6. Quasicontinuum Concurrent and Semi-Analytical Hierarchical Multiscale Methods Across Atoms/Continuum
Published Online: 15 DEC 2010
DOI: 10.1002/9780470972281.ch6
Copyright © 2011 John Wiley & Sons, Ltd
Book Title
Multiscale Analysis of Deformation and Failure of Materials
Additional Information
How to Cite
Fan, J. (2010) Quasicontinuum Concurrent and Semi-Analytical Hierarchical Multiscale Methods Across Atoms/Continuum, in Multiscale Analysis of Deformation and Failure of Materials, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470972281.ch6
Publication History
- Published Online: 15 DEC 2010
- Published Print: 17 DEC 2010
Book Series:
Book Series Editors:
- Ronald Pethig,
- Horatio Dante Espinosa
ISBN Information
Print ISBN: 9780470744291
Online ISBN: 9780470972281
- Summary
- Chapter
- References
Keywords:
- quasicontinuum concurrent and semi-analytical hierarchical multiscale methods - across atoms/continuum;
- basic energy principle - and numerical solution techniques in solid mechanics;
- essential points of finite element methods;
- using Gaussian quadrature - element energy calculation;
- Quasicontinuum (QC) concurrent method of multiscale analysis;
- idea and features of QC method;
- importance of interface treatment - on ghost force;
- fully non-localized QC method;
- deformation gradient and the Cauchy-born rule;
- precision of Cauchy-born rule
Summary
This chapter contains sections titled:
Introduction
Part 6.1 Basic Energy Principle and Numerical Solution Techniques in Solid Mechanics
Principle of Minimum Potential Energy of Solids and Structures
Essential Points of Finite Element Methods
Part 6.2 Quasicontinuum (QC) Concurrent Method of Multiscale Analysis
The Idea and Features of the QC Method
Fully Non-localized QC Method
Applications of the QC Method
Short Discussion about the QC Method
Part 6.3 Analytical and Semi-analytical Multiscale Methods Across Atomic/Continuum Scales
More Discussions about Deformation Gradient and the Cauchy-Born Rule
Analytical/Semi-analytical Methods Across Atom/Continuum Scales Based on the Cauchy-Born Rule
Atomistic-based Continuum Model of Hydrogen Storage with Carbon Nanotubes
Atomistic-based Model for Mechanical, Electrical and Thermal Properties of Nanotubes
A Proof of 3D Inverse Mapping Rule of the GP Method
Concluding Remarks
References