In this work, the mesh-free smoothed particle hydrodynamics (SPH) method is applied in the modelling of the direct laser interference patterning (DLIP) of metal surfaces. The DLIP technique allows the fabrication of periodic microstructures on technical surfaces using nanosecond laser pulses. Here, the interference of two coherent partial beams with a sinusoidal energy density distribution of the interference pattern is concerned, which is employed to generate line-like surface structures. However, the mechanisms effective during nanosecond pulsed DLIP of metals are not yet fully understood. The physical phenomena occurring due to the interaction of laser radiation with metallic materials are first considered and the governing differential equations are stated. The fundamentals of the SPH method and the approaches to the numerical treatment of the conservation equations are presented. Physical processes relevant to the modelling of laser material processing are solved by suitable SPH techniques, i.e. the approximations are verified with respect to test problems with analytical or known numerical solutions. Consequently, the SPH method is used to devise a thermal model of the DLIP process, considering the absorption of the laser radiation, the heat conduction into the workpiece and the latent heat of involved phase changes. This model is extended to compute the melt pool convection during DLIP, which is driven by surface tension gradients due to temperature gradients. For this purpose, an incompressible SPH (ISPH) method is used, representing a novel approach to the modelling of the laser-induced melt pool flow. The numerical model is employed to perform simulations of DLIP on metal substrates. Firstly, the thermal simulation of the single pulse patterning of stainless steel is in good agreement with experimental results. The application of DLIP to stainless steel and aluminium is then simulated by the comprehensive model including the melt pool flow. Moreover, this model is further extended to consider the non-linear temperature dependence of surface tension, as in liquid steel in the presence of a surface active element. The simulation results reveal a distinct behaviour of stainless steel and aluminium substrates. A markedly deeper melt pool and considerable velocity magnitudes of the thermocapillary convection at the melt surface are computed for DLIP of aluminium. In contrast, the melt pool flow is less pronounced during DLIP of stainless steel, whereas higher surface temperatures are predicted. Hence the Marangoni convection is a conceivable effective mechanism during the structuring of aluminium at moderate energy density. The different character of the melt pool convection during DLIP of stainless steel and aluminium is corroborated by experimental observations. Furthermore, the simulations for stainless steel with different sulphur content indicate distinct melt pool flow patterns and support the explanation of the microstructures found after DLIP experiments. The role of vapourisation and the induced recoil pressure in the microstructure evolution due to DLIP on metal substrates at elevated fluences could be prospectively investigated. In this regard, the consideration of the melt pool surface deformation in the ISPH algorithm, and particularly a suitable pressure boundary condition, is required.:I The research problem 1 Motivation 2 Modelling of laser material processing 2.1 Interaction of laser radiation with materials 2.1.1 Absorption of laser radiation 2.1.2 Heat conduction and phase change 2.1.3 Molten pool convection 2.1.4 Vapourisation regime 2.2 Mathematical modelling of laser material interaction 2.2.1 Conservation equations in Lagrangian formulation 2.2.2 Influence of surface tension 3 State of the art in laser microprocessing and the SPH method 3.1 Laser microprocessing 3.2 Simulation of direct laser interference patterning 3.3 The mesh-free smoothed particle hydrodynamics method 3.3.1 Fundamental approximations and kernel function 3.3.2 Particle distribution and interaction length 3.3.3 Approximation of derivatives 3.3.4 Treatment of boundaries 3.3.5 Neighbourhood search 