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Continuum mechanics through the ages - from the Renaissance to the twentieth century : from hydraulics to plasticity
Maugin, Gerard A.
- ISBN:9783319265933
- ISBN:3319265938
- ISBN:9783319265919
- ISBN:3319265911
- Call Number : QA 808 .2 .M38 2016
- Main Entry: Maugin, Gerard A.
- Title:Continuum mechanics through the ages - from the Renaissance to the twentieth century : from hydraulics to plasticity [electronic resource] / Gerard A. Maugin.
- Publisher:Cham : Springer, 2016.
- Physical Description: xii, 306 p.: ill., portraits
- Series:Solid Mechanics and its Applications; V.223
- Notes:Includes bibliographical references and index
- Subject:Continuum mechanics -- History.
Continuum mechanics throughمحتواي کتاب
- Preface
- Contents
- 1 Particles/Molecules Versus Continuum: The Never-Ending Debate
- Abstract
- 1.1 Old Times, New Ideas
- 1.2 Three-Dimensional Elasticity in the Early Nineteenth Century
- 1.2.1 Poisson on Elastic Surfaces (1812)
- 1.2.2 Navier's Corpuscular Theory (1820)
- 1.2.3 Fresnel's Corpuscular Approach to Wave Optics (1822)
- 1.2.4 Cauchy's First Theory (1822--3; 1828)
- 1.2.5 Poisson's Memoir (1827--1828) and Cauchy's Second Theory (1828, 1833)
- 1.2.6 Piola's Original Works (1836, 1845)
- 1.2.7 Green's Energy Argument (1839)
- 1.2.8 Other Works: Lam00E9, Clapeyron, etc.
- 1.3 Action at a Distance, Electromagnetism and Crystal Dynamics
- 1.4 Conclusion
- References
- 2 Hydraulics: The Importance of Observations and Experiments
- Abstract
- 2.1 Introduction
- 2.2 Ancient Times: Hydraulic Technology
- 2.3 The Renaissance Experimentalists-Thinkers: Leonardo, Stevin, Galileo Galilei
- 2.4 Seventeenth Century Experiments: Torricelli, Pascal, Mariotte
- 2.5 Eighteenth Century Theoreticians: Clairaut, Daniel Bernoulli, D'Alembert, Euler
- 2.6 The True Experimentalists: Borda, Bossut, and Du Buat
- 2.7 The Role of Viscosity: Poiseuille, Hagen
- 2.8 Summary and Conclusion
- References
- 3 On Porous Media and Mixtures
- Abstract
- 3.1 Introduction
- 3.2 Reminder: Poiseuille and Blood Flow
- 3.3 Darcy and the Fountains in Dijon
- 3.4 Porous Media and Homogenization Technique
- 3.5 Porous Media and the Theory of Mixtures
- 3.6 Continuum Thermo-Mechanics and Constitutive Modelling
- 3.7 Conclusion
- Appendix: Elements of APH
- References
- Specialized Journals
- 4 Viscosity, Fast Flows and the Science of Flight
- 5 Duhem on Hydrodynamics and Elasticity
- 6 Poincar00E9 and Hilbert on Continuum Mechanics
- Abstract
- 6.1 Introduction
- 6.2 Poincar00E9 on Elasticity
- 6.3 Hilbert on Continuum Mechanics
- 6.3.1 Preliminary Remark
- 6.3.2 Critical Analysis of Hilbert's Lecture Notes
- 6.3.2.1 On the Introduction (pp. 1--7)
- 6.3.2.2 On the Notion of Continuum (Chap. 1, pp. 8--26)
- 6.3.2.3 Elements of Vector Analysis (Chap. 2, pp. 27--41) Vector Analysis
- 6.3.2.4 The Kinematics of Continua (Chap. 3, pp. 41--66)
- 6.3.2.5 Bases of the Dynamics of Continua (Chap. 4, pp. 67--121)
- 6.3.2.6 Special Problems of Hydrodynamics (Chap. 5, pp. 122--171)
- 6.3.2.7 Capillarity (Chap. 6, pp. 172--180)
- 6.3.2.8 Electrodynamics (Chap. 7, pp. 181--225)
- 6.3.2.9 Thermodynamics (Chap. 8, pp. 226--239)
- 6.4 Conclusion
- Appendix
- Mathematical Treatment of the Axioms of Physics
- References
- 7 Viscoelasticity of Solids (Old and New)
- 8 Plasticity Over 150 Years (1864--2014)
- Abstract
- 8.1 By Way of Introduction
- 8.2 Timid Experimental Steps and First Mathematical Modelling
- 8.3 Enter Evolution and Thermodynamics
- 8.4 Mathematical Plasticity and Convexity
- 8.5 Physical Plasticity and Dislocations
- 8.6 Finite-Strain Plasticity
- 8.7 Varia
- 8.8 Conclusion
- 8.9 Note on the Bibliography
- References
- 9 Fracture: To Crack or Not to Crack. That Is the Question
- Abstract
- 9.1 Introduction
- 9.2 The Birth of Fracture Theory: Inglis, Griffith
- 9.3 The Analysis of the Stress Field at Cracks
- 9.4 Irwin and Energy-Release Rate
- 9.5 Accounting for the Plastic Zone
- 9.6 Invariant Integrals as Measures of Toughness
- 9.7 The Realm of Configurational-Material Forces
- 9.8 Dynamic Fracture
- 9.9 Extensions and More Recent Developments
- 9.10 Summary and Conclusion
- References
- 10 Geometry and Continuum Mechanics: An Essay
- Abstract
- 10.1 Introduction
- 10.2 A Fundamental Theorem by Killing
- 10.3 The Role of Elie Cartan
- 10.4 The Influence of the Theory of General Relativity
- 10.5 The Influence of the Theory of Dislocations
- 10.6 The Theory of Local Structural Rearrangements
- 10.7 Modern Differential Geometry and Its Use in Continuum Mechanics
- Gallery of Portraits
- References
- 11 The Masters of Modern Continuum Mechanics
- Abstract
- 11.1 Introduction
- 11.2 Rivlin and Truesdell
- 11.3 The Co-workers and Direct Disciples of Truesdell
- 11.4 The Co-workers and Direct Disciples of Rivlin
- 11.5 A.E. Green and Paul Naghdi
- 11.6 A.C. Eringen and Engineering Science
- 11.7 Outside the USA and the UK
- 11.8 Conclusion: Some Sociological Remarks
- A Gallery of Portraits
- References
- 12 Epilogue
- Index