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Continuum mechanics through the eighteenth and nineteenth centuries. Historical perspectives from John Bernoulli (1727) to Ernst Hellinger (1914). (English) Zbl 1303.74003

Solid Mechanics and Its Applications 214. Cham: Springer (ISBN 978-3-319-05373-8/hbk; 978-3-319-05374-5/ebook). xi, 269 p. (2014).
In this very interesting book, the author analyzes the significant contributions of different European scientists to the field of continuum mechanics, starting from John Bernoulli in the 18th century to Hellinger at the beginning of the 20th century. He divides the analysis in thirteen chapters complemented with a short introduction, plus a gallery of portraits of different scientists whose contributions are analyzed, these portraits having already been presented in their respective chapters.
Throughout the whole book, the author does not restrict his analyses to the scientific contributions, as he also analyzes the filiations and the relationships between these scientists. He indeed analyzes different memoirs and papers which were published by these scientists, but also the letters they exchanged while they were working. Some chapters are completed with appendices which give either translations of significant parts of the original memoirs of the scientists, or further illustrations on the ideas which have been subsequently developed. Each chapter starts with a short abstract describing in a precise way the main ideas which will be treated in the chapter and the position of the contribution in the overall context of continuum mechanics.
Chapter 2 starts with the contributions of John Bernoulli on the principle of virtual work, and then describes the premises of the calculus of variations.
Chapter 3 discusses the contribution of Cauchy concerning the notion of stress. The author shows how this important notion has been developed along the years in order to take into account different materials.
Chapter 4 presents the contributions of Piola and Kirchhoff on the changes of configurations, after the pioneering works by Euler and Lagrange.
In Chapter 5, the author describes the pioneering work of Duhamel and concerns the bases of thermo-elasticity.
Chapter 6 focuses on the development of the elasticity theory, starting with Cauchy and the notion of stress tensor, and going through Saint-Venant and Boussinesq, among others. The author here shows how this elasticity theory has progressively taken into account nonlinear phenomena, for example.
Chapter 7 emphasizes the development of mathematical physics with the main contributions by Helmholtz and Gibbs and their applications by Duhem.
Chapter 8 describes the contributions by the Cosserat brothers on what is called now oriented or polar continua. These contributions occurred at the beginning of the 20th century.
In Chapter 9, the author presents the contribution of the mathematician Carathéodory who linked thermodynamics and topology.
Chapter 10 goes back to the influence on Duhem on both the theory of thermo-mechanics and mathematics.
In Chapter 11, the author comments on the treatise written by Appell on rational mechanics at the very beginning of the 20th century. He shows how Appell gathered the different contributions which were available at that time in a unique book written in French.
Chapter 12 is somehow similar to the previous one, as the author here presents a long synthesis given by Hellinger in Germany on the development of continuum mechanics.
The final and short Chapter 13 describes the method which has been used for the preparation of this book, and gives further comments on the development of continuum mechanics.
Written by a specialist of continuum mechanics, this book describes in a very interesting way the progression of the ideas in this field as developed by eminent scientists of these now historical periods. Without drawing many computations, the author emphasizes the main ideas which have contributed to the progress of this field in connection with other sciences. Thus doing, the author ensures the possibility to different possible readers, specialists or non-specialists of this field, to be acquainted with the progress of scientific ideas along the past centuries.

MSC:

74-03 History of mechanics of deformable solids
80-03 History of classical thermodynamics
01A50 History of mathematics in the 18th century
01A55 History of mathematics in the 19th century
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