Generalized Models and Non-classical Approaches in Complex Materials 2 (Advanced Structured Materials, 90)

✍ Scribed by Holm Altenbach (editor), Joël Pouget (editor), Martine Rousseau (editor), Bernard Collet (editor), Thomas Michelitsch (editor)

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 335
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
Contributors
1 Damping in Materials and Structures: An Overview
Abstract
1.1 Introduction
1.2 Mechanisms of Energy Dissipation
1.2.1 Macroscopic Approach
1.2.1.1 Viscous Dissipation
1.2.1.2 Friction Dissipation
1.2.1.3 Magneto-Mechanic Dissipation
1.2.1.4 Electro-Mechanic Dissipation
1.2.1.5 Plastic Dissipation
1.2.2 Microscopic Approach
1.2.2.1 Atomic Scale Approach
1.2.2.2 Molecular Scale Approach
1.2.2.3 Mesoscopic Scale Approach
1.3 Modelling Energy Dissipation
1.3.1 Internal Forces
1.3.2 Work of Internal Forces: Cycling
1.3.3 Viscous Dissipation
1.3.3.1 Linear Behavior of the Phenomenon
Discrete Bi-parametric Model (Like Voigt Model)
Continuous Multi-parametric Model (Prony Series)
1.3.3.2 Non-linear Behavior of the Phenomenon
Schapery Model
Valanis-Landel Model
Frechet-Volterra Series Model
Linearization of the Phenomenon
1.3.4 Friction Dissipation
1.3.4.1 Coulomb’s Friction Modelling
1.3.4.2 Tresca’s Friction Modelling
1.3.4.3 Dahl’s Friction Modelling
1.3.4.4 Micro-friction
1.4 Conclusion
References
2 The Principle of Virtual Power (PVP): Application to Complex Media, Extension to Gauge and Scale Invariances, and Fundamental Aspects
Abstract
2.1 First Part
2.1.1 Complex Media: Modeling of the Different Continua
2.1.2 Thermo-Electro-Magneto-Mechanical Equations
2.1.2.1 General Principles in Global Form
2.1.2.2 Local Electro-Magneto-Mechanical Balance Equations
2.1.2.3 Local Thermodynamical Equations
2.1.3 Clausius-Duhem Inequality
2.2 Second Part
2.2.1 Extension of the PVP to Gauge and Scale Invariances
2.2.2 Extended form of d’Alembert’s Principle
2.2.3 Unified Global Statement
2.2.4 Derivation of Scale, Gauge and Rotational Invariances
2.2.5 Local Equations
2.2.6 Relativistic Framework
2.3 Third Part
2.3.1 Foundation of the Principle of Virtual Power (PVP)
2.3.2 Main Points of the Leibnizian Dynamical Framework
2.3.3 Determination of the Yet Under-Determinate Framework
2.3.4 Deduction of the PVP Based on Duality
2.3.5 Derivation of Einstein’s Dynamics
Acknowledgements
References
3 The Limitations and Successes of Concurrent Dynamic Multiscale Modeling Methods at the Mesoscale
Abstract
3.1 Introduction
3.2 Review of Dynamic Multiscale Methods
3.2.1 Coupled Atomistic and Discrete Dislocation Dynamics
3.2.2 Coupled Extended Finite Element Method
3.2.3 Concurrent Atomistic Continuum Method
3.2.4 The Hot Quasi-Continuum Method
3.2.5 The Atomistic to Continuum Method
3.3 Analysis
3.3.1 Modeling Materials Beyond Monoatomic Crystals
3.3.2 Modeling of Defects and Waves
3.4 Conclusions
Acknowledgements
References
4 Modeling Semiconductor Crystal Growth Under Electromagnetic Fields
Abstract
4.1 Introduction
4.1.1 Liquid Phase Electroepitaxy
4.1.2 Traveling Heater Method
4.2 Basic Equations of an Electromagnetic Liquid Continuum
4.2.1 Basic Equations
4.2.2 Constitutive Equations
4.3 Liquid Phase Electroepitaxial Growth of Binary Systems Under Magnetic Field
4.3.1 Electromagnetic Mobility
4.4 Growth of Binary Systems by the Traveling Heater Method Under Magnetic Fields
4.4.1 Growth by the Traveling Heater Method Under Static Magnetic Field
4.4.2 Growth by the Traveling Heater Method Under Rotating Magnetic Field
4.5 Conclusions
Acknowledgements
References
5 Dispersion Properties of a Closed-Packed Lattice Consisting of Round Particles
5.1 Introduction
5.2 Discrete Model for a Hexagonal Lattice Consisting of Round Particles
5.3 Derivation of the Dispersion Equation
5.4 Dispersion Properties of Normal Waves
5.5 Conclusions
References
6 Emulating the Raman Physics in the Spatial Domain with the Help of the Zakharov’s Systems
Abstract
6.1 Introduction
6.2 Soliton Dynamics in an Extended Nonlinear Schrödinger Equation with a Pseudo-Raman Effect and Inhomogeneous Dispersion
6.3 Damped Solitons in an Extended Nonlinear Schrödinger Equation with a Pseudo-Raman Effect and Exponentially Decreasing Dispersion
6.4 Soliton in a Higher-Order Nonlinear Schrödinger Equation with Pseudo-Raman Effect and Inhomogeneous Second-Order Diffraction
6.5 Vector Solitons in Coupled Nonlinear Equations with the Pseudo-Raman Effect and Inhomogeneous Dispersion
