دانلود کتاب Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century: From Hydraulics to Plasticity

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.
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In 1800 (An VIII of the First French Republic), the civil engineer
Gaspard-Clair-François-Marie RICHE, Baron de PRONY (1755–1839), published
a book entitled “Mécanique philosophique” (“Philosophical Mechanics”). This title
bears the whole spirit of the approach to science and more generally knowledge that
was expanded during the Enlightenment and its acceptance by contemporaries
of the French Revolution and early nineteenth century. I very much like this title
which in fact is explained by the subtitle (in translation) “Analysis of various parts
of the Science of Equilibrium and Motion.” It is in this state of mind that I have
expanded some aspects of the historical developments of continuum mechanics in
the immediate post-Newtonian era till the second half of the twentieth century in
two previous volumes. The first one1 published in 2013 was neatly characterized by
my own experience in the field with several national institutions that I visited and/or
worked with from time to time (e.g., in the USA, UK, Germany, Italy, Poland,
Japan—and obviously France), and by my friendly relationship with research
leaders of various nationalities whom I practically all knew personally, being aware
of both their strength and pettiness, but always emphasizing the former. The choice
of studied groups and schools as also a selection of particular fields was strictly
personal since I had decided to speak only about what I knew best, although
sometimes superficially and not without some unavoidable misinterpretations and
factual errors. This personal and nonobjective vision was naturally criticized by
some readers. Most of the time, these people complained that I had not treated at all,
or not developed enough, their own field of research—this was the case of
finite-strain elasto-plasticity and phase-transformations in deformable solids,
although this was touched upon but cursorily—for which I thought that some other
scientists would be much more competent than me. Obviously, with a more than
natural humane bias, some complained about not being cited. To these last people I
sincerely apologize. A well-balanced exercise in citation is not easy and is a dangerous
exercise when one deals with his own contemporaries. I did not take any
chance with the second volume2 devoted to the eighteenth and nineteenth centuries
where all contributors could not complain to me orally or via e-mail, save perhaps
in some of my nightmares. Still my choice of subjects and main actors was strictly
personal, although greatly influenced by some famous predecessors such as J.L.
Lagrange, A. Barré de Saint-Venant, P. Duhem, I. Todhunter and K. Pearsons, R.T.
Whittaker, M. Jouguet, and more recently, R. Dugas,3 I. Szabò,4 G.A. Tokaty,5
S.P. Timoshenko,6 and naturally C.A. Truesdell.7
The reader will have noticed that with growing age I am going back in the past.
But this has a technical limit due to my lack of knowledge of some “dead” languages.
Of course, I could deal with ancient Greek having at home all necessary
help for the reading and interpretation of the primary sources. My improved reading
of Latin would require the help of a priest but I am not a religious person.
Furthermore, the reader must realize that I am not concerned with a total history of
mechanics—for which Dugas (see Footnote 3) and Szabó (see Footnote 4) provided
beautiful but not completely satisfactory attempts—but only with that part called
continuum mechanics. This poses the fundamental question of the never-ending
debate between the molecular-particular discrete vision and the continuum one.
This matter touches upon both history and philosophy and a return to the ancient
Greeks may be needed at this very point. But the subject remained of actuality
during all centuries in particular with the early developments of continuum
mechanics with Poisson, Navier, Cauchy, Piola, etc. In this volume, I consider that
continuum mechanics starts with hydrostatics, the notion of pressure, and applications
to hydraulics while modern continuum mechanics starts with hydrodynamics,
three-dimensional elasticity, and the notion of stress tensor. Hydraulics
brings to the foreground the important role of some experimentalists, starting with
the Renaissance but also especially in the eighteenth century. Although a theoretician,
I have made all efforts to deal with this aspect with sympathy.

The main purpose of the present volume is to fill in the gaps left in the previous
two volumes by completing some details of the genesis and birth period and
introducing some important and original fields that I previously neglected. The
same format of interrelated essays has been kept. These essays may be read separately
although many authors, including me, prefer a global orderly reading
of their books. Subject matters that were previously neglected include: a deeper
attention to hydraulics, the question raised by porosity in solids, the theory of
mixtures and reacting media, and the influence of fast flows and of the birth of
aeronautics in fluid mechanics (with Reynolds, Prandtl, von Kármán). This brings
me closer to my initial interest as alumnus of the school of Aeronautics in France.
Also, in my historical approach, I always try to avoid any “precursoritis” and duly
examine the (at the time) contemporary reaction to the then most recent advances.
This can be achieved by carefully perusing the lecture notes and treatises published
by famous scientists—albeit not necessarily the most creative ones in the field of
continuum mechanics—because such works reflect both the state of the art at the
time of their writing and what the author tries to input from his own viewpoint with,
usually, a deeply thought appraisal. I already applied this strategy with the treatise
of Paul Appell in France and the encyclopedic article by Ernst Hellinger in
Germany in my second volume. Here, this is applied to the lecture notes and some
collected technical works of Pierre Duhem on hydrodynamics and elasticity, and the
lecture notes of a course given by Henri Poincaré on elasticity and an introduction
course on continuum mechanics delivered by David Hilbert. To some readers, this
may seem to grant too much importance to the “Belle époque.” Not only is the
viewpoint of two such giants of mathematics as Poincaré and Hilbert of intrinsic
interest, but the period at which the lectures were given was a critical one for the
whole of physics. It is salient to see whether the burgeoning new physics had any
influence on a mature science then thought to have stabilized with magisterial
treatises by H. Lamb and A.E.H. Love, respectively, in fluid mechanics and elasticity.
Furthermore, the synthetic works of Appell, Hellinger, Duhem, Poincaré, and
Hilbert in fact provide the most valuable documentary basis on which a revival of
continuum mechanics and its formalization by Truesdell et al. was built in the
second half of the twentieth century. We are dutifully following the advice of Rabbi
Rashi (Eleventh century) of Troyes in Burgundy: “Ask your master his sources.”
This is already what Duhem did when examining Leonardo and his possible sources
of inspiration in pre-Renaissance times. This is complemented by essays on the
special behaviors of viscoelasticity of solids and plasticity—only superficially
mentioned in the previous volumes—on fracture—so important in continuum
dynamics—the role of geometry as a cornerstone of the field, and a kind of
sociohistorical appraisal of the seminal contributions by our direct masters in the
second half of the twentieth century.