Multiscale Modeling In Solid Mechanics : Computational Approaches.

This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensi...

Full description

Saved in:

Bibliographic Details
Format:	eBook
Language:	English
Published:	World Scientific 2009.
Subjects:	Solids > Mathematical models. Solid state physics. Mechanics. Multiscale modeling. mechanics (physics) Mechanics Multiscale modeling Solid state physics Solids > Mathematical models
Online Access:	Click for online access

Table of Contents:

Cover13;
CONTENTS
Preface
Contributors
Computational Homogenisation for Non-Linear Heterogeneous Solids V.G. Kouznetsova, M.G.D. Geers and W.A.M. Brekelmans
1. Introduction
2. Basic Hypotheses
3. Definition of the Problem on the Microlevel
4. Coupling of the Macroscopic and Microscopic Levels
4.1. Deformation
4.2. Stress
4.3. Internal work
5. FE Implementation
5.1. RVE boundary value problem
5.2. Calculation of the macroscopic stress
5.3. Macroscopic tangent stiffness
6. Nested Solution Scheme
7. Computational Example
8. Concept of an RVE within Computational Homogenisation
9. Extensions of the Classical Computational Homogenisation Scheme
9.1. Homogenisation towards second gradient continuum
9.2. Computational homogenisation for beams and shells
9.3. Computational homogenisation for heat conduction problems
Acknowledgements
References
Two-Scale Asymptotic Homogenisation-Based Finite Element Analysis of Composite Materials Qi-Zhi Xiao and Bhushan Lal Karihaloo
1. Introduction
2. Mathematical Formulation of First- and Higher-Order Two-Scale Asymptotic Homogenisation
2.1. Two-scale expansion
2.2. O(949;.2) equilibrium: Solution structure of ui(0)
2.3. O(949;.1) equilibrium: First-order homogenisation 10;and solution structure of u(1)m
2.4. O(949;0) equilibrium: Second-order homogenisation
2.5. O(949;1) equilibrium: Third-order homogenisation
3. Variational Formulation of Problem (29)
4. Finite Element Methods
4.1. Displacement compatible elements from the potential principle
4.2. Element-free Galerkin method from the potential principle
4.3. Displacement incompatible element from the potential principle
4.4. Hybrid stress elements from the Hellinger8211;Reissner principle
4.5. Enhanced-strain element based on the Hu8211;Washizu principle
4.6. Comments on the various methods
5. Enforcing the Periodicity Boundary Condition and Constraints from Higher-Order Equilibrium in the Analysis of the RUC
6. A Posteriori Recovery of the Gradients
6.1. Superconvergent patch recovery (SPR)
6.2. Moving Least Squares (MLS)
7. Numerical Examples
8. Discussion and Conclusions
References
Multi-Scale Boundary Element Modelling of Material Degradation and Fracture G.K. Sfantos and M.H. Aliabadi
1. Introduction
2. Macromechanics
2.1. Modelling the continuum
3. Artificial Microstructure Generation
4. Microstructure Modelling
4.1. Grain material modelling
4.2. A boundary cohesive element formulation
4.3. Grain discretisation
5. Grain Boundary Interface
6. Microcracking Evolution Algorithm
6.1. Non-local approach
7. Definitions: Averaging Theorems
7.1. RVE boundary conditions
8. Micro8211;Macro Interface
8.1. Coupling with macro-BEM
8.2. Coupling with macro-FEM
9. Multiprocessing Algorithm
10. Multi-Scale Damage Simulations
11. Conclusions
References
Appendix
Non-Uniform Transformation Field Analysis: A Reduced Model for Multiscale Non-Linear Problems in Solid Mechanics Jean-Claude Michel and Pierre Suquet
1. Introduction
2. Structural Problems with Multiple Scales
2.1. Homogenisation and two-scale expansions
2.2. Individual constituents
2.3. Unit-cell problem: Effective response of heterogeneous materials.

Multiscale Modeling In Solid Mechanics : Computational Approaches.

Similar Items