Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century: From Hydraulics to Plasticity (Solid Mechanics and Its Applications Book 223)

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 Mixing Scientific, Historic And Socio-economic Vision, This Unique Book Complements Two Previously Published Volumes On The History Of Continuum Mechanics From This Distinguished Author. In This Volume, Gérard A. Maugin Looks At The Period From The Renaissance To The Twentieth Century And He Includes An Appraisal Of The Ever Enduring Competition Between Molecular And Continuum Modelling Views. Chapters Trace Early Works In Hydraulics And Fluid Mechanics Not Covered In The Other Volumes And The Author Investigates Experimental Approaches, Essentially Before The Introduction Of A True Concept Of Stress Tensor. The Treatment Of Such Topics As The Viscoelasticity Of Solids And Plasticity, Fracture Theory, And The Role Of Geometry As A Cornerstone Of The Field, Are All Explored. Readers Will Find A Kind Of Socio-historical Appraisal Of The Seminal Contributions By Our Direct Masters In The Second Half Of The Twentieth Century. The Analysis Of The Teaching And Research Texts By Duhem, Poincaré And Hilbert On Continuum Mechanics Is Key: These Provide The Most Valuable Documentary Basis On Which A Revival Of Continuum Mechanics And Its Formalization Were Offered In The Late Twentieth Century. Altogether, The Three Volumes Offer A Generous Conspectus Of The Developments Of Continuum Mechanics Between The Sixteenth Century And The Dawn Of The Twenty-first Century. Mechanical Engineers, Applied Mathematicians And Physicists Alike Will All Be Interested In This Work Which Appeals To All Curious Scientists For Whom Continuum Mechanics As A Vividly Evolving Science Still Has Its Own Mysteries. Gérard A. Maugin. Includes Bibliographical References And Index. "Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on continuum mechanics is key: these provide the most valuable documentary basis on which a revival of continuum mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of continuum mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom continuum mechanics as a vividly evolving science still has its own mysteries" -- OhioLink Library Catalog Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on continuum mechanics is key: these provide the most valuable documentary basis on which a revival of continuum mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of continuum mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom continuum mechanics as a vividly evolving science still has its own mysteries