Altenbach / Pouget / Rousseau Generalized Models and Non-classical Approaches in Complex Materials 2

1. Auflage 2018
ISBN: 978-3-319-77504-3
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 90, 335 Seiten, eBook

Reihe: Advanced Structured Materials

This book is the 2nd special volume dedicated to the memory of Gérard Maugin. Over 30 leading scientists present their contribution to reflect the vast field of scientific activity of Gérard Maugin. The topics of contributions employing often non-standard methods (generalized model) in this volume show the wide range of subjects that were covered by this exceptional scientific leader.

The topics rangefrom micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro-macro aspects, computational efforts, possibilities to identify the constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Zielgruppe

Research

Autoren/Hrsg.

Altenbach, Holm

Pouget, Joël

Rousseau, Martine

Collet, Bernard

Michelitsch, Thomas

Inhaltsverzeichnis

1;Preface;7
2;Contents;9
3;Contributors;11
4;1 Damping in Materials and Structures: An Overview;14
4.1;Abstract;14
4.2;1.1 Introduction;14
4.3;1.2 Mechanisms of Energy Dissipation;15
4.3.1;1.2.1 Macroscopic Approach;16
4.3.1.1;1.2.1.1 Viscous Dissipation;17
4.3.1.2;1.2.1.2 Friction Dissipation;17
4.3.1.3;1.2.1.3 Magneto-Mechanic Dissipation;17
4.3.1.4;1.2.1.4 Electro-Mechanic Dissipation;18
4.3.1.5;1.2.1.5 Plastic Dissipation;18
4.3.2;1.2.2 Microscopic Approach;19
4.3.2.1;1.2.2.1 Atomic Scale Approach;19
4.3.2.2;1.2.2.2 Molecular Scale Approach;20
4.3.2.3;1.2.2.3 Mesoscopic Scale Approach;21
4.4;1.3 Modelling Energy Dissipation;22
4.4.1;1.3.1 Internal Forces;22
4.4.2;1.3.2 Work of Internal Forces: Cycling;23
4.4.3;1.3.3 Viscous Dissipation;26
4.4.3.1;1.3.3.1 Linear Behavior of the Phenomenon;26
4.4.3.1.1;Discrete Bi-parametric Model (Like Voigt Model);28
4.4.3.1.2;Continuous Multi-parametric Model (Prony Series);29
4.4.3.2;1.3.3.2 Non-linear Behavior of the Phenomenon;29
4.4.3.2.1;Schapery Model;30
4.4.3.2.2;Valanis-Landel Model;31
4.4.3.2.3;Frechet-Volterra Series Model;32
4.4.3.2.4;Linearization of the Phenomenon;33
4.4.4;1.3.4 Friction Dissipation;33
4.4.4.1;1.3.4.1 Coulomb’s Friction Modelling;34
4.4.4.2;1.3.4.2 Tresca’s Friction Modelling;35
4.4.4.3;1.3.4.3 Dahl’s Friction Modelling;35
4.4.4.4;1.3.4.4 Micro-friction;36
4.5;1.4 Conclusion;37
4.6;References;38
5;2 The Principle of Virtual Power (PVP): Application to Complex Media, Extension to Gauge and Scale Invariances, and Fundamental Aspects;41
5.1;Abstract;41
5.2;2.1 First Part;42
5.2.1;2.1.1 Complex Media: Modeling of the Different Continua;42
5.2.2;2.1.2 Thermo-Electro-Magneto-Mechanical Equations;44
5.2.2.1;2.1.2.1 General Principles in Global Form;44
5.2.2.2;2.1.2.2 Local Electro-Magneto-Mechanical Balance Equations;50
5.2.2.3;2.1.2.3 Local Thermodynamical Equations;52
5.2.3;2.1.3 Clausius-Duhem Inequality;52
5.3;2.2 Second Part;53
5.3.1;2.2.1 Extension of the PVP to Gauge and Scale Invariances;53
5.3.2;2.2.2 Extended form of d’Alembert’s Principle;54
