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Continuum mechanics through the ages - from the Renaissance to the twentieth century : from hydraulics to plasticity
Maugin, Gerard A.
اطلاعات کتابشناختی
Continuum mechanics through the ages - from the Renaissance to the twentieth century : from hydraulics to plasticity
Author :
Maugin, Gerard A.
Publisher :
Springer,
Pub. Year :
2016
Subjects :
Continuum mechanics -- History.
Call Number :
QA 808 .2 .M38 2016
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Preface
(6)
Acknowledgments
(9)
Contents
(10)
1 Particles/Molecules Versus Continuum: The Never-Ending Debate
(14)
Abstract
(14)
1.1 Old Times, New Ideas
(14)
1.2 Three-Dimensional Elasticity in the Early Nineteenth Century
(20)
1.2.1 Poisson on Elastic Surfaces (1812)
(20)
1.2.2 Navier's Corpuscular Theory (1820)
(21)
1.2.3 Fresnel's Corpuscular Approach to Wave Optics (1822)
(23)
1.2.4 Cauchy's First Theory (1822--3; 1828)
(24)
1.2.5 Poisson's Memoir (1827--1828) and Cauchy's Second Theory (1828, 1833)
(25)
1.2.6 Piola's Original Works (1836, 1845)
(26)
1.2.7 Green's Energy Argument (1839)
(30)
1.2.8 Other Works: Lam00E9, Clapeyron, etc.
(31)
1.3 Action at a Distance, Electromagnetism and Crystal Dynamics
(32)
1.4 Conclusion
(35)
References
(36)
2 Hydraulics: The Importance of Observations and Experiments
(39)
Abstract
(39)
2.1 Introduction
(39)
2.2 Ancient Times: Hydraulic Technology
(40)
2.3 The Renaissance Experimentalists-Thinkers: Leonardo, Stevin, Galileo Galilei
(41)
2.4 Seventeenth Century Experiments: Torricelli, Pascal, Mariotte
(44)
2.5 Eighteenth Century Theoreticians: Clairaut, Daniel Bernoulli, D'Alembert, Euler
(47)
2.6 The True Experimentalists: Borda, Bossut, and Du Buat
(50)
2.7 The Role of Viscosity: Poiseuille, Hagen
(54)
2.8 Summary and Conclusion
(57)
References
(67)
3 On Porous Media and Mixtures
(69)
Abstract
(69)
3.1 Introduction
(69)
3.2 Reminder: Poiseuille and Blood Flow
(70)
3.3 Darcy and the Fountains in Dijon
(71)
3.3.1 Generalizations of Darcy's Law
(74)
3.4 Porous Media and Homogenization Technique
(75)
3.5 Porous Media and the Theory of Mixtures
(77)
3.6 Continuum Thermo-Mechanics and Constitutive Modelling
(81)
3.7 Conclusion
(82)
Appendix: Elements of APH
(88)
References
(88)
Specialized Journals
(91)
4 Viscosity, Fast Flows and the Science of Flight
(92)
Abstract
(92)
4.1 Introduction
(92)
4.2 The World of Vortices
(93)
4.3 Reynolds and the Transition to Turbulence
(97)
4.4 Prandtl and Boundary-Layer Theory
(102)
4.5 The Science of Non-dimensional Numbers
(111)
4.6 Summary
(113)
References
(114)
5 Duhem on Hydrodynamics and Elasticity
(117)
Abstract
(117)
5.1 Introduction
(117)
5.2 The Lectures of 1890--1891
(120)
5.3 Duhem's General Views on Continuum Mechanics
(120)
5.4 Advances in Hydrodynamics
(121)
5.5 Advances in Elasticity
(126)
5.6 Contemporary Reception of Duhem's HEA and His Two ``Recherches'' Volumes
(132)
5.7 Conclusion
(133)
References
(134)
6 Poincar00E9 and Hilbert on Continuum Mechanics
(138)
Abstract
(138)
6.1 Introduction
(138)
6.2 Poincar00E9 on Elasticity
(142)
6.2.1 Preliminary Remark
(142)
6.2.2 The Course on Elasticity
(143)
6.2.3 Concluding Comments
(148)
6.3 Hilbert on Continuum Mechanics
(149)
6.3.1 Preliminary Remark
(149)
6.3.2 Critical Analysis of Hilbert's Lecture Notes
(150)
6.3.2.1 On the Introduction (pp. 1--7)
(151)
6.3.2.2 On the Notion of Continuum (Chap. 1, pp. 8--26)
(151)
6.3.2.3 Elements of Vector Analysis (Chap. 2, pp. 27--41) Vector Analysis
(152)