6.5.1 Analytical Results
6.5.2 Numerical Results
6.6 Solitons in a Forced Nonlinear Schrödinger Equation with the Pseudo-Raman Effect
6.7 Conclusion
Acknowledgements
References
7 Generalized Differential Effective Medium Method for Simulating Effective Physical Properties of 2D Percolating Composites
Abstract
7.1 Introduction
7.2 Generalized Differential Effective Medium Method for Elastic Moduli and Conductivity Prediction
7.3 Elastic Properties Calculations
7.4 Effective Conductivity Calculations
7.5 Concluding Remarks
Acknowledgements
References
8 Nonlinear Acoustic Wedge Waves
Abstract
8.1 Introduction
8.2 Evolution Equation with Second-Order Nonlinearity Only
8.3 Nonlinear Evolution of Acoustic Wedge Pulses
8.4 Evolution Equation with Second- and Third-Order Nonlinearity
8.5 Conclusions
Acknowledgements
Appendix A
Appendix B
References
9 Analysis of Nonlinear Wave Propagation in Hyperelastic Network Materials
Abstract
9.1 Introduction
9.2 Incremental Scheme for the Computation of the Effective Hyperelastic Effective Models
9.3 Identification of a Hyperelastic Strain Energy Density for the Hexagonal Lattice, the Re-entrant Lattice and Plain Weave Textile
9.4 Analysis of Nonlinear Wave Propagation in the Homogenized Hyperelastic Continua
9.4.1 Wave Propagation Analysis for the Form 1 of the Hyperelastic Effective Medium Energy
9.4.2 Wave Propagation Analysis for Form 2 of the Hyperelastic Energy
9.5 Conclusion
References
10 Multiscale Modeling of 2D Material MoS2 from Molecular Dynamics to Continuum Mechanics
Abstract
10.1 Introduction
10.2 Crystal Structure and Interatomic Potential of MoS2
10.3 Molecular Dynamics
10.4 Thermoelasticity and Sequential Multiscale Modeling
10.4.1 Governing Equations of Thermoelasticity
10.4.2 Elastic Constants
10.4.3 Thermal Conductivity
10.4.4 Specific Heat and Thermal Expansion Coefficient
10.5 Concurrent Multiscale Modeling from Atoms to Genuine Continuum
10.5.1 Interfacial Conditions
10.5.2 Multiple Time Scale Algorithm
10.5.3 Sample Problems and Numerical Results
10.5.3.1 Material Constants Obtained from MD Simulations
10.5.3.2 Case Study
10.6 Conclusion and Future Work
References
11 Gradient Elasticity Effects on the Two-Phase Lithiation of LIB Anodes
Abstract
11.1 Introduction
11.2 Theoretical Framework of Gradient Chemoelasticity
11.3 Modeling Lithiation of a Spherical Silicon Particle
11.3.1 Governing Equations
11.3.2 Material and Model Parameters
11.3.3 Initial and Boundary Conditions
11.3.4 Numerical Solution
11.3.5 Stress and Strain Radial Profiles
11.4 Conclusions
Acknowledgements
References
12 Generalized Continua Concepts in Coarse-Graining Atomistic Simulations
Abstract
12.1 Generalized Continuum Mechanics (GCM)
12.2 Atomistic Field Theory (AFT)
12.3 The Concurrent Atomistic-Continuum (CAC) Method
12.3.1 A Comparison Between CAC and Other Multiscale Methods
12.3.2 Code Development
12.3.3 Numerical Implementations in PyCAC
12.4 Applications of the CAC Method to Metal Plasticity
12.4.1 Static Dislocation Properties
12.4.2 Fast Moving Dislocations and Phonons
12.4.3 Dislocation/GB Interactions
12.5 Conclusions
Acknowledgements
References
13 Bending of a Cantilever Piezoelectric Semiconductor Fiber Under an End Force
Abstract
13.1 Introduction
13.2 Three-Dimensional Equations
13.3 One-Dimensional Equations
13.4 A Cantilever Under a Transverse End Force
13.5 Numerical Results and Discussion
13.6 Conclusions
Acknowledgements
References
14 Contact Mechanics in the Framework of Couple Stress Elasticity
Abstract
14.1 Introduction
14.2 Basic Equations in Plane-Strain
14.3 Green’s Functions
14.4 Formulation of Contact Problems
14.5 Singular Integral Equation Approach
14.5.1 Indentation by a Flat Punch
14.5.1.1 Complete Contact
14.5.1.2 Receding Contact
14.5.2 Indentation by a Cylindrical Indenter
14.5.3 Indentation by a Wedge Indenter
14.6 Results and Discussion
14.7 Conclusions
References
15 Radiation from Equivalent Body Forces for Scattering of Surface Waves by a Near-Surface Cylindrical Cavity
Abstract
15.1 Introduction
15.2 Formulation
15.3 Equivalent Body Forces
15.4 Surface Waves Generated by the Equivalent Body Forces
15.4.1 Surface Waves Generated by the Equivalent Body Forces Due to u_{x}
15.4.2 Surface Waves Generated by the Equivalent Body Forces Due to u_{z}
15.5 Conclusions
Acknowledgements
References
16 Correction to: Generalized Models and Non-classical Approaches in Complex Materials 2
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