understood, serving as a guide for the development of new experiments. All the models and analysis contained in this thesis are focused on single cells, firstly due to the complexity and marked differences with respect to collective cell migration, and secondly owing to the importance of individual migration in important processes such as metastatic tumor cell migration. In addition, since three- dimensional environments are physiologically more relevant, 3D approaches have been considered in most of the models here developed to better mimic in vivo conditions. Firstly, single cell migration of a cell embedded in a three-dimensional matrix was studied, regulating its velocity and polarization through mechanical clues. For this purpose, a finite element (FE) based mechanosensing model was developed, analyzing cell behavior according to different ECM rigidities and boundary conditions at the cell scale. As work advanced, results from the model together with recent findings from literature strengthened the idea that mechanosensing plays a critical role in cell motility driving processes. For this reason, a deeper understanting of this mechanism was needed, resulting in the development of a specific and more detailed model (at the intracellular scale). Hence, the cytoskeletal structure response to mechanical stimuli has been explored using a discrete particle-based Brownian dynamics model. This model was used to simulate the formation of actin networks (through actin polymerization) cross-linked with proteins (ACPs) and molecular motors. Specifically, the active role of molecular motors and their role as mechanosensors were studied, so that the results of the intracellular scale approach allowed the validation of the previous model main assumptions. As a consequence, the mechanical hypothesis were revised and a temporal dependence was incorporated, obtaining a new continuum model able to predict macroscopic cell responses based on microstructural components behavior. In other words, this simplification allowed introducing the emergent macroscopic response obtained from the active behavior of the microstructure, saving large amounts of computational time and permitting simulations at higher time and length scales. Next, the new hypotheses were incorporated into a probabilistic, FE-voxel-based cell-scale migration model, permitting simultaneously the study of macro-scale factors (velocities, trajectories) and cell-scale ones (polarization, adhesion area, cell stress, ECM displacements etc.). Additionally this model includes the effect of fluid-chemical stimuli, which was also analyzed by means of FE-simulations. With all this, the developed models still lacked a detailed description of important processes involved in cell migration such as membrane protrusion, actin polymerization or focal adhesion (FA) formation. As a result, a continuum model was designed to study the lamellipodium dynamics and the major role of actin polymerization and focal adhesions (FA) at the cell front during cell migration

New Trends in 3D Printing

A quarter century period of the 3D printing technology development affords ground for speaking about new realities or the formation of a new technological system of digital manufacture and partnership. The up-to-date 3D printing is at the top of its own overrated expectations. So the development of scalable, high-speed methods of the material 3D printing aimed to increase the productivity and operating volume of the 3D printing machines requires new original decisions. It is necessary to study the 3D printing applicability for manufacturing of the materials with multilevel hierarchical functionality on nano-, micro- and meso-scales that can find applications for medical, aerospace and/or automotive industries. Some of the above-mentioned problems and new trends are considered in this book

On the control of propagating acoustic waves in sonic crystals: analytical, numerical and optimization techniques

El control de las propiedades acústicas de los cristales de sonido (CS) necesita del estudio de la distribución de dispersores en la propia estructura y de las propiedades acústicas intrínsecas de dichos dispersores. En este trabajo se presenta un estudio exhaustivo de diferentes distribuciones, así como el estudio de la mejora de las propiedades acústicas de CS constituidos por dispersores con propiedades absorbentes y/o resonantes. Estos dos procedimientos, tanto independientemente como conjuntamente, introducen posibilidades reales para el control de la propagación de ondas acústicas a través de los CS. Desde el punto de vista teórico, la propagación de ondas a través de estructuras periódicas y quasiperiódicas se ha analizado mediante los métodos de la dispersión múltiple, de la expansión en ondas planas y de los elementos finitos. En este trabajo se presenta una novedosa extensión del método de la expansión en ondas planas que permite obtener las relaciones complejas de dispersión para los CS. Esta técnica complementa la información obtenida por los métodos clásicos y permite conocer el comportamiento evanescente de los modos en el interior de las bandas de propagación prohibida del CS, así como de los modos localizados alrededor de posibles defectos puntuales en CS. La necesidad de medidas precisas de las propiedades acústicas de los CS ha provocado el desarrollo de un novedoso sistema tridimensional que sincroniza el movimiento del receptor y la adquisición de señales temporales. Los resultados experimentales obtenidos en este trabajo muestran una gran similitud con los resultados teóricos. La actuación conjunta de distribuciones de dispersores optimizadas y de las propiedades intrínsecas de éstos, se aplica para la generación de dispositivos que presentan un rango amplio de frecuencias atenuadas. Se presenta una alternativa a las barreras acústicas tradicionales basada en CS donde se puede controlar el paso de ondas a su través. Los resultados ayudan a entender correctamente el funcionamiento de los CS para la localización de sonido, y para el guiado y filtrado de ondas acústicas.Romero García, V. (2010). On the control of propagating acoustic waves in sonic crystals: analytical, numerical and optimization techniques [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8982Palanci