5.3.3;2.2.3 Unified Global Statement;54
5.3.4;2.2.4 Derivation of Scale, Gauge and Rotational Invariances;56
5.3.5;2.2.5 Local Equations;57
5.3.6;2.2.6 Relativistic Framework;58
5.4;2.3 Third Part;59
5.4.1;2.3.1 Foundation of the Principle of Virtual Power (PVP);59
5.4.2;2.3.2 Main Points of the Leibnizian Dynamical Framework;60
5.4.3;2.3.3 Determination of the Yet Under-Determinate Framework;61
5.4.4;2.3.4 Deduction of the PVP Based on Duality;62
5.4.5;2.3.5 Derivation of Einstein’s Dynamics;62
5.5;Acknowledgements;63
5.6;References;63
6;3 The Limitations and Successes of Concurrent Dynamic Multiscale Modeling Methods at the Mesoscale;66
6.1;Abstract;66
6.2;3.1 Introduction;67
6.3;3.2 Review of Dynamic Multiscale Methods;68
6.3.1;3.2.1 Coupled Atomistic and Discrete Dislocation Dynamics;68
6.3.2;3.2.2 Coupled Extended Finite Element Method;70
6.3.3;3.2.3 Concurrent Atomistic Continuum Method;72
6.3.4;3.2.4 The Hot Quasi-Continuum Method;74
6.3.5;3.2.5 The Atomistic to Continuum Method;76
6.4;3.3 Analysis;78
6.4.1;3.3.1 Modeling Materials Beyond Monoatomic Crystals;78
6.4.2;3.3.2 Modeling of Defects and Waves;81
6.5;3.4 Conclusions;83
6.6;Acknowledgements;84
6.7;References;85
7;4 Modeling Semiconductor Crystal Growth Under Electromagnetic Fields;89
7.1;Abstract;89
7.2;4.1 Introduction;89
7.2.1;4.1.1 Liquid Phase Electroepitaxy;90
7.2.2;4.1.2 Traveling Heater Method;92
7.3;4.2 Basic Equations of an Electromagnetic Liquid Continuum;94
7.3.1;4.2.1 Basic Equations;94
7.3.2;4.2.2 Constitutive Equations;96
7.4;4.3 Liquid Phase Electroepitaxial Growth of Binary Systems Under Magnetic Field;99
7.4.1;4.3.1 Electromagnetic Mobility;101
7.5;4.4 Growth of Binary Systems by the Traveling Heater Method Under Magnetic Fields;102
7.5.1;4.4.1 Growth by the Traveling Heater Method Under Static Magnetic Field;103
7.5.2;4.4.2 Growth by the Traveling Heater Method Under Rotating Magnetic Field;105
7.6;4.5 Conclusions;106
7.7;Acknowledgements;107
7.8;References;107
8;5 Dispersion Properties of a Closed-Packed Lattice Consisting of Round Particles;111
8.1;5.1 Introduction;112
8.2;5.2 Discrete Model for a Hexagonal Lattice Consisting of Round Particles;114
8.3;5.3 Derivation of the Dispersion Equation;119
8.4;5.4 Dispersion Properties of Normal Waves;121
8.5;5.5 Conclusions;124
8.6;References;126
9;6 Emulating the Raman Physics in the Spatial Domain with the Help of the Zakharov’s Systems;128
9.1;Abstract;128
9.2;6.1 Introduction;128
9.3;6.2 Soliton Dynamics in an Extended Nonlinear Schrödinger Equation with a Pseudo-Raman Effect and Inhomogeneous Dispersion;131
9.4;6.3 Damped Solitons in an Extended Nonlinear Schrödinger Equation with a Pseudo-Raman Effect and Exponentially Decreasing Dispersion;134
9.5;6.4 Soliton in a Higher-Order Nonlinear Schrödinger Equation with Pseudo-Raman Effect and Inhomogeneous Second-Order Diffraction;138
9.6;6.5 Vector Solitons in Coupled Nonlinear Equations with the Pseudo-Raman Effect and Inhomogeneous Dispersion;140
9.6.1;6.5.1 Analytical Results;141
9.6.2;6.5.2 Numerical Results;144
