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

Treating inextensibility constraints in hyperelastic materials with inequality level sets

Elastomers are viscoelastic polymers with low Young's modulus and high failure strain that are used in many c ivil e ngineering applications, including bridge bearings, seismic isolators for buil dings and resilient rail wheels. Their constitutive behaviour i s characterized by a nonlinear stress - strain relation with an extensibility limit . This contrasts with materials that have instead a limit on the tensile stresses, such as mild steel. This MSc thesis is concerned with the numerical modeling of elastomers. T his involves dealing with a medium with two phases: a constrained region, wher e the particles have reached their maxi mum allowable deformation, and a free region, where the inextensibility constraint is still inactive. Moreover, one can think of an interf ace splitting the two phases of the medium. If the focus is put in obtaining methods to locate and evolve such interface, then a two phase medium with a moving interface is considered. From the mathematical point of view, this is a constrained minimization problem. One of the strategies to solve it is to turn the minimization problem into a shape equilibrium one. This approach has b een successfully employed for an interface location problem in small strains and serves as the starting point of this work. T hu s, t he main purpose of this thesis is to extend this formulation to a large strains interface locating and evolving scenario. A first analysis of the problem reveals two sources of nonlinearity : the inextensibility constraint and the kinematics in large st rains. A simple but thorough one - dimensional study of the problem is then developed to find methods to sort out both nonlinearities. Following this, explicit iterative schemes to locate and evolve one or multiple interfaces are straightforwardly obtained i n 1D linear elasticity. However, the same ideas applied to a simple St.Venant - Kirchhoff hyperelasticity model , evidences that even very simple 1D problems become rather complex and cannot be solved as directly and explicit as before. Numerical examples are provided throughout this analysis and they are also useful to conclude that both locating and evolving the interface can be essentially seen as the same problem, but with different driving effects. After that, an extension of the one - dimensional schemes t o two or more dimensions is explored . Although the same ideas can be applied, more sophisticated modeling tools are required, namely, the X - FEM and Level set methods, the shape sensitivity analysis and the Arbitrary Lagrangian - Eulerian methods . A complemen tary numerical implementation of the pr oposed strategy is to show its computational benefits. In particular, a combination of the three previous techniques shall make unnecessary a stepwise update of the Level set. T he work presented here may not be limite d to this particular case and be r elevant to other engineering problems involving moving interfaces and boundaries , such as plasticity analysis or the saturation of a porous medium

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

Treating inextensibility constraints in hyperelastic materials with inequality level sets

Elastomers are viscoelastic polymers with low Young's modulus and high failure strain that are used in many c ivil e ngineering applications, including bridge bearings, seismic isolators for buil dings and resilient rail wheels. Their constitutive behaviour i s characterized by a nonlinear stress - strain relation with an extensibility limit . This contrasts with materials that have instead a limit on the tensile stresses, such as mild steel. This MSc thesis is concerned with the numerical modeling of elastomers. T his involves dealing with a medium with two phases: a constrained region, wher e the particles have reached their maxi mum allowable deformation, and a free region, where the inextensibility constraint is still inactive. Moreover, one can think of an interf ace splitting the two phases of the medium. If the focus is put in obtaining methods to locate and evolve such interface, then a two phase medium with a moving interface is considered. From the mathematical point of view, this is a constrained minimization problem. One of the strategies to solve it is to turn the minimization problem into a shape equilibrium one. This approach has b een successfully employed for an interface location problem in small strains and serves as the starting point of this work. T hu s, t\ud he main purpose of this thesis is to extend this formulation to a large strains interface locating and evolving scenario. A first analysis of the problem reveals two sources of nonlinearity : the inextensibility constraint and the kinematics in large st rains. A simple but thorough one - dimensional study of the problem is then developed to find methods to sort out both nonlinearities. Following this, explicit iterative schemes to locate and evolve one or multiple interfaces are straightforwardly obtained i n 1D linear elasticity. However, the same ideas applied to a simple St.Venant - Kirchhoff hyperelasticity model , evidences that even very simple 1D problems become rather complex and cannot be solved as directly and explicit as before. Numerical examples are provided throughout this analysis and they are also useful to conclude that both locating and evolving the interface can be essentially seen as the same problem, but with different driving effects. After that, an extension of the one - dimensional schemes t o two or more dimensions is explored . Although the same ideas can be applied, more sophisticated modeling tools are required, namely, the X - FEM and Level set methods, the shape sensitivity analysis and the Arbitrary Lagrangian - Eulerian methods . A complemen tary numerical implementation of the pr oposed strategy is to show its computational benefits. In particular, a combination of the three previous techniques shall make unnecessary a stepwise update of the Level set. T he work presented here may not be limite d to this particular case and be r elevant to other engineering problems involving moving interfaces and boundaries , such as plasticity analysis or the saturation of a porous medium

