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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: World Scientific 2009.
Temas:
Acceso en línea:Texto completo

MARC

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245 0 0 |a Multiscale Modeling In Solid Mechanics :  |b Computational Approaches. 
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505 0 |a 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. 
520 |a 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 comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approa. 
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