9.7;6.6 Solitons in a Forced Nonlinear Schrödinger Equation with the Pseudo-Raman Effect;147
9.8;6.7 Conclusion;151
9.9;Acknowledgements;151
9.10;References;151
10;7 Generalized Differential Effective Medium Method for Simulating Effective Physical Properties of 2D Percolating Composites;154
10.1;Abstract;154
10.2;7.1 Introduction;154
10.3;7.2 Generalized Differential Effective Medium Method for Elastic Moduli and Conductivity Prediction;156
10.4;7.3 Elastic Properties Calculations;159
10.5;7.4 Effective Conductivity Calculations;163
10.6;7.5 Concluding Remarks;166
10.7;Acknowledgements;167
10.8;References;167
11;8 Nonlinear Acoustic Wedge Waves;169
11.1;Abstract;169
11.2;8.1 Introduction;170
11.3;8.2 Evolution Equation with Second-Order Nonlinearity Only;174
11.4;8.3 Nonlinear Evolution of Acoustic Wedge Pulses;179
11.5;8.4 Evolution Equation with Second- and Third-Order Nonlinearity;182
11.6;8.5 Conclusions;187
11.7;Acknowledgements;187
11.8;Appendix A;188
11.9;Appendix B;189
11.10;References;190
12;9 Analysis of Nonlinear Wave Propagation in Hyperelastic Network Materials;193
12.1;Abstract;193
12.2;9.1 Introduction;194
12.3;9.2 Incremental Scheme for the Computation of the Effective Hyperelastic Effective Models;196
12.4;9.3 Identification of a Hyperelastic Strain Energy Density for the Hexagonal Lattice, the Re-entrant Lattice and Plain Weave Textile;197
12.5;9.4 Analysis of Nonlinear Wave Propagation in the Homogenized Hyperelastic Continua;201
12.5.1;9.4.1 Wave Propagation Analysis for the Form 1 of the Hyperelastic Effective Medium Energy;201
12.5.2;9.4.2 Wave Propagation Analysis for Form 2 of the Hyperelastic Energy;203
12.6;9.5 Conclusion;206
12.7;References;207
13;10 Multiscale Modeling of 2D Material MoS2 from Molecular Dynamics to Continuum Mechanics;209
13.1;Abstract;209
13.2;10.1 Introduction;209
13.3;10.2 Crystal Structure and Interatomic Potential of MoS2;210
13.4;10.3 Molecular Dynamics;212
13.5;10.4 Thermoelasticity and Sequential Multiscale Modeling;214
13.5.1;10.4.1 Governing Equations of Thermoelasticity;214
13.5.2;10.4.2 Elastic Constants;216
13.5.3;10.4.3 Thermal Conductivity;217
13.5.4;10.4.4 Specific Heat and Thermal Expansion Coefficient;218
13.6;10.5 Concurrent Multiscale Modeling from Atoms to Genuine Continuum;219
13.6.1;10.5.1 Interfacial Conditions;221
13.6.2;10.5.2 Multiple Time Scale Algorithm;222
13.6.3;10.5.3 Sample Problems and Numerical Results;223
13.6.3.1;10.5.3.1 Material Constants Obtained from MD Simulations;223
13.6.3.2;10.5.3.2 Case Study;224
13.7;10.6 Conclusion and Future Work;226
13.8;References;227
14;11 Gradient Elasticity Effects on the Two-Phase Lithiation of LIB Anodes;228
14.1;Abstract;228
14.2;11.1 Introduction;228
14.3;11.2 Theoretical Framework of Gradient Chemoelasticity;230
14.4;11.3 Modeling Lithiation of a Spherical Silicon Particle;232
14.4.1;11.3.1 Governing Equations;232
14.4.2;11.3.2 Material and Model Parameters;234
14.4.3;11.3.3 Initial and Boundary Conditions;235
14.4.4;11.3.4 Numerical Solution;236
14.4.5;11.3.5 Stress and Strain Radial Profiles;238