A parallel finite-element framework for the thermal analysis of metal additive manufacturing with powder methods

A numerical simulation and experimental calibration for the heat transfer analysis of additive manufacturing by blown powder technologies for metal components has been recently carried out with successful results [1]. However, dealing with the computational cost of this simulation is still an open question. The purpose of this work is to address this unsolved problem with a strategy to transform the serial implementation devised in [1] into a parallel one, that can efficiently exploit the computational resources of a supercomputer.Virtual design process and validation of products built with metal additive manufacturing technologies with powder methods is not possible without a coupled thermomechanical numerical analysis tool that is capable of predicting the final distortion and the residual stresses of a piece and gets round a slow and expensive experimental campaign. However, the numerical analyses of metal AM processes are a remarkable challenge because they involve growing geometries, complex constitutive nonlinear thermomechanical laws, different scales in space and time and, most importantly, dealing efficiently with the massive computational cost of these simulations. This Master Thesis establishes the foundation stone of an innovative high performance scientific framework that will bring at last a reliable and computationally efficient answer to the current industrial needs. More precisely, it presents a parallel finite-element framework for the heat transfer analysis of metal additive manufacturing with powder methods. The main ingredient of this parallel finite-element model consists of a finite-element activation procedure that allows one to follow the energy input from the laser in space and time in a parallel environment. This moving heat source also governs the evolution of the geometry during the printing process. That is why the procedure is also responsible for the update of the computational domain. This model has been implemented in an advanced highly-performing object-oriented research code (FEMPAR), after thoroughly redesigning an existing serial implementation from another standard and procedural research code (COMET). The numerical experiments show that this novel framework reproduces in a parallel environment the behaviour of the original serial implementation, marking not only the achievement of the objective of this Master Thesis, but also an important milestone in the long-term goal of creating a high performance scientific tool for these kind of simulations

Treating inextensibility constraints in hyperelastic materials with inequality level sets

Elastomers are viscoelastic polymers with low Young's modulus and high failure strain that are used in many c ivil e ngineering applications, including bridge bearings, seismic isolators for buil dings and resilient rail wheels. Their constitutive behaviour i s characterized by a nonlinear stress - strain relation with an extensibility limit . This contrasts with materials that have instead a limit on the tensile stresses, such as mild steel. This MSc thesis is concerned with the numerical modeling of elastomers. T his involves dealing with a medium with two phases: a constrained region, wher e the particles have reached their maxi mum allowable deformation, and a free region, where the inextensibility constraint is still inactive. Moreover, one can think of an interf ace splitting the two phases of the medium. If the focus is put in obtaining methods to locate and evolve such interface, then a two phase medium with a moving interface is considered. From the mathematical point of view, this is a constrained minimization problem. One of the strategies to solve it is to turn the minimization problem into a shape equilibrium one. This approach has b een successfully employed for an interface location problem in small strains and serves as the starting point of this work. T hu s, t he main purpose of this thesis is to extend this formulation to a large strains interface locating and evolving scenario. A first analysis of the problem reveals two sources of nonlinearity : the inextensibility constraint and the kinematics in large st rains. A simple but thorough one - dimensional study of the problem is then developed to find methods to sort out both nonlinearities. Following this, explicit iterative schemes to locate and evolve one or multiple interfaces are straightforwardly obtained i n 1D linear elasticity. However, the same ideas applied to a simple St.Venant - Kirchhoff hyperelasticity model , evidences that even very simple 1D problems become rather complex and cannot be solved as directly and explicit as before. Numerical examples are provided throughout this analysis and they are also useful to conclude that both locating and evolving the interface can be essentially seen as the same problem, but with different driving effects. After that, an extension of the one - dimensional schemes t o two or more dimensions is explored . Although the same ideas can be applied, more sophisticated modeling tools are required, namely, the X - FEM and Level set methods, the shape sensitivity analysis and the Arbitrary Lagrangian - Eulerian methods . A complemen tary numerical implementation of the pr oposed strategy is to show its computational benefits. In particular, a combination of the three previous techniques shall make unnecessary a stepwise update of the Level set. T he work presented here may not be limite d to this particular case and be r elevant to other engineering problems involving moving interfaces and boundaries , such as plasticity analysis or the saturation of a porous medium