3.4 Numerical modelling of laser material processing by SPH II SPH model development for direct laser interference patterning 4 SPH modelling of heat transfer and fluid flow 4.1 Solution of the heat diffusion equation 4.2 Formulation of equations governing fluid flow 4.2.1 Equation of continuity 4.2.2 Approximation of pressure gradient term 4.2.3 Treatment of viscosity 4.3 Weakly compressible SPH method for solving fluid flow 4.3.1 Particle motion 4.3.2 Time integration 4.3.3 Time step criteria 4.4 Incompressible SPH method for solving fluid flow 4.4.1 Time integration 4.4.2 Discrete incompressible SPH algorithm 4.4.3 Time step criteria 4.5 Simulation of thermal fluid flow using ISPH 4.5.1 Semi-implicit time integration 4.5.2 Solution of the pressure Poisson equation 5 Verification of the SPH implementation 5.1 Transient heat conduction in laser-irradiated plate 5.1.1 Problem description 5.1.2 Dimensionless formulation 5.1.3 Numerical solution and results 5.2 Viscous flow 5.2.1 Couette flow 5.2.2 Poiseuille flow 5.3 Thermal convection 5.3.1 Natural convection in a square cavity 5.3.2 Rayleigh--Marangoni--Bénard convection in liquid aluminium 6 SPH model of direct laser interference patterning 6.1 Characteristics of the process 6.2 Thermal model 6.2.1 Non-dimensionalisation 6.2.2 Numerical solution of governing equation 6.2.3 Verification of the computation 6.2.4 Numerical test 6.3 Thermofluiddynamic model 6.3.1 Non-dimensionalisation 6.3.2 Numerical solution of governing equations 6.3.3 Discretisation 6.3.4 Resolution independence study 7 SPH simulation of direct laser interference patterning 7.1 Thermal model 7.1.1 DLIP experiments on stainless steel substrates 7.1.2 Thermal simulation of DLIP on steel substrate 7.2 Thermofluiddynamic model 7.2.1 Material properties and simulation parameters 7.2.2 Numerical results for steel substrate 7.2.3 Numerical results for aluminium substrate 7.2.4 Discussion and comparison with experiments 7.3 Extended thermofluiddynamic model 7.3.1 Model parameters 7.3.2 Influence of sulphur content on DLIP of stainless steel 8 Conclusions and outlook Bibliography / In dieser Arbeit wird die direkte Laserinterferenzstrukturierung (Direct Laser Interference Patterning, DLIP) von Metallen mit der netzfreien Smoothed Particle Hydrodynamics (SPH) Methode modelliert. Das DLIP-Verfahren ermöglicht die Fertigung periodischer Mikrostrukturen auf technischen Oberflächen mit Nanosekunden-Laserpulsen. Hier wird die Zweistrahlinterferenz mit einer sinusförmigen Energiedichteverteilung des Interferenzmusters behandelt, die linienförmige Oberflächenstrukturen erzeugt. Die bei der direkten Interferenzstrukturierung von Metallen mit Nanosekunden-Laserpuls wirksamen Mechanismen sind jedoch noch nicht verstanden. Die aufgrund der Wechselwirkung von Laserstrahlung mit metallischen Werkstoffen auftretenden physikalischen Phänomene werden zuerst betrachtet und die sie bestimmenden Differentialgleichungen angegeben. Die Grundlagen der SPH-Methode sowie deren Herangehensweisen an die numerische Behandlung der Erhaltungsgleichungen werden vorgestellt. Für die Modellierung der Lasermaterialbearbeitung relevante physikalische Vorgänge werden mittels geeigneter SPH-Ansätze gelöst, d. h. anhand von Testproblemen mit bekannter Lösung verifiziert. Das mit SPH zunächst erstellte thermische Modell des DLIP-Prozesses berücksichtigt die Absorption der Laserstrahlung, die Wärmeleitung im Werkstück und die Enthalpien der Phasenübergänge. Das Modell wird zur Berechnung der Schmelzbadströmung bei der DLIP-Anwendung, angetrieben von Oberflächenspannungsgradienten verursacht durch Temperaturgradienten, erweitert. Hierbei wird eine inkompressible SPH (ISPH) Methode eingesetzt, in der Simulation laserinduzierter Schmelzbäder ein neuartiger Ansatz. Mit dem numerischen Modell werden Simulationen des DLIP-Verfahrens für metallische Substrate durchgeführt. Die thermische Simulation der Strukturierung von Edelstahl stimmt gut mit einem Experiment überein. Weiterhin wird die Anwendung von DLIP auf Edelstahl und Aluminium mit dem thermofluiddynamischen Modell simuliert. Außerdem wird das Modell um eine nichtlinear