Download Continuum Mechanics Through the Eighteenth and Nineteenth by Gérard A. Maugin PDF

By Gérard A. Maugin

Conceived as a chain of kind of independent essays, the current booklet severely exposes the preliminary advancements of continuum thermo-mechanics in a put up Newtonian interval extending from the inventive works of the Bernoullis to the 1st global battle, i.e., approximately in the course of first the “Age of cause” and subsequent the “Birth of the fashionable world”. The emphasis is rightly put on the unique contributions from the “Continental” scientists (the Bernoulli relations, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in festival with their British friends (Green, Kelvin, Stokes, Maxwell, Rayleigh, Love,..). It underlines the most breakthroughs in addition to the secondary ones. It highlights the function of scientists who left crucial prints during this background of clinical principles. The booklet exhibits how the ambitious advancements that blossomed within the 20th century (and perused in a prior booklet of the writer within the related Springer sequence: “Continuum Mechanics during the 20th Century”, Springer 2013) came upon wealthy compost within the positive foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is definitely summarized by way of an intensive research of treatises (Appell, Hellinger) released at the moment. English translations by way of the writer of most important texts in French or German are given to the good thing about the readers.

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Additional info for Continuum Mechanics Through the Eighteenth and Nineteenth Centuries: Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914)

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However, this remark makes one ponder the case of an infinite body and the second Cauchy’s theory (CAUCHY-2) of elasticity proposed by Cauchy in 1828 on the basis of molecular considerations [5]. 5 This was proposed a priori to close the obtained system of differential equations in terms of the elastic displacement gradient. This a priori construct that involves a representation theorem—also attributed to Cauchy—for a second-order tensor is referred to as Cauchy’s elasticity by Truesdell, Toupin and Noll [47, 48].

This name, that properly signifies the science of powers or motive causes, could at first seem inadequate since I envisage Mechanics rather like the science of effects than that of causes [this is the most important point for d’Alembert; exit the notion of force to start with]; nonetheless as the word ‘‘Dynamics’’ is very much used among scientists to designate the science of the motion of bodies, which act among themselves in whatever way, I thought to keep the term, in order to announce to geometers by the very title of this treatise that I envisage principally to aim at perfecting and enlarging this part of Mechanics.

Cauchy frequently used this possibility an as expedient way to publish in print his own lectures at Polytechnique and also many of his memoirs. This was the case of his landmark paper of 1822 on continuum mechanics which was published in 1828 (cf. Cauchy [4]) in the second volume of ‘‘Exercices de Mathématiques’’, a kind of privately produced series published between 1826 and 1830. Cauchy was the only author published in this surprising scientific periodical. 3 The Main Contents of Cauchy’s 1822/1828 Memoir What we call the first theory (CAUCHY-1) of general continuum mechanics and elasticity of Cauchy is a purely phenomenological continuum theory which does not use the notion of constituent ‘‘molecules’’ and at-a-distance interactions between them (contrary to the second theory of Cauchy; see below).

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