Simulation of Additive Manufacturing using Meshfree Methods: With Focus on Requirements for an Accurate Solution

Description

This book provides a detailed instruction to virtually reproduce the processes of Additive Manufacturing on a computer. First, all mathematical equations needed to model these processes are presented. Due to their flexibility, meshfree methods represent optimal computational solution schemes to simulate Additive Manufacturing processes. On the other hand, these methods usually do not guarantee an accurate solution. For this reason, this monograph is dedicated in detail to the necessary criteria for computational solution schemes to provide accurate results. Several meshfree methods are examined with respect to these conditions. Two different 3D printing techniques are presented in detail. The results obtained from the simulation are investigated and compared with experimental data. This work is addressed to both scientists and professionals working in the field of development who are interested to learn the secrets behind meshfree methods or get into the modeling of Additive Manufacturing. Preface Contents 1 Introduction References 2 Additive Manufacturing Processes 2.1 Potentials 2.2 Printing Technologies 2.2.1 Melting 2.2.2 Photopolymerization 2.3 Applications 2.3.1 Aerospace Industry 2.3.2 Automotive Industry 2.3.3 Biomedical Technology 2.3.4 Bioprinting 2.3.5 Defense Industry 2.3.6 Civil Engineering 2.4 Gaps and Needs 2.4.1 Machines and Materials 2.4.2 Design and Control References 3 Differential Equations 3.1 Modeling of Continua 3.2 Mechanical Differential Equation 3.2.1 Strong Form for Compressible Materials 3.2.2 Strong Form for Incompressible Materials 3.2.3 Boundary and Initial Conditions 3.2.4 Interface Effects 3.2.5 Weak Form 3.3 Thermal Differential Equation 3.3.1 Strong Form 3.3.2 Boundary and Initial Conditions 3.3.3 Interface Effects 3.3.4 Weak Form 3.4 Chemical Differential Equation 3.4.1 Initial Conditions References 4 Meshfree Discretization Schemes 4.1 Points and Neighborhoods 4.2 Discretization Concepts 4.2.1 Weak Form 4.2.2 Strong Form 4.2.3 Reduced Order Strong Form 4.2.4 Weak Form Based on Differences 4.3 Solution Schemes 4.4 Reference Configurations 4.4.1 Total Lagrangian Formulation 4.4.2 Current Lagrangian Formulation 4.4.3 Updated Lagrangian Formulation 4.4.4 Isoparametric Concept 4.5 Requirements on Spatial Discretization Schemes 4.5.1 Definitions 4.5.2 Reproducing Conditions 4.5.3 Integration Constraint 4.5.4 Configurational Consistency 4.5.5 Discrete Conservation Properties 4.5.6 Continuity 4.5.7 Kronecker-δ Property 4.5.8 Search Algorithm 4.5.9 Stability 4.6 Shape Functions 4.6.1 Least Square Functions 4.6.2 Radial Functions 4.6.3 Local Maximum Entropy Functions 4.6.4 Integral Functions References 5 Meshfree Galerkin Methods 5.1 Reproducing Kernel Particle Method 5.1.1 Search Algorithm 5.1.2 Rank Instability 5.1.3 Integration Constraint 5.2 Optimal Transportation Meshfree Method 5.2.1 Tensile Instability 5.2.2 Support Domain 5.2.3 Integration Constraint 5.2.4 Configurational Consistency 5.2.5 Rank Instability 5.2.6 Petrov Galerkin OTM Method References 6 Smoothed Particle Hydrodynamics 6.1 Discretization Concept 6.2 Equivalence Weak Form and Reduced Order Strong Form 6.3 Integration Constraint 6.4 Alternative Derivative Rules 6.4.1 Product Rule 6.4.2 Quotient Rule 6.5 Reproducing Conditions 6.6 Discrete Conservation Properties 6.6.1 Product Rule 6.6.2 Quotient Rule 6.7 Search Algorithm 6.8 Tensile Instability 6.9 SPH for Solids 6.10 SPH for Fluids 6.11 Boundary Conditions 6.12 Oscillations 6.13 Rank Instability References 7 Peridynamics 7.1 Correspondence Formulation 7.1.1 Theory 7.1.2 Relation to Weak Form 7.1.3 Discretization 7.2 Reproducing Conditions 7.3 Discrete Conservation Properties 7.4 Integration Constraint 7.5 Search Algorithm 7.6 Configurational Consistency 7.7 Rank Instability 7.7.1 Alternative Formulations 7.7.2 Generalization of Peridynamics 7.8 Boundary Conditions References 8 Modeling Selective Laser Melting 8.1 Physical Phenomena 8.1.1 Laser Matter Interaction 8.1.2 Heat Transfer 8.1.3 Heat Capacity and Phase Change 8.1.4 Surface Tension and Wetting 8.1.5 Marangoni Convection and Viscosity 8.1.6 Recoil Pressure 8.1.7 Chemical Reactions 8.1.8 Powder Flow 8.2 Experimental Observations 8.2.1 Denudation Zone 8.2.2 Irregular Tracks 8.2.3 Pores and Surface Roughness 8.2.4 Residual Stresses 8.3 Laser Modeling 8.3.1 Ray-Tracing 8.3.2 Volumetric Heat Source 8.4 Modeling of Material Response 8.4.1 Kinematics 8.4.2 Constitutive Equations Solid Phase 8.4.3 Constitutive Equations Fluid Phase 8.4.4 Thermal Constitutive Equations 8.4.5 Neumann Boundary Conditions 8.5 Solution Using SPH 8.5.1 Spatial Discretization 8.5.2 Temporal Discretization 8.6 Solution Using OTM 8.6.1 Spatial Discretization 8.6.2 Temporal Discretization 8.7 Computational Studies 8.7.1 Comparison of Laser Modeling 8.7.2 Comparison of Solution Schemes 8.7.3 Residual Stresses 8.7.4 Single Track Computations References 9 Modeling Direct Poly Printing 9.1 Physical Phenomena 9.1.1 Laser Matter Interaction 9.1.2 Heat Transfer 9.1.3 Heat Capacity and Crosslinking 9.1.4 Surface Tension and Wetting 9.1.5 Viscosity 9.2 Experimental Observations 9.2.1 Drop Radius 9.2.2 Printing Shape 9.3 Laser Modeling 9.4 Modeling of Material Response 9.4.1 Mechanical Constitutive Equations 9.4.2 Thermal Constitutive Equations 9.4.3 Chemical Constitutive Equations 9.5 Discretization Using Peridynamics 9.5.1 Time Integration 9.6 Computational Studies 9.6.1 Influence of Extrusion Velocity 9.6.2 Influence of Laser Power 9.6.3 Conclusion References