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E-raamat: Modeling and Simulation of Functionalized Materials for Additive Manufacturing and 3D Printing: Continuous and Discrete Media: Continuum and Discrete Element Methods

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Modeling and Simulation of Functionalized Materials for Additive Manufacturing and 3D Printing: Continuous and Discrete Media: Continuum and Discrete Element MethodsSuurem pilt
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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.

1 Introduction: Additive/3D Printing Materials---Filaments, Functionalized Inks, and Powders
1(8)
1.1 Objectives
5(4)
References
6(3)
2 Continuum Methods (CM): Basic Continuum Mechanics
9(12)
2.1 Notation
9(1)
2.2 Kinematics of Deformations
9(3)
2.2.1 Deformation of Line Elements
11(1)
2.3 Equilibrium/Kinetics of Continua
12(2)
2.3.1 Postulates on Volume and Surface Quantities
12(2)
2.3.2 Balance Law Formulations
14(1)
2.4 The First Law of Thermodynamics/An Energy Balance
14(2)
2.5 Linearly Elastic Constitutive Equations
16(5)
2.5.1 The Infinitesimal Strain Case
16(1)
2.5.2 Material Response
16(2)
2.5.3 Material Component Interpretation
18(2)
References
20(1)
3 CM Approaches: Characterization of Particle-Functionalized Materials
21(10)
3.1 Introduction
21(1)
3.2 Basic Micro--Macro Concepts
22(9)
3.2.1 Testing Procedures
23(1)
3.2.2 The Average Strain Theorem
24(1)
3.2.3 The Average Stress Theorem
25(1)
3.2.4 Satisfaction of Hill's Energy Condition
25(1)
3.2.5 The Hill--Reuss--Voigt Bounds
26(1)
3.2.6 Improved Estimates
27(1)
References
28(3)
4 CM Approaches: Estimation and Optimization of the Effective Properties of Mixtures
31(12)
4.1 Combining Bounds
31(1)
4.2 Local Fields: Stresses and Strains
32(2)
4.3 Optimization: Formulation of a Cost Function
34(6)
4.4 Suboptimal Properties Due to Defects---Effects of Pores/voids
40(3)
References
41(2)
5 CM Approaches: Numerical Thermo-Mechanical Formulations
43(40)
5.1 Transient Thermo-Mechanical Coupled Fields
44(2)
5.2 Iterative Staggering Scheme
46(4)
5.3 Temporal Discretization of Fields
50(1)
5.4 The Overall Solution Scheme
51(3)
5.5 Numerical Examples
54(5)
5.6 Summary and Extensions
59(3)
5.7
Chapter Appendix 1: Summary of Spatial Finite Difference Stencils
62(1)
5.8
Chapter Appendix 2: Second-Order Temporal Discretization
63(2)
5.9
Chapter Appendix 3: Temporally Adaptive Iterative Methods
65(2)
5.10
Chapter Appendix 4: Laser Processing
67(16)
5.10.1 Formulations for Particulate-Laden Continua
68(1)
5.10.2 A Specific Numerical Example---Controlled Heating
69(1)
5.10.3 Numerical Examples
70(5)
5.10.4 Extensions: Advanced Models for Conduction Utilizing Thermal Relaxation
75(3)
References
78(5)
6 PART II---Discrete Element Method (DEM) Approaches: Dynamic Powder Deposition
83(38)
6.1 Direct Particle Representation/Calculations
86(7)
6.1.1 Comments on Rolling
86(1)
6.1.2 Particle-to-particle Contact Forces
87(1)
6.1.3 Particle-Wall Contact
88(1)
6.1.4 Contact Dissipation
88(1)
6.1.5 Regularized Contact Friction Models
89(1)
6.1.6 Particle-to-particle Bonding Relation
90(1)
6.1.7 Electromagnetic Forces
90(1)
6.1.8 Inter-particle Near-Field Interaction
91(1)
6.1.9 Magnetic Forces
92(1)
6.1.10 Interstitial Damping
92(1)
6.2 Time-Stepping
93(4)
6.2.1 Iterative (Implicit) Solution Method
93(2)
6.2.2 Algorithm
95(2)
6.3 Thermal Fields
97(3)
6.3.1 Heat Transfer Model
97(1)
6.3.2 Lasers---Various Levels of Description
98(2)
6.3.3 Numerical Integration
100(1)
6.4 Total System Coupling: Multiphysical Staggering Scheme
