Maugin Non-Classical Continuum Mechanics

A Dictionary
1. Auflage 2017
ISBN: 978-981-10-2434-4
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 51, 268 Seiten

Reihe: Advanced Structured Materials

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, every entry is followed by a cross-reference to other related subject entries in the dictionary.

Gérard A. Maugin (born December 2, 1944 in Angers) is a French engineering scientist. Maugin acquired his engineering degree in mechanical engineering in 1966 at the Ecole Nationale Supérieure d'Arts et Métiers (Ensam) and he continued his studies at the school of aeronautics Sup Aéro in Paris until 1968. In 1966 he worked for the French Ministry of Defence on ballistic missiles. In 1968 he received his (DEA) degree in hydrodynamics in Paris. In 1969, he earned his master's degree from Princeton University, where he graduated in 1971 (Ph.D.). He was a NASA International Fellow between 1968 and 1970. In 1971/72 he was an officer in the French Air Force. In 1975 he received his doctorate in mathematics (Doctorat d'Etat) at the University of Paris VI (Pierre et Marie Curie), where he also taught and directed a team at the Laboratoire de Mécanique Théorique conducting research since 1985 on Continuum mechanics and Theoretical Mechanics. After its name change to the Laboratoire de Modélisation en Mécanique (LMM), he headed this from 1998. From 1979 he was Director of Research at CNRS. He was a visiting professor and visiting scientist at Princeton, Belgrade, Warsaw, Istanbul, at the Royal Institute of Technology in Stockholm, at the TU Berlin, Rome, Tel Aviv, the Lomonosov University, Kyoto, Darmstadt and Berkeley. His work deals with continuum mechanics, including relativistic continuum mechanics, micro magnetism, electrodynamics of continua, thermo mechanics, surface waves and nonlinear waves in continua, lattice dynamics, material equations and biomechanical applications (tissue growth). In 2001 he received the Max Planck Research Award, was the 1991/92 Fellow of the Berlin Institute for Advanced Study, and in 2001 received an honorary doctorate from the Technical University of Darmstadt . In 1982 he received the mechanics Prize of French Academy of Sciences and in 1977 the Medal of the CNRS in physics and engineering. He is a member of the Polish Academy of Sciences (1994) and the Estonian Academy of Sciences and has an honorary professorship at the Moscow State University. In 2003, he received the A. Cemal Eringen Medal.

Autoren/Hrsg.

Maugin, Gérard A.

