Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.Comment: 20 pages, 12 figure

A Painless Automatic hp-Adaptive Strategy for Elliptic Problems

International audienceIn this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping quasi-optimal results. We employ a multi-level hierarchical data structure imposing Dirichlet nodes to manage the so-called hanging nodes. The hp-adaptive strategy is based on performing quasi-optimal unrefinements. Taking advantage of the hierarchical structure of the basis functions both in terms of the element size h and the polynomial order of approximation p, we mark those with the lowest contributions to the energy of the solution and remove them. This straightforward unrefinement strategy does not require from a fine grid or complex data structures, making the algorithm flexible to many practical situations and existing implementations. On the other side, we also identify some limitations of the proposed strategy, namely: (a) data structures only support isotropic h-refinements (although p-anisotropic refinements are enabled), (b) we assume certain quasi-orthogonality properties of the basis functions in the energy norm, and (c) in this work, we restrict to symmetric and positive definite problems. We illustrate these and other advantages and limitations of the proposed hp-adaptive strategy with several one-and two-dimensional Poisson examples

A hierarchical computational model for moving thermal loads and phase changes with applications to selective laser melting

none5siComputational heat transfer analysis often involves moving fluxes which induce traveling fronts of phase change coupled to one or more field variables. Examples are the transient simulation of melting, welding or of additive manufacturing processes, where material changes its state and the controlling fields are temperature and structural deformation. One of the challenges for a numerical computation of these processes is their multi-scale nature with a highly localized zone of phase transition which may travel over a large domain of a body. Here, a transient local adaptation of the approximation, with not only a refinement at the phase front, but also a de-refinement in regions, where the front has passed is of advantage because the de-refinement can assure a bounded number of degrees of freedom which is independent from the traveling length of the front. We present a computational model of this process which involves three novelties: (a) a very low number of degrees of freedom which yet yields a comparatively high accuracy. The number of degrees of freedom is, additionally, kept practically constant throughout the duration of the simulation. This is achieved by means of the multi-level hp-finite element method. Its exponential convergence is verified for the first time against a semi-analytic, three-dimensional transient linear thermal benchmark with a traveling source term which models a laser beam. ( b) A hierarchical treatment of the state variables. To this end, the state of the material is managed on a separate, octree-like grid. This material grid may refine or coarsen independently of the discretization used for the temperature field. This methodology is verified against an analytic benchmark of a melting bar computed in three dimensions in which phase changes of the material occur on a rapidly advancing front. (c) The combination of these technologies to demonstrate its potential for the computational modeling of selective laser melting processes. To this end, the computational methodology is extended by the finite cell method which allows for accurate simulations in an embedded domain setting. This opens the new modeling possibility that neither a scan vector nor a layer of material needs to conform to the discretization of the finite element mesh but can form only a fraction within the discretization of the field- and state variables.restrictedKollmannsberger, S.; Özcan, A.; Carraturo, M.; Zander, N.; Rank, E.Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Zander, N.; Rank, E

Development of a high-performance artificial neural network model integrated with finite element analysis for residual stress simulation of the direct metal deposition process

Additive manufacturing (AM) processes are among the manufacturing methods implemented in various industries. Direct metal deposition (DMD) is part of AM processes that uses the laser heat source to deposit the metallic material in the form of powder or wire onto a substrate and build a component in a layer-by-layer scheme. The DMD process is known to be cost-effective and easily adaptable for building complex structures. During a DMD process, material experiences several heating and cooling cycles which lead to the formation of residual stresses and distortions of the fabricated part. There are several experimental-based methods and techniques for measuring the residual stresses of metallic components. However, the application of these methods can damage the fabricated parts or may require considerable time and tooling expenses for the experiment. Alternative solutions such as finite element (FE) analysis were developed to predict the residual stresses without damaging the part. The application of the FE in assessing the residual stress distribution is time-efficient and cost-effective. The FE analysis of DMD process includes thermal and mechanical analyses; the temperature history of the elements is obtained by performing a pure heat transfer analysis, then it is applied to the mechanical model to calculate the structural response of the part. One of the shortcomings of the FE analysis of DMD process corresponds to the high computational time of the mechanical analysis. Therefore, several techniques and approaches were developed in the literature to address this issue and improve the computational efficiency of the FE method. Throughout this thesis, a novel approach of integrating the FE analysis with artificial neural networks (ANNs) is presented as an efficient method for improving the computational time of predicting the residual stresses in DMD fabricated parts. ANNs are part of machine learning (ML) algorithms that tries to determine the logical relationship between the given inputs and the associated output(s). A feed-forward ANN with gradient descent backpropagation developed in Keras was implemented. The ANN is trained by feeding the dataset into the network and minimizing the error function. In the present study, several structures made from AISI 304L with 12-layers and 18-layers deposition were considered. and a detailed thermomechanical FE analysis was performed on them. Temperature history of the elements along with their dimensional features of 12-layers structures were extracted as the inputs and the corresponding residual stress components were recorded as the outputs to train the ANN. On the other hand, the temperature history of the elements and their geometrical features extracted from 18-layers structures were fed into the trained ANN for making predictions. The results of the integrated ANN-FE are compared with the results of the residual stresses of 18-layers obtained from the detailed thermomechanical analysis. The prediction errors were calculated and shown in the form of 3D contours and scattered errors. Moreover, the histogram analysis was performed for each 18-layers structures to better present the fraction of the elements with the associated error ranges. Finally, the computational times are recorded and compared with the results of the detailed FE analysis to evaluate the efficiency and performance of the proposed novel ANN-FE method. The results showed that for almost all of the structures and all the stress components, the predicted pattern and magnitude of the residual stress were consistent with the detailed FE analysis. For some of the structures, very high errors were observed which were associated with the low-stress state zones in which the actual stress magnitude was low and the high errors pose no critical condition. Although there are some predictions showing higher errors in some regions, the majority of the elements in the structures showed prediction errors of less than 15% supported by the histogram analysis. Significant improvement in the computational time of the 18-layers structures was also achieved (6 times as an average). The computational time of predicting the residual stresses in the DMD parts was improved substantially with low loss in the accuracy of the predicted results. Therefore, the proposed method can be implemented for investigating the effects of the hyperparameters on the residual stresses in DMD process