100(4)
6.4.1 A General Iterative Framework
101(1)
6.4.2 Overall Solution Algorithm
101(1)
6.4.3 Interaction Lists
102(2)
6.5 Numerical Examples
104(4)
6.6 Summary for DEM Approaches
108(1)
6.7
Chapter Appendix 1: Contact Area Parameter and Alternative Models
109(3)
6.8
Chapter Appendix 2: Phase Transformations
112(9)
References
113(8)
7 DEM Extensions: Electrically Driven Deposition of Polydisperse Particulate Powder Mixtures
121(14)
7.1 Introduction
121(1)
7.2 Algorithm
122(1)
7.3 Numerical Examples of Involving Polydisperse Depositions
123(12)
References
133(2)
8 DEM Extensions: Electrically Aided Compaction and Sintering
135(20)
8.1 Introduction
135(2)
8.1.1 Objectives
135(2)
8.2 Direct Particle Representation
137(1)
8.3 Thermal Fields
138(2)
8.3.1 Governing Equations
138(1)
8.3.2 Numerical Integration
139(1)
8.4 Modeling of Current Flow
140(4)
8.4.1 Particle Model Simplification
140(1)
8.4.2 Iterative Flux Summation/Solution Process
141(2)
8.4.3 Overall Solution Algorithm
143(1)
8.5 Numerical Examples
144(4)
8.5.1 STEP 1: Pouring the Particles
145(1)
8.5.2 STEP 2: Compacting the Particles
145(3)
8.6 Extensions and Conclusions
148(1)
8.7
Chapter Appendix 1: Joule-Heating
149(1)
8.7.1 Characterizing Electrical Losses
149(1)
8.7.2 Joule-Heating
150(1)
8.8
Chapter Appendix 2: Time-Scaling Arguments for ∂p/∂t = 0
150(5)
References
151(4)
9 DEM Extensions: Flexible Substrate Models
155(16)
9.1 Introduction
155(1)
9.2 A Multibody Dynamics Model for the Particles
156(1)
9.2.1 Overall Contributing Forces
156(1)
9.3 Induced Substrate Stresses
157(4)
9.3.1 Individual Particle Contributions---Normal Load
157(1)
9.3.2 Individual Particle Contributions---Tangential Load
158(1)
9.3.3 Superposition of Contributions for the Total Substrate Stresses
159(2)
9.4 Numerical Examples
161(4)
9.5 Summary, Conclusions, and Extensions
165(6)
References
166(5)
10 DEM Extensions: Higher-Fidelity Laser Modeling
171(26)
10.1 Propagation of Electromagnetic Energy
172(8)
10.1.1 Electromagnetic Wave Propagation
172(1)
10.1.2 Plane Harmonic Wave Fronts
173(1)
10.1.3 Special Case: Natural (Random) Electromagnetic Energy Propagation
174(1)
10.1.4 Beam Decomposition into Rays
174(6)
10.2 Thermal Conversion of Beam (Optical) Losses
180(2)
10.2.1 Algorithmic Details
181(1)
10.3 Phase Transformations: Solid ⇒ Liquid ⇒ Vapor
182(3)
10.3.1 Optional Time Scaling and Simulation Acceleration
183(2)
10.4 Numerical Examples
185(5)
10.5 Summary and Extensions
190(2)
10.6
Chapter Appendix: Geometrical Ray Theory
192(5)
References
194(3)
11 DEM Extensions: Acoustical Pre-Processing
197(22)
11.1 Introduction
197(3)
11.2 Dynamic Response of an Agglomeration
200(1)
11.3 Particle-Shock Wave Contact
200(5)
11.3.1 Ray-Tracing: Incidence, Reflection, and Transmission
201(2)
11.3.2 Acoustical-Pulse Computational Algorithm
203(1)
11.3.3 Iterative (Implicit) Solution Method Algorithm
204(1)
11.4 Numerical Example
205(3)
11.5 Closing Statements
208(3)
11.6
Chapter Appendix: Basics of Acoustics
211(8)
References
214(5)
12 Summary and Closing Remarks
219(6)
References
222(3)
Monograph Appendix A Elementary Notation and Mathematical Operations 225(8)
Monograph Appendix B CM Approaches: Effective Electrical Properties of Mixtures 233(24)
Monograph Appendix C CM Approaches: Extensions to Multiphase Materials 257(10)
Monograph Appendix D Pumping of Fluidized Particle-Laden Materials 267(12)
Monograph Appendix E Hybrid DEM-CM Approaches for Particle-Functionalized Fluids 279
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