Zohdi Modeling and Simulation of Functionalized Materials for Additive Manufacturing and 3D Printing: Continuous and Discrete Media

Continuum and Discrete Element Methods
1. Auflage 2018
ISBN: 978-3-319-70079-3
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 60, 308 Seiten

Reihe: Lecture Notes in Applied and Computational Mechanics

Within the last decade, several industrialized countries have stressed the importance of advanced manufacturing to their economies. Many of these plans have highlighted the development of additive manufacturing techniques, such as 3D printing which, as of 2018, are still in their infancy. The objective is to develop superior products, produced at lower overall operational costs. For these goals to be realized, a deep understanding of the essential ingredients comprising the materials involved in additive manufacturing is needed. The combination of rigorous material modeling theories, coupled with the dramatic increase of computational power can potentially play a significant role in the analysis, control, and design of many emerging additive manufacturing processes. Specialized materials and the precise design of their properties are key factors in the processes. Specifically, particle-functionalized materials play a central role in this field, in three main regimes:  (1) to enhance overall filament-based material properties, by embedding particles within a binder, which is then passed through a heating element and the deposited onto a surface,  (2) to 'functionalize' inks by adding particles to freely flowing solvents forming a mixture, which is then deposited onto a surface and  (3) to directly deposit particles, as dry powders, onto surfaces and then to heat them with a laser, e-beam or other external source, in order to fuse them into place. The goal of these processes is primarily to build surface structures which are extremely difficult to construct using classical manufacturing methods. The objective of this monograph is introduce the readers to basic techniques which can allow them to rapidly develop and analyze particulate-based materials needed in such additive manufacturing processes. This monograph is broken into two main parts: 'Continuum Method' (CM) approaches and 'Discrete Element Method' (DEM) approaches. The materials associated with methods (1) and (2) are closely related types of continua (particles embedded in a continuous binder) and are treated using continuum approaches. The materials in method (3), which are of a discrete particulate character, are analyzed using discrete element methods.

Autoren/Hrsg.

Zohdi, Tarek I.

