Reconstruction of three-dimensional porous media using generative adversarial neural networks

To evaluate the variability of multi-phase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the inherent material properties is often experimentally not feasible. We present a novel method to reconstruct the solid-void structure of porous media by applying a generative neural network that allows an implicit description of the probability distribution represented by three-dimensional image datasets. We show, by using an adversarial learning approach for neural networks, that this method of unsupervised learning is able to generate representative samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such as the Euler characteristic, two-point statistics and directional single-phase permeability of synthetic realizations with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that GANs can be used to reconstruct high-resolution three-dimensional images of porous media at different scales that are representative of the morphology of the images used to train the neural network. The fully convolutional nature of the trained neural network allows the generation of large samples while maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the implicit representation of the learned data distribution can be stored and reused to generate multiple realizations of the pore structure very rapidly.Comment: 21 pages, 20 figure

Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation

Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However, the complexity of the SLM process, and the need for predictive relation of powder and process parameters to the part properties, demands further development of computational and experimental methods. This review addresses the fundamental physical phenomena of SLM, with a special emphasis on the associated thermal behavior. Simulation and experimental methods are discussed according to three primary categories. First, macroscopic approaches aim to answer questions at the component level and consider for example the determination of residual stresses or dimensional distortion effects prevalent in SLM. Second, mesoscopic approaches focus on the detection of defects such as excessive surface roughness, residual porosity or inclusions that occur at the mesoscopic length scale of individual powder particles. Third, microscopic approaches investigate the metallurgical microstructure evolution resulting from the high temperature gradients and extreme heating and cooling rates induced by the SLM process. Consideration of physical phenomena on all of these three length scales is mandatory to establish the understanding needed to realize high part quality in many applications, and to fully exploit the potential of SLM and related metal AM processes

