Muñoz-Rojas Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials

1. Auflage 2016
ISBN: 978-3-319-04265-7
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 49, 392 Seiten

Reihe: Advanced Structured Materials

This volume presents recent research work focused in the development of adequate theoretical and numerical formulations to describe the behavior of advanced engineering materials. Particular emphasis is devoted to applications in the fields of biological tissues, phase changing and porous materials, polymers and to micro/nano scale modeling. Sensitivity analysis, gradient and non-gradient based optimization procedures are involved in many of the chapters, aiming at the solution of constitutive inverse problems and parameter identification. All these relevant topics are exposed by experienced international and inter institutional research teams resulting in a high level compilation. The book is a valuable research reference for scientists, senior undergraduate and graduate students, as well as for engineers acting in the area of computational material modeling.

Autoren/Hrsg.

Muñoz-Rojas, Pablo Andrés

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Micro and Nanoscale Modeling;10
4;On the Variational Analysis of Vibrations of Prestressed Six-Parameter Shells;11
4.1;1 Introduction;11
4.2;2 Dynamics and Statics of Micropolar Plates and Shells;13
4.3;3 Linearized Boundary-Value Problems;17
4.4;4 Eigen-Vibrations of Prestressed Micropolar Shells;20
4.5;5 Rayleigh Principle;20
4.6;6 Conclusions;24
4.7;References;24
5;Multi-objective Topology Optimization Design of Micro-structures;28
5.1;1 Introduction;28
5.2;2 Multi-objective Problem Formulation;29
5.2.1;2.1 Preliminaries in the Multi-scale Modeling;30
5.2.2;2.2 The Homogenized Conductivity Tensor;31
5.2.3;2.3 The Homogenized Elasticity Tensor;34
5.3;3 Topological Derivative;37
5.4;4 Numerical Results;42
5.4.1;4.1 Example 1. Bulk Modulus and Horizontal Conductivity Maximization;45
5.4.2;4.2 Example 2. Bulk Modulus and Orthogonal Conductivity Maximization;46
5.4.3;4.3 Example 3. Poisson's Ratio and Horizontal Conductivity Maximization;47
5.4.4;4.4 Example 4. Poisson's Ratio Minimization and Horizontal Conductivity Maximization;48
5.4.5;4.5 Example 5. Poisson Ratio Minimization and Orthogonal Conductivity Maximization;49
5.4.6;4.6 Example 6. Shear Modulus and Horizontal Conductivity Maximization;51
5.5;5 Concluding Remarks;52
5.6;References;52
6;3 Sensitivity Analysis of Micro Models for Solidification of Pure Metals;55
6.1;Abstract;55
6.2;1 Introduction;55
6.3;2 Governing Equations;57
6.4;3 Nucleation and Nuclei Growth;60
6.5;4 Sensitivity Analysis;65
6.6;5 Final Remarks;69
6.7;Acknowledgments;69
6.8;References;69
7;Biological Tissues;71
8;Variational Constituive Models for Soft Biological Tissues;72
8.1;1 Background;72
8.2;2 Variational Framework;73
8.3;3 A Set of Variational Inelastic Models;76
8.3.1;3.1 A Viscoelastic Model for Isotropic Soft Materials;77
8.3.2;3.2 A Viscoelastic Model for Fiber-Reinforced Soft Materials;79
8.3.3;3.3 A Viscoplastic Model for Isotropic Soft Materials Undergoing Permanent Deformations;82
8.3.4;3.4 Material Models;84
8.3.5;3.5 Tangent Moduli;86
8.4;4 Numerical Examples;87
8.4.1;4.1 Isotropic Viscoelastic Case;88
8.4.2;4.2 Viscoelastic Fiber-Reinforced Case;88
8.4.3;4.3 Elasto-Vicoplastic Model;90
8.5;5 Concluding Remarks;92
8.6;References;92
9;5 Sensitivity Analysis of Temperature Field and Parameter Identification in Burned and Healthy Skin Tissue;94
9.1;Abstract;94
9.2;1 Introduction;95
9.3;2 Governing Equations;96
9.4;3 Sensitivity Analysis;97
9.5;4 Boundary Element Method;99