Inhaltsverzeichnis

1;Preface;7
2;Contents;9
3;List of Figures;14
4;1 Introduction: Additive/3D Printing Materials---Filaments, Functionalized Inks, and Powders;1
4.1;1.1 Objectives;23
4.2;References;24
5;2 Continuum Methods (CM): Basic Continuum Mechanics;26
5.1;2.1 Notation;26
5.2;2.2 Kinematics of Deformations;26
5.2.1;2.2.1 Deformation of Line Elements;28
5.3;2.3 Equilibrium/Kinetics of Continua;29
5.3.1;2.3.1 Postulates on Volume and Surface Quantities;29
5.3.2;2.3.2 Balance Law Formulations;31
5.4;2.4 The First Law of Thermodynamics/An Energy Balance;31
5.5;2.5 Linearly Elastic Constitutive Equations;33
5.5.1;2.5.1 The Infinitesimal Strain Case;33
5.5.2;2.5.2 Material Response;33
5.5.3;2.5.3 Material Component Interpretation;35
5.6;References;37
6;3 CM Approaches: Characterization of Particle-Functionalized Materials;38
6.1;3.1 Introduction;38
6.2;3.2 Basic Micro--Macro Concepts;39
6.2.1;3.2.1 Testing Procedures;40
6.2.2;3.2.2 The Average Strain Theorem;41
6.2.3;3.2.3 The Average Stress Theorem;42
6.2.4;3.2.4 Satisfaction of Hill's Energy Condition;42
6.2.5;3.2.5 The Hill--Reuss--Voigt Bounds;43
6.2.6;3.2.6 Improved Estimates;44
6.3;References;45
7;4 CM Approaches: Estimation and Optimization of the Effective Properties of Mixtures;48
7.1;4.1 Combining Bounds;48
7.2;4.2 Local Fields: Stresses and Strains;49
7.3;4.3 Optimization: Formulation of a Cost Function;51
7.4;4.4 Suboptimal Properties Due to Defects---Effects of Pores/voids;57
7.5;References;58
8;5 CM Approaches: Numerical Thermo-Mechanical Formulations;60
8.1;5.1 Transient Thermo-Mechanical Coupled Fields;61
8.2;5.2 Iterative Staggering Scheme;63
8.3;5.3 Temporal Discretization of Fields;67
8.4;5.4 The Overall Solution Scheme;68
8.5;5.5 Numerical Examples;71
8.6;5.6 Summary and Extensions;76
8.7;5.7 Chapter Appendix 1: Summary of Spatial Finite Difference Stencils;79
8.8;5.8 Chapter Appendix 2: Second-Order Temporal Discretization;80
8.9;5.9 Chapter Appendix 3: Temporally Adaptive Iterative Methods;82
8.10;5.10 Chapter Appendix 4: Laser Processing;84
8.10.1;5.10.1 Formulations for Particulate-Laden Continua;85
8.10.2;5.10.2 A Specific Numerical Example---Controlled Heating;86
8.10.3;5.10.3 Numerical Examples;87
8.10.4;5.10.4 Extensions: Advanced Models for Conduction Utilizing Thermal Relaxation;92
8.11;References;95
9;6 PART II---Discrete Element Method (DEM) Approaches: Dynamic Powder Deposition;99
9.1;6.1 Direct Particle Representation/Calculations;102
9.1.1;6.1.1 Comments on Rolling;102
9.1.2;6.1.2 Particle-to-particle Contact Forces;103
9.1.3;6.1.3 Particle-Wall Contact;104
9.1.4;6.1.4 Contact Dissipation;104
9.1.5;6.1.5 Regularized Contact Friction Models;105
9.1.6;6.1.6 Particle-to-particle Bonding Relation;106
9.1.7;6.1.7 Electromagnetic Forces;106
9.1.8;6.1.8 Inter-particle Near-Field Interaction;107
9.1.9;6.1.9 Magnetic Forces;108
9.1.10;6.1.10 Interstitial Damping;108
9.2;6.2 Time-Stepping;109
9.2.1;6.2.1 Iterative (Implicit) Solution Method;109
9.2.2;6.2.2 Algorithm;111
9.3;6.3 Thermal Fields;113
9.3.1;6.3.1 Heat Transfer Model;113
9.3.2;6.3.2 Lasers---Various Levels of Description;114
9.3.3;6.3.3 Numerical Integration;116
9.4;6.4 Total System Coupling: Multiphysical Staggering Scheme;116
9.4.1;6.4.1 A General Iterative Framework;117
9.4.2;6.4.2 Overall Solution Algorithm;117
9.4.3;6.4.3 Interaction Lists;118
9.5;6.5 Numerical Examples;120
9.6;6.6 Summary for DEM Approaches;124
9.7;6.7 Chapter Appendix 1: Contact Area Parameter and Alternative Models;125
9.8;6.8 Chapter Appendix 2: Phase Transformations;128
9.9;References;129
10;7 DEM Extensions: Electrically Driven Deposition of Polydisperse Particulate Powder Mixtures;1
10.1;7.1 Introduction;136
10.2;7.2 Algorithm;137
10.3;7.3 Numerical Examples of Involving Polydisperse Depositions;138
10.4;References;148
11;8 DEM Extensions: Electrically Aided Compaction and Sintering;150
11.1;8.1 Introduction;150
11.1.1;8.1.1 Objectives;150
11.2;8.2 Direct Particle Representation;152
11.3;8.3 Thermal Fields;153
11.3.1;8.3.1 Governing Equations;153
11.3.2;8.3.2 Numerical Integration;154
11.4;8.4 Modeling of Current Flow;155
11.4.1;8.4.1 Particle Model Simplification;155
11.4.2;8.4.2 Iterative Flux Summation/Solution Process;156
11.4.3;8.4.3 Overall Solution Algorithm;158
11.5;8.5 Numerical Examples;159
11.5.1;8.5.1 STEP 1: Pouring the Particles;160
11.5.2;8.5.2 STEP 2: Compacting the Particles;160
11.6;8.6 Extensions and Conclusions;163
11.7;8.7 Chapter Appendix 1: Joule-Heating;164
11.7.1;8.7.1 Characterizing Electrical Losses;164
11.7.2;8.7.2 Joule-Heating;165
11.8;8.8 Chapter Appendix 2: Time-Scaling Arguments for calPtapprox0;165
11.9;References;166
12;9 DEM Extensions: Flexible Substrate Models;169
12.1;9.1 Introduction;169
12.2;9.2 A Multibody Dynamics Model for the Particles;170
12.2.1;9.2.1 Overall Contributing Forces;170
12.3;9.3 Induced Substrate Stresses;171