Finite element simulation of additive manufacturing with enhanced accuracy

Tesi en modalitat de compendi de publicacionsThis thesis develops numerical methods to improve the accuracy and computational efficiency of the part-scale simulation of Additive Manufacturing (AM) (or 3D printing) metal processes. AM is characterized by multiple scales in space and time, as well as multiple complex physics that occur in three-dimensional growing-in-time geometries, making its simulation a remarkable computational challenge. To this end, the computational framework is built by addressing four key topics: (1) a Finite Element technology with enhanced stress/strain accuracy including the incompressible limit; (2) an Adaptive Mesh Refinement (AMR) strategy accounting for geometric and solution accuracies; (3) a coarsening correction strategy to avoid loss of information in the coarsening AMR procedure, and (4) a GCodebased simulation tool that uses the exact geometric and process parameters data provided to the actual AM machinery. In this context, the mixed displacement/deviatoric-strain/pressure u/e/p FE formulation in (1) is adopted to solve incompressible problems resulting from the isochoric plastic flow in the Von Mises criterion typical of metals. The enhanced stress/strain accuracy of the u/e/p over the standard and u/p FE formulations is verified in a set of numerical benchmarks in iso-thermal and non-isothermal conditions. A multi-criteria AMR strategy in (2) is used to improve computational efficiency while keeping the number of FEs controlled and without the strictness of imposing the commonly adopted 2:1 balance scheme. Avoiding this enables to use high jumps on the refinement level between adjacent FEs; this improves the mesh resolution on the region of interest and keeps the mesh coarse elsewhere. Moving the FE solution from a fine mesh to a coarse mesh introduces loss of information. To prevent this, a coarsening correction strategy presented in (3) restores the fine solution in the coarse mesh, providing computational cost reduction and keeping the accuracy of the fine mesh solution accuracy. Lastly, design flexibility is one of the main advantages of AM over traditional manufacturing processes. This flexibility is observed in the design of complex components and the possibility to change the process parameters, i.e. power input, speed, waiting pauses, among others, throughout the process. In (4) a GCode-based simulation tool that replicates the exact path travelled and process parameters delivered to the AM machiney is developed. Furthermore, the GCode-based tool together with the AMR strategy allows to automatically generate an embedded fitted cartesian FE mesh for the evolving domain and removes the challenging task of mesh manipulation by the end-user. The FE framework is built on a high-performance computing environment. This framework enables to accelerate the process-to-performance understanding and to minimize the number of trial-and-error experiments, two key aspects to exploit the technology in the industrial environment.Esta tesis tiene como objetivo desarrollar métodos numéricos para mejorar la precisión y eficiencia computacionales en simulaciones de piezas fabricadas mediante Manufactura Aditiva (MA), también conocida como Impresión 3D. La manufactura aditiva es un problema complejo que involucra múltiples fenómenos físicos, que se desarolla en múltiples escalas, y cuya geometría evoluciona en el tiempo. Para tal fin, se plantean cuatro objetivos: (1) Desarrollo de una tecnología de elementos finitos para capturar con mayor precisión tanto tensiones como deformaciones en casos en el que el material tiene comportamiento isocórico; (2) Una estrategia de adaptividad de malla (AMR), que busca modificar la malla teniendo en cuenta la geometría y los errores en la solución numérica; (3) Una estrategia para minimizar la aproximación numérica durante el engrosamiento (coarsening) de la malla, crucial en la reducción de tiempos de cómputo en casos de piezas de grandes dimensiones; y (4) Un marco de simulación basado en la lectura de ficheros GCode, ampliamente usado por maquinaria de impresión en procesos de manufactura aditiva, un formato que no sólo proporciona los datos asociados a la geometría, sino también los parámetros de proceso. Con respecto a (1), esta tesis propone el uso de una formulación mixta en desplazamientos /deformación-desviadora / presión (u/e/p), para simular la deposición de materiales con deformación inelástica isocórica, como ocurre en los metales. En cuanto a la medición de la precisión en el cálculo de las tensiones y las deformaciones, en esta tesis se realiza un amplio número de experimentos tanto en condiciones isotérmicas como no isotérmicas para establecer una comparativa entre las dos formulaciones mixtas, u/e/p y u/p. Con respecto a (2), para mejorar la eficiencia computacional manteniendo acotado el número total de elementos finitos, se desarrolla una novedosa estrategia multicriterio de refinamiento adaptativo. Esta estrategia no se restringe a mallas con balance 2:1, permitiendo así tener saltos de nivel mayores entre elementos adyacentes. Por otra parte, para evitar la pérdida de información al proyectar la solución a mallas más gruesas, se plantee una corrección en (3), que tiene como objetivo recuperar la solución de la malla fina, garantizando así que la malla gruesa conserve la precisión obtenida en la malla fina. El proceso de manufactura aditiva se distingue por su gran flexibilidad comparándolo con otros métodos tradicionales de manufactura. Esta flexibilidad se observa en la posibilidad de construir piezas de gran complejidad geométrica, optimizando propiedades mecánicas durante el proceso de deposición. Por ese motivo, (4) se propone la lectura de ficheros en formato GCode que replica la ruta exacta del recorrido del láser que realiza la deposición del material. Los ingredientes lectura de comandos escritos en lenguaje Gcode, multicriterio de adaptividad de malla y el uso de mallas estructuradas basadas en octrees, permiten capturar con gran precisión el dominio discreto eliminando así la engorrosa tarea de generar un dominio discreto ad-hoc para la pieza a modelar. Los desarrollos de esta tesis se realizan en un entorno de computación de altas prestaciones (HPC) que permite acelerar el estudio de la ejecución del proceso de impresión y por ende reducir el número de experimentos destructivos, dos aspectos clave que permiten explorar y desarrollar nuevas técnicas en manufactura aditiva de piezas industriales.Postprint (published version