9.6;5 Inverse Problem;107
9.7;6 Shape Sensitivity Analysis;108
9.8;7 Results of Computations;109
9.9;8 Conclusions;116
9.10;Acknowledgements;116
9.11;References;116
10;Application of the hp-FEM for Hyperelastic Problems with Isotropic Damage;118
10.1;1 Introduction;118
10.2;2 Hyperelasticity;120
10.2.1;2.1 Compressible Neo-Hookean Material;120
10.2.2;2.2 Nearly-Incompressible Mooney-Rivlin Material;121
10.2.3;2.3 Principle of Virtual Power (PVP);123
10.2.4;2.4 Linearization of the Weak Form;124
10.2.5;2.5 High-Order Shape Functions;127
10.2.6;2.6 Local Finite Element Discretization;128
10.2.7;2.7 Local Pressure Projection;128
10.2.8;2.8 Discretization of the Equilibrium Equation;132
10.2.9;2.9 Discretization of the Linearized Equilibrium Equation;133
10.2.10;2.10 Global Newton-Raphson Equation;134
10.3;3 Hyperelastic Damage;135
10.3.1;3.1 Mullins Effect in Hyperelastic Materials;135
10.3.2;3.2 Damage Variable and Thermodynamic Aspects;136
10.3.3;3.3 Damage Criterion;138
10.3.4;3.4 Damage Evolution Law;139
10.3.5;3.5 Constitutive Relations;140
10.3.6;3.6 Damage Algorithm;141
10.4;4 Convergence Tests;143
10.4.1;4.1 Test 1---Nearly-Incompressible Mooney-Rivlin Material;144
10.4.2;4.2 Test 2---Damaged Neo-Hookean Material;149
10.4.3;4.3 Test 3---Damaged Nearly-Incompressible Mooney-Rivlin Material;150
10.5;5 Conclusion;153
10.6;References;154
11;Mechanical Characterization of the Human Aorta: Experiments, Modeling and Simulation;156
11.1;1 Introduction;157
11.2;2 Materials and Methods;161
11.2.1;2.1 Experimental Procedure;161
11.2.2;2.2 Constitutive Modeling;170
11.2.3;2.3 Material Characterization via the Tensile Test;172
11.2.4;2.4 Analysis of the Pressurization Test;174
11.3;3 Results;175
11.3.1;3.1 Ascending Aorta;175
11.3.2;3.2 Aortic Arch;178
11.3.3;3.3 Descending Aorta;186
11.4;4 Discussion;191
11.4.1;4.1 Ascending Aorta;191
11.4.2;4.2 Aortic Arch;195
11.4.3;4.3 Descending Aorta;199
11.5;5 Conclusions;200
11.6;6 Conflicts of Interest;202
11.7;References;203
12;Porous and Multiphase Materials;208
13;8 Optimization of Functionally Graded Materials Considering Dynamical Analysis;209
13.1;Abstract;209
13.2;1 Introduction;210
13.3;2 Functionally Graded Materials;211
13.4;3 Topology Optimization Method for FGM Design;214
13.4.1;3.1 Basics of the Topology Optimization Method;214
13.4.2;3.2 Topology Optimization of FGMs;218
13.5;4 Topology Optimization of Dynamically Loaded Structures;220
13.5.1;4.1 Dynamic Finite Element Analysis;220
13.5.2;4.2 Topology Optimized Structures Under Impact Loads;224
13.5.3;4.3 Equivalent Static Loads;226
13.5.4;4.4 The Optimization Process with ESLs;226
13.6;5 TOM-Based Design of FGMs Under Impact Loads;228
13.6.1;5.1 Heuristic Approach;228
13.6.2;5.2 Optimized Approach;233
13.7;6 Conclusions of the Chapter;240
13.8;Acknowledgments;240
13.9;References;240
14;Complex Variable Semianalytical Method for Sensitivity Evaluation in Nonlinear Path Dependent Problems: Applications to Periodic Truss Materials;242
14.1;1 Introduction;242
14.2;2 Nonlinear Truss Finite Element Formulation;244
14.2.1;2.1 Virtual Work;246
14.2.2;2.2 Internal Force Vector;247
14.2.3;2.3 Tangent Stiffness Matrix;248
14.2.4;2.4 Geometric Nonlinearity;249
14.2.5;2.5 Material Nonlinearity: A Coupled Elastoplastic Model for Ductile Damage;250
14.2.6;2.6 Tangent Modulus;255
14.3;3 Sensitivity Analysis;255
14.3.1;3.1 Sensitivity Analysis for Path Independent Problems;256
14.3.2;3.2 Sensitivity Analysis for Path Dependent Problems;260
14.4;4 Periodic Truss Material;264
14.4.1;4.1 Sensitivity Analysis of Periodic Truss Materials;264
14.4.2;4.2 Bulk Modulus Sensitivity Expression;267
