By Gerard A Maugin
Preface 1. The Land Clearers and the "Classics" 2. Transition to the 20 th Century three. Rheology and Nonlinear Elasticity four. the yank Society of Mechanical Engineers Spirit five. Axiomatization and Thermo-Mechanics 6. The British university of Elasticity, Plasticity and Defects: utilized arithmetic 7. The French Masters eight. The Polish energy nine. German Revival in Continuum Mechanics After WWII 10. eu Miscellanei and Asia eleven. The Soviet and Russian colleges 12. Continuum Mechanics and Electromagnetism thirteen. Generalized Continuum Mechanics: a number of Paths 14. Configurational Mechanics 15. Relativistic Continuum Mechanics: A twentieth Century experience sixteen. Epilogue Appendix: chosen Biographies of Mechanicians
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Additional resources for Continuum Mechanics Through the Twentieth Century A Concise Historical Perspective
K Mises R. von (1913) Mechanik der festen Körper im plastisch deformalen Zustand. Gött Nach Math-Phys Kl, 582–592 Mohr O (1900) Welche Umstände bedingen die Elastizitätgrenz und den Bruch einen Materials. VDI 44:1524–1530 Sudria J (1926) Contribution à la théorie de l’action euclidienne. Ann. Fac. Sci. Toulouse (3), 17 (1925), 63–152 Sudria J (1935) L’action euclidienne de déformation et de mouvement. Mém. Sci. Phys. P (1953) History of Strength of Materials, McGraw Hill, New York (1953) [Dover reprint, New York, 1983] Toupin RA (1964) Theories of elasticity with couple-stress.
Henri E. Tresca (1814–1885), a professor at a Paris institution known as the Conservatoire National des Arts et Métiers (for short, CNAM) conducted in the early 1870s a series of fine experiments on metals whereby he constructed in an appropriate representation of the principal stresses the elastic limit of the said metals (cf. Tresca 1872). C. Barré de Saint– Venant (1797–1886) gave the mathematical formulation of these results (1871). Three important remarks are in order: first, it is noticed that no change in volume (so called isochoric deformation in the modern jargon) is observed during plastic deformation; second, the directions of the principal stresses coincide with those of the principal stresses (this assumes an isotropic response); third, the maximum shearing (or tangential) stress at a point is equal to a specific constant.
Hugoniot (1815–1887), and Jacques C. E. 3 New Interests of Investigation 25 nonlinear dynamics in continua. Having established the required equations governing the discontinuities of fields, these scientists could prove the existence and propagation of shock waves and also detonation waves (Jouguet 1906). Duhem also studied such waves in nonlinear elasticity and his friend Jacques Hadamard (1865–1963) provided a useful classification of propagating discontinuities depending on what is the order of the derivative of the basic field that is discontinuous (cf.