Large-scale tree-based unfitted finite elements for metal additive manufacturing

This thesis addresses large-scale numerical simulations of partial differential equations posed on evolving geometries. Our target application is the simulation of metal additive manufacturing (or 3D printing) with powder-bed fusion methods, such as Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) or Electron-Beam Melting (EBM). The simulation of metal additive manufacturing processes is a remarkable computational challenge, because processes are characterised by multiple scales in space and time and multiple complex physics that occur in intricate three-dimensional growing-in-time geometries. Only the synergy of advanced numerical algorithms and high-performance scientific computing tools can fully resolve, in the short run, the simulation needs in the area. The main goal of this Thesis is to design a a novel highly-scalable numerical framework with multi-resolution capability in arbitrarily complex evolving geometries. To this end, the framework is built by combining three computational tools: (1) parallel mesh generation and adaptation with forest-of-trees meshes, (2) robust unfitted finite element methods and (3) parallel finite element modelling of the geometry evolution in time. Our numerical research is driven by several limitations and open questions in the state-of-the-art of the three aforementioned areas, which are vital to achieve our main objective. All our developments are deployed with high-end distributed-memory implementations in the large-scale open-source software project FEMPAR. In considering our target application, (4) temporal and spatial model reduction strategies for thermal finite element models are investigated. They are coupled to our new large-scale computational framework to simplify optimisation of the manufacturing process. The contributions of this Thesis span the four ingredients above. Current understanding of (1) is substantially improved with rigorous proofs of the computational benefits of the 2:1 k-balance (ease of parallel implementation and high-scalability) and the minimum requirements a parallel tree-based mesh must fulfil to yield correct parallel finite element solvers atop them. Concerning (2), a robust, optimal and scalable formulation of the aggregated unfitted finite element method is proposed on parallel tree-based meshes for elliptic problems with unfitted external contour or unfitted interfaces. To the author’s best knowledge, this marks the first time techniques (1) and (2) are brought together. After enhancing (1)+(2) with a novel parallel approach for (3), the resulting framework is able to mitigate a major performance bottleneck in large-scale simulations of metal additive manufacturing processes by powder-bed fusion: scalable adaptive (re)meshing in arbitrarily complex geometries that grow in time. Along the development of this Thesis, our application problem (4) is investigated in two joint collaborations with the Monash Centre for Additive Manufacturing and Monash University in Melbourne, Australia. The first contribution is an experimentally-supported thorough numerical assessment of time-lumping methods, the second one is a novel experimentally-validated formulation of a new physics-based thermal contact model, accounting for thermal inertia and suitable for model localisation, the so-called virtual domain approximation. By efficiently exploiting high-performance computing resources, our new computational framework enables large-scale finite element analysis of metal additive manufacturing processes, with increased fidelity of predictions and dramatical reductions of computing times. It can also be combined with the proposed model reductions for fast thermal optimisation of the manufacturing process. These tools open the path to accelerate the understanding of the process-to-performance link