14.4.3;4.3 Numerical Evaluation of the Bulk Modulus Sensitivity;268
14.5;5 Conclusion;270
14.6;References;271
15;10 Laser Beam Drilling of Cellular Metals: Numerical Simulation;274
15.1;Abstract;274
15.2;1 Introduction;275
15.3;2 Fundamentals of Laser Technology;276
15.3.1;2.1 Laser Beam Drilling Technology;276
15.3.2;2.2 Laser Beam Behavior;276
15.3.3;2.3 Homogenization and RVE;281
15.4;3 Program Code;283
15.4.1;3.1 Flow Chart of the Program Code;283
15.4.2;3.2 Finite Volume Method;284
15.5;4 Results;286
15.5.1;4.1 Sintered and Soldered Cells;288
15.5.2;4.2 Thermal Conductivity Influence;289
15.5.3;4.3 Considerations About the Results;293
15.6;5 Gradient of Temperature and Velocity of Drilling;294
15.7;6 Total Heat and Expected Heat;295
15.8;7 Drilling Width;296
15.9;8 Conclusions;298
15.10;References;299
16;11 Metallic Foam Density Distribution Optimization Using Genetic Algorithms and Voronoi Tessellation;301
16.1;Abstract;301
16.2;1 Introduction;302
16.3;2 Modeling of Open-Cell Foam Structures;303
16.4;3 Optimization;305
16.4.1;3.1 Density Modification of Foam;305
16.4.2;3.2 Genetic Algorithms;306
16.4.2.1;3.2.1 Selection;307
16.4.2.2;3.2.2 Crossover;307
16.4.2.3;3.2.3 Mutation;308
16.4.3;3.3 Fitness Function Evaluation;308
16.4.4;3.4 Algorithm;310
16.5;4 Applications;311
16.5.1;4.1 Example 1;311
16.5.2;4.2 Example 2;314
16.5.3;4.3 Example 3;316
16.6;5 Conclusions;317
16.7;Acknowledgments;318
16.8;References;318
17;Polymers;320
18;12 Modeling Material Behavior of Polymers;321
18.1;Abstract;321
18.2;1 Introduction;321
18.2.1;1.1 Micromolecular Background to Viscous and Solid Behavior;322
18.2.2;1.2 Types of Polymers and Their Tensile and Compressive Behavior;323
18.2.3;1.3 Experimental Considerations;327
18.2.4;1.4 Polymer Material Testing at the University of Waterloo;328
18.3;2 Constitutive Modeling;332
18.3.1;2.1 Micro- and Macro-Scale Modeling;332
18.3.2;2.2 Viscoelastic Modeling;333
18.3.3;2.3 Viscoplastic Modeling;335
18.4;3 Parameter Estimation for Linear Modeling;336
18.5;4 Nonlinear Modeling;339
18.5.1;4.1 Methods for ‘Nonlinearization’ of the Model Parameters;340
18.6;5 Extending the Material Parameters to Longer Times Frames;343
18.6.1;5.1 Using Short Term Testing for Predictions at Longer Time Frames;343
18.6.2;5.2 Viscoelastic (NVE) and Viscoplastic (NVP) Long Term Responses;344
18.7;6 Modeling the Response Under Varying Stress;346
18.7.1;6.1 Modified Superposition Principle (MSP);346
18.8;7 Conclusion;349
18.9;References;350
19;Material Model Based on Response Surfaces of NURBS Applied to Isotropic and Orthotropic Materials;353
19.1;1 Introduction;354
19.2;2 Nonuniform Rational B-Spline Curves and Surfaces;355
19.2.1;2.1 Tensor Product Surfaces;355
19.2.2;2.2 Definition of B--Spline Basis Functions;356
19.2.3;2.3 Definition of B--Spline Curves;356
19.2.4;2.4 Definition of B--Spline Surfaces;357
19.2.5;2.5 Definition of NURBS Surfaces;359
19.2.6;2.6 Derivatives of a NURBS Surface;359
19.3;3 Data Fitting;361
19.4;4 Material Model Based on NURBS for Principal Directions (NURBS--Material);362
19.5;5 Application of NURBS--Material in Membrane Finite Element Modeling;366
19.5.1;5.1 Comparison with Elastoplastic Material Model;366
19.5.2;5.2 Comparison with an Orthotropic Material Model;370
19.6;6 Conclusions;372
19.7;References;373
20;14 Characterization of Constitutive Parameters for Hyperelastic Models Considering the Baker-Ericksen Inequalities;374
20.1;Abstract;374
20.2;1 Introduction;374
20.3;2 Constitutive Parameters Optimization Technique;376
20.4;3 Imposing the Inequalities to the Models;380
20.5;4 Experimental Data;383
20.6;5 Results;384
20.7;6 Conclusions;390
20.8;References;391