Inhaltsverzeichnis

1;Foreword;7
2;Preface;9
3;Contents;12
4;Prerequisites;17
5;1 What Is Classical Continuum Mechanics?;18
5.1;Introduction;18
5.2;Balance Equations;19
5.3;Reminder: The Most Classical Behaviours of Classical Continuum Thermo-Mechanics;23
5.3.1;Finite-Strain Thermoelasticity;23
5.3.2;Linear Homogeneous Isotropic Elasticity;24
5.3.3;Linear Elastic Crystals;25
5.3.4;Eulerian Fluids;25
5.3.5;Newtonian-Stokesian Fluids;25
5.3.6;Fourier Heat Conduction and Linear Thermoelasticity (Duhamel-Neumann);26
5.3.7;Linear Piezoelectricity;27
5.4;References;28
6;2 What Is Generalized Continuum Mechanics (GCM)?;29
6.1;Introduction;29
6.2;Asymmetric Stress;29
6.3;Surface Couples;30
6.4;Eringen-Mindlin Micromorphic Model of Microstructured Continua;31
6.5;Weakly Nonlocal Modelling;33
6.6;Strongly Nonlocal Modelling;34
6.7;The Loss of Euclidean Structure;35
7;The Dictionary in Alphabetic Order;38
8;3 A–B: From “Aifantis E.C” to “Biot’s Poro-Elasticity”;39
8.1;Aifantis E.C;39
8.2;Anisotropic Fluids;40
8.3;Asymmetric Elasticity;44
8.4;Auxetic Materials;45
8.5;Biot’s Theory of Poro-elasticity;46
9;4 C: From “Capillarity” to “Couple Stress (in Medium with Constrained Rotation)”;49
9.1;Capillarity;49
9.2;Cellular Materials as Generalized Continua;50
9.3;Configurational Mechanics;52
9.4;Connection and Torsion;56
9.5;Contiguity;58
9.6;Continua with Latent Microstructure;59
9.7;Continuously Defective Materials;60
9.8;Cosserat Continua;60
9.9;Cosserat Continua (Experimental Confrontation);62
9.10;Cosserat Eugène and François;63
9.11;Cosserat Point;64
9.12;Couple Stress;65
9.13;Couple Stress (in Medium with Constrained Rotation);66
10;5 D: From “Defects in GCM” to “Duhem Pierre”;69
10.1;Defects in GCM;69
10.2;Density-Gradient Fluids;71
10.3;Differential Geometry in Nonclassical Continuum Mechanics;71
10.4;Dilatational Elasticity;72
10.5;Dipolar Continua;72
10.6;Directors’ Theory;73
10.7;Dislocations and Disclinations;74
10.8;Double Force;76
10.9;Duhem Pierre;78
11;6 E: From “Edelen D.G.B.” to “Extra-Entropy Flux”;80
11.1;Edelen D.G.B;80
11.2;EDGE FORCES;81
11.3;Electric Quadrupoles;81
11.4;Electromagnetic Continua;81
11.5;Ericksen J.L;82
11.6;Eringen A. Cemal;83
11.7;Eringen-Mindlin Medium;84
11.8;Extended Thermodynamics;84
11.9;Extra-Entropy Flux;85
12;7 F: From “Ferroelectric Crystals (Elasticity of)” to “Fractal Continua”;87
12.1;Ferroelectric Crystals (Elasticity of);87
12.1.1;Modelling;87
12.1.2;Approach via the Principle of Virtual Power;90
12.1.3;Analogy with Cosserat Continua;92
12.1.4;Reduction to a Model Without Microstructure;92
12.1.5;Antiferroelectric Materials;93
12.2;Ferroic States;94
12.3;Fractal Continua;95
13;8 G: From “Generalized Continuum Mechanics” to “Green A.E.”;99
13.1;Generalized Continuum Mechanics (GCM);99
13.2;Generalized Internal Forces;99
13.3;Generalized Thermo-Elasticity;99
13.4;Gradient Elasticity;102
13.5;Gradient Plasticity;108
13.6;Granular Materials as Generalized Continua;111
13.7;Green A.E;116
14;9 H–I: From “Higher-Order Gradient Theories” to “Ionic Crystals (Elasticity of)”;117
14.1;Higher-Order Gradient Theories;117
14.2;Homogenization;120
14.3;Hyperstress (Notion of);121
14.4;Implicit Gradient Elasticity Models;122
14.5;Internal Degrees of Freedom;122
14.6;Internal Variables of State;124
14.7;Interstitial Working;128
14.8;Ionic Crystals (Elasticity of);130
14.8.1;Remark on electric quadrupoles;133
15;10 K–L: From “Kelvin Continuum” to “Long-Range Interactions”;136
15.1;Kelvin Continuum;136
15.2;Kondo K;137
15.3;Korteweg Fluids;138
15.4;Kröner Ekkehart;140
15.5;Kunin I.A;141
15.6;Lattice Dynamics;142
15.7;Le Roux Elasticity;144
15.8;Liquid Crystals as Continua;146
15.9;Liquid Crystals (Ericksen-Leslie Theory);148
15.9.1;Interaction With Electromagnetic Fields;152
15.10;Liquid Crystals (Eringen-Lee theory);153
15.11;Liquid Crystals (Landau-De Gennes theory);154
15.12;Long-Range Interactions;156
16;11 M: From “Material Growth (Theory of)” to “Micromagnetism in Elastic Solids”;158
16.1;Material Growth (theory of);158
16.2;Material Inhomogeneities (Theory of);162
16.3;Materials with Voids;162
16.4;Mesoscopic Theory of Complex Continua;163
16.5;Metamaterials;166
16.6;Micromagnetism in Elastic Solids;167
16.6.1;Continuum Modelling;168
16.6.2;Global Balance Laws;170
16.6.3;Local Balance Laws;171
16.6.4;Approach via the Principle of Virtual Power;174
16.6.5;Hamiltonian Variational Formulation;177
16.6.6;Ferrimagnetic and Antiferromagnetic Materials;177
16.6.7;Analogy with Cosserat Continua;177
16.6.8;Reduction to a Model Without Microstructure (Paramagnetic and Soft-ferromagnetic Bodies);178
16.7;Micromorphic Continua;180
16.8;Micromorphic Fluids;180
16.9;Micropolar Continua (Cf. Cosserat Continua);183
16.9.1;Linear Strain Measures;184
16.10;Micropolar Elasticity;185
16.10.1;Theory for Small Strains and Small Internal Rotation Angles;188
16.11;Micropolar Fluids;192
16.12;Microstretch Continua;195
16.12.1;Constitutive Equations;197
16.12.2;Microstretch Elasticity;197
16.12.3;Microstretch Fluids;199
16.13;Microstructure;201
16.14;Microstructured Continuum Theory (Eringen);202
16.14.1;Special cases;204
16.15;Microsctructured Continuum Theory (Mindlin);206
16.15.1;Field Equations;207
16.16;Microstructured Fluids;208
16.17;Mindlin R.D;208
16.18;Mixtures (Mechanics of);209
16.19;Multipolar Continua (Green-Rivlin);211
17;12 N: From “Naghdi P.M.” to “Nowacki W.”;214
17.1;Naghdi P.M;214
17.2;Non-euclidean Geometry of Defective Materials;215
17.3;Non-holonomic Continua;215
17.4;Nonlinear Waves in Generalized Continua;217
17.5;Nonlocal Damage;219
17.5.1;Weak Nonlocality;221
17.6;Nonlocality (as Opposed to Contiguity);223
17.7;Nonlocality (Strong);224
17.8;Nonlocality (Weak);228
17.9;Nowacki W;228
18;13 O–P: From “Oriented Media (with Directors)” to “Porous Media as Seen in GCM”;230
18.1;Oriented Media (with Directors);230
18.2;Peridynamics;233
18.2.1;Introduction;233
18.2.2;The Main Idea;233
18.3;Polarization Gradient;235
18.4;Ponderomotive Couple;235
18.5;Porous Media (as Seen in GCM);237
18.6;Porous Media and the Theory of Mixtures;240
19;14 Q–R: From “Quasi-crystals (Elasticity of)” to “Rogula R.D.”;244
19.1;Quasi-crystals (Elasticity of);244
19.1.1;Introduction;244
19.1.2;General Field Equations;245
19.1.3;Nonlinearity and Plasticity of Quasicrystals;248
19.1.4;Conclusion;249
19.2;Relaxed Micromorphic Continua;251
19.3;Rivlin R.S;252
19.4;Rogula D;252
20;15 S–T: From “Solitons (in on-Classical Continua)” to “Truesdell C.A.”;254
20.1;Solitons (in Non-classical Continua);254
20.2;Solutions of Macromolecules;255
20.2.1;Introduction;255
20.2.2;Microstructure and Conformation;256
20.2.3;Constitutive Relations;257
20.3;Superfluids;261
20.3.1;Two-Fluid Model and Internal Momentum;262
20.4;Surface Tension;265
20.5;Toupin R.A;266
20.6;Truesdell C.A;267
21;Conclusion;268