12.3.1;9.3.1 Individual Particle Contributions---Normal Load;171
12.3.2;9.3.2 Individual Particle Contributions---Tangential Load;172
12.3.3;9.3.3 Superposition of Contributions for the Total Substrate Stresses;173
12.4;9.4 Numerical Examples;175
12.5;9.5 Summary, Conclusions, and Extensions;179
12.6;References;180
13;10 DEM Extensions: Higher-Fidelity Laser Modeling;185
13.1;10.1 Propagation of Electromagnetic Energy;186
13.1.1;10.1.1 Electromagnetic Wave Propagation;186
13.1.2;10.1.2 Plane Harmonic Wave Fronts;187
13.1.3;10.1.3 Special Case: Natural (Random) Electromagnetic Energy Propagation;188
13.1.4;10.1.4 Beam Decomposition into Rays;188
13.2;10.2 Thermal Conversion of Beam (Optical) Losses;194
13.2.1;10.2.1 Algorithmic Details;195
13.3;10.3 Phase Transformations: Solid Liquid Vapor;196
13.3.1;10.3.1 Optional Time Scaling and Simulation Acceleration;197
13.4;10.4 Numerical Examples;199
13.5;10.5 Summary and Extensions;204
13.6;10.6 Chapter Appendix: Geometrical Ray Theory;206
13.7;References;208
14;11 DEM Extensions: Acoustical Pre-Processing;211
14.1;11.1 Introduction;211
14.2;11.2 Dynamic Response of an Agglomeration;214
14.3;11.3 Particle-Shock Wave Contact;214
14.3.1;11.3.1 Ray-Tracing: Incidence, Reflection, and Transmission;215
14.3.2;11.3.2 Acoustical-Pulse Computational Algorithm;217
14.3.3;11.3.3 Iterative (Implicit) Solution Method Algorithm;218
14.4;11.4 Numerical Example;219
14.5;11.5 Closing Statements;222
14.6;References;228
15;12 Summary and Closing Remarks;232
15.1;References;235
16;Appendix Monograph Appendix A: Elementary Notation and Mathematical Operations;238
16.1;A.1 Vectors, Products, and Norms;238
16.2;A.2 Basic Linear Algebra;239
16.3;A.3 Integral Transformations;243
17;Appendix Monograph Appendix B---CM Approaches: Effective Electrical Properties of Mixtures;245
17.1;B.1 Computing the Effective Electrical Conductivity;246
17.2;B.2 Concentration Tensors and Load-Sharing;247
17.3;B.3 ``Load-Sharing'' Interpretation;248
17.4;B.4 Joule-Heating;249
17.5;B.5 The Controllable Quantities: langleJrangle? and langleErangle?;251
17.6;B.6 Joule-Heating Load-Shares;253
17.7;B.7 Examples of Joule-Heating Load-Sharing;256
17.8;B.7.1 A General Dielectric Mixture;256
17.9;B.7.2 An Extreme Mixture: High-Conductivity (``Superconducting'') Particles in a Low-Conductivity Matrix;257
17.10;B.7.3 An Extreme Mixture: Low-Conductivity (``Insulator'') Particles in a High-Conductivity Matrix;258
17.11;B.8 Optimization Example: Dielectric Properties Using Genetic Algorithms;259
17.12;B.9 Additional Dielectric Properties: Electrical Permittivity and Magnetic Permeability;261
17.13;B.10 The Concentration Tensor;261
17.14;B.11 ``Load-Sharing'' Interpretation;264
17.15;B.12 Thermal Conductivity;264
18;Appendix Monograph Appendix C---CM Approaches: Extensions to Multiphase Materials;268
18.1;C.1 Electrical Conductivity;268
18.2;C.1.1 The Hill--Reuss--Voigt--Weiner (HRVW) Bounds;269
18.3;C.1.2 The Hashin--Shtrikman (HS) Bounds;269
18.4;C.2 Electrical Permittivity;270
18.5;C.2.1 The Hill--Reuss--Voigt--Weiner Bounds;270
18.6;C.2.2 The Hashin--Shtrikman Bounds;270
18.7;C.3 Magnetic Permeability;271
18.8;C.3.1 The Hill--Reuss--Voigt--Weiner Bounds;271
18.9;C.3.2 The Hashin--Shtrikman Bounds;271
18.10;C.4 Thermal Conductivity;272
18.11;C.4.1 The Hill--Reuss--Voigt--Weiner Bounds;272
18.12;C.4.2 The Hashin--Shtrikman Bounds;272
18.13;C.5 Elastic Moduli;273
18.14;C.5.1 Bulk Modulus;273
18.15;C.5.1.1 The Hill--Reuss--Voigt--Weiner Bounds;273
18.16;C.5.1.2 The Hashin--Shtrikman Bounds;273
18.17;C.5.2 Shear Modulus;274
18.18;C.5.2.1 The Hill--Reuss--Voigt--Weiner Bounds;274
18.19;C.5.2.2 The Hashin--Shtrikman Bounds;275
18.20;C.6 Concentration Tensors for Multiphase materials;275
19;Appendix Monograph Appendix D---Pumping of Fluidized Particle-Laden Materials;278
19.1;D.1 Introduction;278
19.2;D.2 Channel Flow;279
19.3;D.3 Pressure Gradients;280
19.4;D.4 Velocity Profile Characteristics;281
19.5;D.5 Models for Effective Properties of Particle-Laden Fluids;282
19.6;D.5.1 Effective Density;282
19.7;D.5.2 Ancillary Effective Viscosities;283
19.8;D.6 Correlation of Pressure Gradient to Particle Volume Fraction;283
19.9;D.7 Trends;284
19.10;D.8 Summary;285
20;Appendix Monograph Appendix E---Hybrid DEM-CM Approaches for Particle-Functionalized Fluids;289
20.1;E.1 Applications;289
20.2;E.2 A Quick Review of General Governing Fluid Equations;292
20.3;E.3 Numerical Simulation of Coupled Fluid--Multiparticle Systems;295
20.4;E.4 The Overall Approach;295
20.5;E.5 Simplifying Assumptions;295
20.6;E.6 Modeling and Simulation of the Particle Dynamics Problem;296
20.7;E.7 Characterization of Particle/Fluid Interaction;297
20.8;E.8 Discretization of the Fluid;299
20.9;E.8.1 Temporal Discretization;299
20.10;E.8.2 Spatial Discretization: Spatial Finite Difference Stencils;300
20.11;E.9 Overall Iterative (Implicit) Solution Method;301