temperaturabhängige Oberflächenspannung, wie sie für Stahlschmelze in Anwesenheit eines oberflächenaktiven Elements vorliegt, ergänzt. Die Simulationen zeigen ein verschiedenes Verhalten von Edelstahl und Aluminium. Bei der Strukturierung von Aluminium treten ein deutlich tieferes Schmelzbad und erhebliche Geschwindigkeitsbeträge der thermokapillaren Konvektion an der Schmelzeoberfläche auf. Hingegen ist die Strömung bei der DLIP-Anwendung auf Edelstahl schwächer ausgeprägt und höhere Oberflächentemperaturen werden erreicht. Die Marangoni-Konvektion ist daher ein wirksamer Schmelzeverdrängungsmechanismus bei der Strukturierung von Aluminium mit moderater Energiedichte. Die unterschiedliche Schmelzbadströmung für die beiden Werkstoffe wird durch experimentelle Beobachtungen bestätigt. In Abhängigkeit des Schwefelgehalts von Edelstahl zeigen Simulationen verschiedene Strömungsmuster im Schmelzbad und unterstützen die Erklärung experimentell festgestellter Mikrostrukturen. Die Untersuchung der Wirkung der Verdampfung und des induzierten Rückstoßdruckes auf die Strukturausbildung bei höheren Fluenzen erfordert die Berücksichtigung der Oberflächendeformation sowie eine geeignete Druckrandbedingung im ISPH-Algorithmus.:I The research problem 1 Motivation 2 Modelling of laser material processing 2.1 Interaction of laser radiation with materials 2.1.1 Absorption of laser radiation 2.1.2 Heat conduction and phase change 2.1.3 Molten pool convection 2.1.4 Vapourisation regime 2.2 Mathematical modelling of laser material interaction 2.2.1 Conservation equations in Lagrangian formulation 2.2.2 Influence of surface tension 3 State of the art in laser microprocessing and the SPH method 3.1 Laser microprocessing 3.2 Simulation of direct laser interference patterning 3.3 The mesh-free smoothed particle hydrodynamics method 3.3.1 Fundamental approximations and kernel function 3.3.2 Particle distribution and interaction length 3.3.3 Approximation of derivatives 3.3.4 Treatment of boundaries 3.3.5 Neighbourhood search 3.4 Numerical modelling of laser material processing by SPH II SPH model development for direct laser interference patterning 4 SPH modelling of heat transfer and fluid flow 4.1 Solution of the heat diffusion equation 4.2 Formulation of equations governing fluid flow 4.2.1 Equation of continuity 4.2.2 Approximation of pressure gradient term 4.2.3 Treatment of viscosity 4.3 Weakly compressible SPH method for solving fluid flow 4.3.1 Particle motion 4.3.2 Time integration 4.3.3 Time step criteria 4.4 Incompressible SPH method for solving fluid flow 4.4.1 Time integration 4.4.2 Discrete incompressible SPH algorithm 4.4.3 Time step criteria 4.5 Simulation of thermal fluid flow using ISPH 4.5.1 Semi-implicit time integration 4.5.2 Solution of the pressure Poisson equation 5 Verification of the SPH implementation 5.1 Transient heat conduction in laser-irradiated plate 5.1.1 Problem description 5.1.2 Dimensionless formulation 5.1.3 Numerical solution and results 5.2 Viscous flow 5.2.1 Couette flow 5.2.2 Poiseuille flow 5.3 Thermal convection 5.3.1 Natural convection in a square cavity 5.3.2 Rayleigh--Marangoni--Bénard convection in liquid aluminium 6 SPH model of direct laser interference patterning 6.1 Characteristics of the process 6.2 Thermal model 6.2.1 Non-dimensionalisation 6.2.2 Numerical solution of governing equation 6.2.3 Verification of the computation 6.2.4 Numerical test 6.3 Thermofluiddynamic model 6.3.1 Non-dimensionalisation 6.3.2 Numerical solution of governing equations 6.3.3 Discretisation 6.3.4 Resolution independence study 7 SPH simulation of direct laser interference patterning 7.1 Thermal model 7.1.1 DLIP experiments on stainless steel substrates 7.1.2 Thermal simulation of DLIP on steel substrate 7.2 Thermofluiddynamic model 7.2.1 Material properties and simulation parameters 7.2.2 Numerical results for steel substrate 7.2.3 Numerical results for aluminium substrate 7.2.4 Discussion and comparison with experiments 7.3 Extended thermofluiddynamic model 7.3.1 Model parameters 7.3.2 Influence of sulphur content on DLIP of stainless steel 8 Conclusions and outlook Bibliography