Efficient computational mesoscale modeling of concrete under cyclic loading

Tesi amb diferents seccions retallades per drets de l'editor.Concrete is a complex material and can be modeled on various spatial and temporal scales. While simulations on coarse scales are practical for engineering applications, a deeper understanding of the material is gained on finer scales. This is at the cost of an increased numerical effort that can be reduced by the three methods developed and used in this work, each corresponding to one publication. The coarse spatial scale is related to fully homogenized models. The material is described in a phenomenological approach and the numerous parameters sometimes lack a physical meaning. Resolving the three-phase mesoscopic structure consisting of aggregates, the mortar matrix and the interfaces between them allow to describe similar effects with simpler models. This work addresses two computational challenges related to mesoscale modeling. First, aggregate particles take up a high volume fraction and an efficient particle-packing algorithm is required to generate non-overlapping, random esostructures. Enforcing an additional distance between the aggregates is essential to obtain undistorted meshes for finite element simulations, but further complicates the packing problem. An event-driven molecular-dynamics algorithm is applied to this problem that, in contrast to traditional methods, allows movement and a dense arrangement of the aggregates. This allows creating concrete mesostructures with realistic aggregate volume fractions. The second challenge concerns stability problems in mesoscale simulations of concrete fracture. The geometric complexity and the combination of three material laws for each of the phases leads to numerical instabilities, even for regularized material models. This requires tiny time steps and numerous iterations per time step when integrated with a classic backward Euler scheme. The implicit–explicit (IMPL-EX) integration extrapolates internal variables that account for the nonlinear behavior. This linearizes the equations, provides additional robustness and a computational speedup. In combination with a novel time step control method, a three-dimensional mesoscale compression test is accelerated by a factor of 40, compared to an adaptive backward Euler algorithm. The life time of concrete under cyclic loads is commonly predicted with empirical Wöhler lines. They relate the number of endured cycles with the applied load amplitude and can be included in constitutive formulations. They can, however, hardly be generalized to geometries and load configurations other than the ones tested. On a finer temporal scale, fatigue failure is modeled by the accumulation of damage within each loading cycle. This resolves the whole process of failure, includes stress redistributions and size effects and can easily be extended to multiphysics phenomena. The third computational challenge solved here is the efficient temporal integration that would not be feasible in a naive cycle-by-cycle integration of thousands or millions of cycles. The cost of evaluating a single cycle is reduced by reformulating the problem in the frequency space. It is sufficient to equilibrate the structure once for each Fourier coefficient which significantly speeds up this evaluation. The accumulated damage of one cycle is integrated in time using an adaptive cycle jump concept. For a two dimensional void test structure, the combination of both techniques leads to a 25 times faster simulation compared to the full integration. These three main contributions decrease the numerical cost of mesoscale simulations, allow larger and more detailed models and are a basis to deepen the understanding of the complex failure patterns in concrete.El hormigón es un material complejo y puede ser modelado en varias escalas espaciales y temporales. Mientras que las simulaciones en escalas gruesas son prácticas para aplicaciones de ingeniería, se obtiene una comprensión más profunda del material en escalas más finas. Esto es a costa de un mayor esfuerzo numérico que puede ser reducido por los tres métodos desarrollados y utilizados en este trabajo, cada uno de los cuales corresponde a una publicación. La escala espacial gruesa está relacionada con modelos totalmente homogeneizados. El material se describe con un enfoque fenomenológico y los numerosos parámetros a veces carecen de significado físico. La resolución de la estructura mesoscópica trifásica formada por los áridos, la matriz de mortero y las interfaces entre ellos permite describir efectos similares con modelos más sencillos. Este trabajo aborda dos retos computacionales relacionados con el modelado a mesoescala. En primer lugar, las partículas agregadas absorben una fracción de gran volumen y se requiere un algoritmo eficiente de empaquetamiento de partículas para generar mesoestructuras aleatorias que no se solapen. Hacer cumplir una distancia adicional entre los agregados es esencial para obtener mallas no distorsionadas para simulaciones de elementos finitos, pero complica aún más el problema de empaquetado. A este problema se le aplica un algoritmo de dinámica molecular impulsado por eventos que, a diferencia de los métodos tradicionales, permite el movimiento y una disposición densa de los agregados. Esto permite crear mesoestructuras de hormigón con fracciones de volumen de agregado realistas. El segundo reto se refiere a los problemas de estabilidad en las simulaciones mesoescalares de fracturas de hormigón. La complejidad geométrica y la combinación de tres leyes materiales para cada una de las fases conduce a inestabilidades numéricas, incluso para modelos materiales regularizados. Esto requiere pequeños pasos de tiempo y numerosas iteraciones por paso de tiempo cuando se integra con un esquema clásico de Euler hacia atrás. La integración implícita- explícita (IMPL-EX) extrapola variables internas que dan cuenta del comportamiento no lineal. Esto linealiza las ecuaciones, proporciona robustez adicional y una aceleración computacional. En combinación con un nuevo método de control de paso en el tiempo, una prueba de compresión tridimensional de mesoescala es acelerada por un factor de 40, en comparación con un algoritmo adaptativo de Euler hacia atrás. La vida útil del hormigón bajo cargas cíclicas se predice comúnmente con las líneas empíricas de Wöhler. Relacionan el número de ciclos soportados con la amplitud de carga aplicada y pueden ser incluidos en formulaciones constitutivas. Sin embargo, difícilmente pueden generalizarse a geometrías y configuraciones de carga distintas a las probadas. En una escala temporal más fina, la falla por fatiga es modelada por la acumulación de daño dentro de cada ciclo de carga. Esto resuelve todo el proceso de fracaso, incluye redistribuciones de estrés y efectos de tamaño, y puede extenderse fácilmente a fenómenos multifísicos. El tercer reto computacional resuelto aquí es la integración temporal eficiente que no sería factible en una integración costosa de miles o millones de ciclos ciclo a ciclo. El costo de evaluar un solo ciclo se reduce reformulando el problema en el espacio de frecuencias. Es suficiente equilibrar la estructura una vez para cada coeficiente de Fourier, lo que acelera significativamente esta evaluación. El daño acumulado de un ciclo se integra en el tiempo utilizando un concepto de salto de ciclo adaptativo. Para una estructura de prueba de vacío bidimensional, la combinación de ambas técnicas conduce a una simulación 25 veces más rápida en comparación con la integración completa.Postprint (published version

A parameterized approximation scheme for the 2D-Knapsack problem with wide items

We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box without overlap. Naturally, this problem is NP-complete. Recently, Grandoni et al. [ESA'19] showed that it is also W[1]-hard when parameterized by the size $k$ of the sought packing, and they presented a parameterized approximation scheme (PAS) for the variant where we are allowed to rotate the rectangles by 90{\textdegree} before packing them into the box. Obtaining a PAS for the original 2D-Knapsack problem, without rotation, appears to be a challenging open question. In this work, we make progress towards this goal by showing a PAS under the following assumptions: - both the box and all the input rectangles have integral, polynomially bounded sidelengths; - every input rectangle is wide -- its width is greater than its height; and - the aspect ratio of the box is bounded by a constant.Our approximation scheme relies on a mix of various parameterized and approximation techniques, including color coding, rounding, and searching for a structured near-optimum packing using dynamic programming