and digital product design and certification in metal additive manufacturing, two milestones that are vital to exploit the technology for mass-production.Aquesta tesi tracta la simulació a gran escala d'equacions en derivades parcials sobre geometries variables. L'aplicació principal és la simulació de procesos de fabricació additiva (o impressió 3D) amb metalls i per mètodes de fusió de llit de pols, com ara Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) o Electron-Beam Melting (EBM). La simulació d'aquests processos és un repte computacional excepcional, perquè els processos estan caracteritzats per múltiples escales espaitemporals i múltiples físiques que tenen lloc sobre geometries tridimensionals complicades que creixen en el temps. La sinèrgia entre algorismes numèrics avançats i eines de computació científica d'alt rendiment és la única via per resoldre completament i a curt termini les necessitats en simulació d'aquesta àrea. El principal objectiu d'aquesta tesi és dissenyar un nou marc numèric escalable de simulació amb capacitat de multiresolució en geometries complexes i variables. El nou marc es construeix unint tres eines computacionals: (1) mallat paral·lel i adaptatiu amb malles de boscs d'arbre, (2) mètodes d'elements finits immersos robustos i (3) modelització en paral·lel amb elements finits de geometries que creixen en el temps. Algunes limitacions i problemes oberts en l'estat de l'art, que són claus per aconseguir el nostre objectiu, guien la nostra recerca. Tots els desenvolupaments s'implementen en arquitectures de memòria distribuïda amb el programari d'accés obert FEMPAR. Quant al problema d'aplicació, (4) s'investiguen models reduïts en espai i temps per models tèrmics del procés. Aquests models reduïts s'acoplen al nostre marc computacional per simplificar l'optimització del procés. Les contribucions d'aquesta tesi abasten els quatre punts de dalt. L'estat de l'art de (1) es millora substancialment amb proves riguroses dels beneficis computacionals del 2:1 balancejat (fàcil paral·lelització i alta escalabilitat), així com dels requisits mínims que aquest tipus de mallat han de complir per garantir que els espais d'elements finits que s'hi defineixin estiguin ben posats. Quant a (2), s'ha formulat un mètode robust, òptim i escalable per agregació per problemes el·líptics amb contorn o interface immerses. Després d'augmentar (1)+(2) amb un nova estratègia paral·lela per (3), el marc de simulació resultant mitiga de manera efectiva el principal coll d'ampolla en la simulació de processos de fabricació additiva en llits de pols de metall: adaptivitat i remallat escalable en geometries complexes que creixen en el temps. Durant el desenvolupament de la tesi, es col·labora amb el Monash Centre for Additive Manufacturing i la Universitat de Monash de Melbourne, Austràlia, per investigar el problema d'aplicació. En primer lloc, es fa una anàlisi experimental i numèrica exhaustiva dels mètodes d'aggregació temporal. En segon lloc, es proposa i valida experimental una nova formulació de contacte tèrmic que té en compte la inèrcia tèrmica i és adequat per a localitzar el model, l'anomenada aproximació per dominis virtuals. Mitjançant l'ús eficient de recursos computacionals d'alt rendiment, el nostre nou marc computacional fa possible l'anàlisi d'elements finits a gran escala dels processos de fabricació additiva amb metalls, amb augment de la fidelitat de les prediccions i reduccions significatives de temps de computació. Així mateix, es pot combinar amb els models reduïts que es proposen per l'optimització tèrmica del procés de fabricació. Aquestes eines contribueixen a accelerar la comprensió del lligam procés-rendiment i la digitalització del disseny i certificació de productes en fabricació additiva per metalls, dues fites crucials per explotar la tecnologia en producció en massa.Postprint (published version