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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 http://liminfang.gbaopan.com/files/1128b3ae706f47e4a9f9b57cf57fd3d2.gbp |
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