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[资源] eBook:Computational Nanomechanics of Materials

Computational Nanomechanics of Materials
Wing Kam Liu*
Department of Mechanical Engineering
Northwestern University
2145 Sheridan Road
Evanston, IL 60208, USA
Phone: +1 847 491 7094
Fax: +1 847 491 3915
email: w-liu@northwestern.edu
Sukky Jun
Department of Mechanical and Materials Engineering
Florida International University
10555 West Flagler Street, EC 3463
Miami, FL 33174, USA
Phone: +1 305 348 1217
Fax: +1 305 348 1932
email: juns@fiu.edu
Dong Qian
Department of Mechanical, Industrial and Nuclear Engineering
University of Cincinnati, PO Box 210072
Cincinnati, OH 45221, USA
Phone: +1 513 556 0422
Fax: +1 513 556 3390
email: Dong.Qian@uc.edu
*Corresponding Author
Accepted for publication in Handbook of Theoretical and Computational
Nanotechnology edited by M. Rieth and W. Schommers, American
Scientific Publishers, Stevenson Ranch, CA (March 2005)

Contents
1 Introduction 3
1.1 Atomic and Electronic Origins of Mechanical Behaviors . . . 4
1.2 Hierarchies of Spatial and Temporal Scales . . . . . . . . . . 6
1.3 Mechanics-Induced Multiphysics Nature . . . . . . . . . . . . 10
1.4 Scope and Outline . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Electronic Origins of Materials Mechanics 12
2.1 Quantum Mechanical Total-Energy Calculations . . . . . . . 12
2.1.1 Born-Oppenheimer Approximation . . . . . . . . . . . 12
2.1.2 Tight-Binding Method . . . . . . . . . . . . . . . . . . 14
2.1.3 Density Functional Theory . . . . . . . . . . . . . . . 18
2.2 Ideal Strength and Stability . . . . . . . . . . . . . . . . . . 24
2.3 Plasticity and Dislocation Core . . . . . . . . . . . . . . . . . 26
2.4 Other Examples . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Molecular Dynamics Simulations of Materials Mechanics 32
3.1 Basics of Molecular Dynamics . . . . . . . . . . . . . . . . . . 32
3.1.1 Lagrange Equations of Motion . . . . . . . . . . . . . 34
3.1.2 Hamilton’s Equations of Motion . . . . . . . . . . . . 36
3.1.3 Interatomic Potentials . . . . . . . . . . . . . . . . . . 38
3.2 Fracture and Failure . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Dislocation Motion . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Polycrystals and Grain Boundaries . . . . . . . . . . . . . . . 53
3.5 Defects Generation by Nanoindentation and
Nanoscatching . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Multiscale Modelling of Materials Mechanics 62
4.1 Energetic Link between MD and Quantum Mechanics . . . . 63
4.2 Limitations of Molecular Dynamics Simulations . . . . . . . . 67
4.2.1 Effect of Boundary Conditions . . . . . . . . . . . . . 67
4.2.2 Coupling to External Bath . . . . . . . . . . . . . . . 71
4.2.3 Issues on Time Step . . . . . . . . . . . . . . . . . . . 73
4.3 Brief Overview of Multiscale Simulation Methods . . . . . . . 73
4.4 Virtual Atom Cluster (VAC) Model . . . . . . . . . . . . . . 78
4.4.1 Motivations and General Formulation . . . . . . . . . 78
4.4.2 Basic Ideas of VAC Model . . . . . . . . . . . . . . . . 85
4.4.3 Three-Way Concurrent Scheme for the Coupling with
QM Method . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.4 Tight-Binding Method for Carbon Systems . . . . . . 90
4.4.5 Coupling with VAC Model . . . . . . . . . . . . . . . 93
4.5 Meshfree Method for Mechanics-Induced Multiphysics Simulations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5 Conclusion and Future Prospect 97
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