14.5;11.4 Conclusions;240
14.6;Acknowledgements;240
14.7;References;240
15;12 Generalized Continua Concepts in Coarse-Graining Atomistic Simulations;243
15.1;Abstract;243
15.2;12.1 Generalized Continuum Mechanics (GCM);244
15.3;12.2 Atomistic Field Theory (AFT);245
15.4;12.3 The Concurrent Atomistic-Continuum (CAC) Method;249
15.4.1;12.3.1 A Comparison Between CAC and Other Multiscale Methods;249
15.4.2;12.3.2 Code Development;251
15.4.3;12.3.3 Numerical Implementations in PyCAC;252
15.5;12.4 Applications of the CAC Method to Metal Plasticity;253
15.5.1;12.4.1 Static Dislocation Properties;254
15.5.2;12.4.2 Fast Moving Dislocations and Phonons;256
15.5.3;12.4.3 Dislocation/GB Interactions;258
15.6;12.5 Conclusions;260
15.7;Acknowledgements;261
15.8;References;261
16;13 Bending of a Cantilever Piezoelectric Semiconductor Fiber Under an End Force;267
16.1;Abstract;267
16.2;13.1 Introduction;268
16.3;13.2 Three-Dimensional Equations;268
16.4;13.3 One-Dimensional Equations;270
16.5;13.4 A Cantilever Under a Transverse End Force;274
16.6;13.5 Numerical Results and Discussion;276
16.7;13.6 Conclusions;281
16.8;Acknowledgements;282
16.9;References;282
17;14 Contact Mechanics in the Framework of Couple Stress Elasticity;285
17.1;Abstract;285
17.2;14.1 Introduction;286
17.3;14.2 Basic Equations in Plane-Strain;288
17.4;14.3 Green’s Functions;291
17.5;14.4 Formulation of Contact Problems;298
17.6;14.5 Singular Integral Equation Approach;301
17.6.1;14.5.1 Indentation by a Flat Punch;301
17.6.1.1;14.5.1.1 Complete Contact;302
17.6.1.2;14.5.1.2 Receding Contact;303
17.6.2;14.5.2 Indentation by a Cylindrical Indenter;304
17.6.3;14.5.3 Indentation by a Wedge Indenter;304
17.7;14.6 Results and Discussion;305
17.8;14.7 Conclusions;310
17.9;References;310
18;15 Radiation from Equivalent Body Forces for Scattering of Surface Waves by a Near-Surface Cylindrical Cavity;313
18.1;Abstract;313
18.2;15.1 Introduction;313
18.3;15.2 Formulation;315
18.4;15.3 Equivalent Body Forces;318
18.5;15.4 Surface Waves Generated by the Equivalent Body Forces;322
18.5.1;15.4.1 Surface Waves Generated by the Equivalent Body Forces Due to u_{x};322
18.5.2;15.4.2 Surface Waves Generated by the Equivalent Body Forces Due to u_{z};329
18.6;15.5 Conclusions;332
18.7;Acknowledgements;333
18.8;References;333
19;16 Correction to: Generalized Models and Non-classical Approaches in Complex Materials 2;335
19.1;Correction to: H. Altenbach et al. (eds.), Generalized Models and Non-classical Approaches in Complex Materials 2, Advanced Structured Materials 90, https://doi.org/10.1007/978-3-319-77504-3;335

Über Autor(innen)

The authors of the book dedicated this book to Gérard A. Maugin, an exceptional French engineering scientist and philosopher. Maugin’s achievements in the fields of Physical Sciences and Engineering embrace relativistic continuum mechanics, micro magnetism, electrodynamics of continua, thermo mechanics, surface waves and nonlinear waves in continua, lattice dynamics, material equations and biomechanical applications.