Sadowski / Trovalusci Multiscale Modeling of Complex Materials

Phenomenological, Theoretical and Computational Aspects
1. Auflage 2014
ISBN: 978-3-7091-1812-2
Verlag: Springer Vienna
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 556, 285 Seiten

Reihe: CISM International Centre for Mechanical Sciences

The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.

Autoren/Hrsg.

Sadowski, Tomasz

Trovalusci, Patrizia

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Atomistic-Continuum Couplings for Dynamic Fracture;9
3.1;1 Introduction;9
3.2;2 Molecular Dynamics;11
3.2.1;2.1 Governing equations in the atomistic domain;11
3.2.2;2.2 Equilibrium of the atomistic domain;12
3.3;3 Continuum Model;13
3.4;4 Coupling Scheme;14
3.4.1;4.1 Coupling functions;14
3.4.2;4.2 Discretized problem;16
3.4.3;4.3 Time integration scheme;18
3.4.4;4.4 Energy transfer between the atomistics and continuum domains;20
3.5;5 Mechanical quantities in the atomistic domain;25
3.6;6 Examples: Crack propagation under velocity loading;27
3.7;7 Concluding Remarks;31
3.8;Bibliography;33
4;On the method of virtual power in the mechanics of non-classical continua;37
4.1;1 Classical mechanics and classical continua;37
4.1.1;1.1 The traditional approach;38
4.1.2;1.2 Sketch of the proofs;39
4.1.3;1.3 The indifference of power;44
4.1.4;1.4 The method of virtual power;45
4.1.5;1.5 The variational approach;46
4.1.6;1.6 Bounded Cauchy fluxes;47
4.2;2 Non-classical continua;50
4.2.1;2.1 Continua with microstructure;50
4.2.2;2.2 Continua with scalar microstructure;53
4.2.3;2.3 Continua with vectorial microstructure;54
4.2.4;2.4 Continua with tensorial microstructure;57
4.2.5;2.5 Second-gradient continua;60
4.3;Bibliography;62
5;Adaptive Concurrent Multi-level Modeling of Multi-scale Ductile Failure in Heterogeneous Metallic Materials;67
5.1;1 Introduction;67
5.2;2 Levels in the Concurrent Multi-Scale Modeling Framework;71
5.2.1;2.1 Computational Subdomain Level-0 (?l0);72
5.2.2;2.2 Computational Sub-domain Level-1 ?l1;79
5.2.3;2.3 Computational Sub-domain Level-2 (?l2);82
5.2.4;2.4 Computational Sub-domain Level-tr (?tr);82
5.3;3 Mesh Adaptivity and Level Change Criteria;82
5.3.1;3.1 Mesh Refinement for level-0 Elements;83
5.3.2;3.2 Criteria for Switching from Level-0 to Level-1 Elements;83
5.3.3;3.3 Criteria for Switching from Level-1 to Level-2 Elements;84
5.4;4 Coupling Multiple Levels in the Concurrent Setting;85
5.4.1;4.1 Weak Form for the Concurrent Multi-scale Model;85
5.4.2;4.2 Finite Element Discretization for Multi-scale Analysis;87
5.4.3;4.3 Iterative Solution of the Coupled Multi-Scale System;88
5.5;5 Numerical Studies and Validations;90
5.5.1;5.1 Effect of Interface ?int between Macro and Micro Sub-domains;90
5.5.2;5.2 Calibration and Validation of the Level-1 to Level-2 Criteria;93
5.5.3;5.3 Validation of the Multi-level Model Against Micromechanical Analysis;96
5.6;6 Ductile Failure of a Cast Aluminum Tension Bar;99
5.6.1;6.1 Parameters in the HCPD Model for Level-0 Elements;102
5.6.2;6.2 Initial Model and Level Changes in a Tension Test;103
5.6.3;6.3 Simulation Through Complete Micro-cracking;104
5.7;7 Summary and Conclusions;108
5.8;8 Acknowledgments;109
5.9;Bibliography;110
6;Fractals and Randomness in Mechanics of Materials;115
6.1;1 Mechanics of Random Media;116
6.1.1;1.1 Basic Concepts;116
6.1.1.1;The RVE postulate;119
6.1.1.2;Hill condition - mechanical versus energy definitions;120
6.1.1.3;Hierarchies of mesoscale bounds;122
6.1.1.4;Examples of hierarchies of mesoscale bounds;125
6.1.1.4.1;Physically nonlinear elastic microstructures;125
6.1.1.4.2;Power-law materials;126
6.1.1.5;Finite elasticity of random composites;127
6.1.1.6;Elastic-plastic microstructures;131
6.1.1.7;Viscoelastic microstructures;135
6.1.1.8;Thermoelastic microstructures;136
6.1.1.8.1;Linear case;136
6.1.1.8.2;Non-linear case;141
6.1.1.9;Comparison of scaling trends;143
6.1.1.10;Scaling and stochastic evolution in damage phenomena;145
6.1.2;1.2 Fractals in Mechanics of Materials;149
6.1.2.1;Morphogenesis of fractals at elasto-plastic transitions;149
6.1.2.1.1;Background;149
6.1.2.1.2;Model 3d material;149
6.1.2.1.3;Scaling function at the elastic-plastic transition;151
6.1.2.2;Fractals and avalanches at elastic-plastic-brittle transitions in disordered media;153
6.1.2.3;Homogenization of fractal media;154
6.1.3;1.3 Closing Comments;154
6.1.4;Acknowledgement;154
6.1.5;References;155
7;Modelling of damage and fracture processes of ceramic matrix composites under mechanical loading;159
7.1;1. Introduction – variety of different composite materials;159
7.2;2. Strategy in the Multiscale Modelling of CMC’s;162
7.3;3. Experimental Prerequisites for the Multiscale Model;164
7.4;4. Multiscale model for the two-phase ceramic composites;167
7.5;5. Numerical examples;178
7.6;6. Conclusions;181
7.7;Acknowledgement;182
7.8;7. References;182
8;Multiscale Modeling of Damage in Composite Materials;187
8.1;1. Introduction;187
8.2;2. Damage in composite materials;188
8.3;3. Damage mechanics;193
8.4;4. Synergistic Damage Mechanics (SDM);212
8.5;5. Concluding Remarks;215
8.6;Acknowledgement;216
8.7;References;216
9;Molecular Approaches for Multifield Continua: origins and current developments;218
9.1;1 Introduction. Multiscale approaches: a short review;219
9.2;2 The Nineteenth century molecular models with a glance at modern discrete–continuum theories;226
9.2.1;2.1 Cauchy model for elasticity;227
9.2.2;2.2 Voigt’s model with particle rotations;231
9.2.3;2.3 Poincaré’s refined molecular model for elasticity;235
9.2.4;2.4 Discrete–continuum theories: new perspectives;238
9.3;3 Multifield continua, basics synoptic;240
9.4;4 A molecular–multifield model for composites;249
9.4.1;4.1 Lattice model of a material with fibres and flaws;250
9.4.2;4.2 Micro–macro transition;253
9.4.3;4.3 Continuum with rigid and affine structure;256
9.5;5 Case study: a one–dimensional microcracked bar;262
9.6;6 Final remarks;267
9.7;Acknowledgements;268
9.8;Bibliography;268