6.3.2.4 The Kinematics of Continua (Chap. 3, pp. 41--66)
(153)
6.3.2.5 Bases of the Dynamics of Continua (Chap. 4, pp. 67--121)
(153)
6.3.2.6 Special Problems of Hydrodynamics (Chap. 5, pp. 122--171)
(155)
6.3.2.7 Capillarity (Chap. 6, pp. 172--180)
(156)
6.3.2.8 Electrodynamics (Chap. 7, pp. 181--225)
(157)
6.3.2.9 Thermodynamics (Chap. 8, pp. 226--239)
(159)
6.4 Conclusion
(160)
Appendix
(161)
Mathematical Treatment of the Axioms of Physics
(161)
References
(162)
7 Viscoelasticity of Solids (Old and New)
(165)
Abstract
(165)
7.1 Introduction
(165)
7.2 Early Developments (1860--1950)
(166)
7.3 Early Thermodynamics (1940--1965)
(170)
7.4 Engineering Viscoelasticity (1940--1960), Dynamic Studies
(173)
7.5 Mathematical Visco-Elasticity (1960--1975)
(175)
7.6 Recent Developments
(178)
7.7 Conclusion
(180)
References
(181)
8 Plasticity Over 150 Years (1864--2014)
(185)
Abstract
(185)
8.1 By Way of Introduction
(185)
8.2 Timid Experimental Steps and First Mathematical Modelling
(187)
8.3 Enter Evolution and Thermodynamics
(190)
8.3.1 Duhem's Pioneering Works
(190)
8.3.2 Incremental Laws
(193)
8.3.3 Rate Equations
(196)
8.3.4 Prandtl-Reuss Relations
(196)
8.3.5 Hypo-elasticity as a Path to Elasto-Plasticity
(198)
8.4 Mathematical Plasticity and Convexity
(198)
8.4.1 Variational Principles
(198)
8.4.2 Application of Convex Analysis
(201)
8.4.3 Uniqueness and Existence of Solutions
(203)
8.5 Physical Plasticity and Dislocations
(203)
8.6 Finite-Strain Plasticity
(206)
8.7 Varia
(210)
8.7.1 Anisotropy
(210)
8.7.2 Numerical Plasticity
(210)
8.7.3 Homogenization in Elastoplasticity
(211)
8.7.4 Viscoplasticity
(211)
8.7.5 Coupling with Other Properties (Porosity, Damage, Magnetism)
(212)
8.7.6 Gradient Plasticity
(213)
8.8 Conclusion
(215)
8.9 Note on the Bibliography
(216)
References
(217)
9 Fracture: To Crack or Not to Crack. That Is the Question
(223)
Abstract
(223)
9.1 Introduction
(223)
9.2 The Birth of Fracture Theory: Inglis, Griffith
(225)
9.3 The Analysis of the Stress Field at Cracks
(227)
9.4 Irwin and Energy-Release Rate
(229)
9.5 Accounting for the Plastic Zone
(232)
9.6 Invariant Integrals as Measures of Toughness
(233)
9.7 The Realm of Configurational-Material Forces
(237)
9.8 Dynamic Fracture
(238)
9.9 Extensions and More Recent Developments
(240)
9.9.1 Electro-Magneto-Elastic Generalizations
(240)
9.9.2 The Consideration of Generalized Functions
(241)
9.9.3 Computational Mechanics of Material Forces
(242)
9.9.4 Peridynamics
(244)
9.9.5 Size Effects
(245)
9.10 Summary and Conclusion
(246)
References
(247)
10 Geometry and Continuum Mechanics: An Essay
(251)
Abstract
(251)
10.1 Introduction
(251)
10.2 A Fundamental Theorem by Killing
(252)
10.3 The Role of Elie Cartan
(256)
10.4 The Influence of the Theory of General Relativity
(258)
10.5 The Influence of the Theory of Dislocations
(259)
10.6 The Theory of Local Structural Rearrangements
(260)
10.7 Modern Differential Geometry and Its Use in Continuum Mechanics
(261)
Gallery of Portraits
(263)
References
(267)
11 The Masters of Modern Continuum Mechanics
(270)
Abstract
(270)
11.1 Introduction
(270)
11.2 Rivlin and Truesdell
(272)
11.3 The Co-workers and Direct Disciples of Truesdell
(276)
11.4 The Co-workers and Direct Disciples of Rivlin
(281)
11.5 A.E. Green and Paul Naghdi
(283)
11.6 A.C. Eringen and Engineering Science
(284)
11.7 Outside the USA and the UK
(287)
11.8 Conclusion: Some Sociological Remarks
(292)
A Gallery of Portraits
(295)
References
(300)
12 Epilogue
(305)
References
(308)
Index
(309)
