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Piola and Kirchhoff: On Changes of Configurations

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Continuum Mechanics Through the Eighteenth and Nineteenth Centuries

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 214))

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Abstract

The seminal contribution of Gabrio Piola to the foundations of continuum mechanics is critically examined directly on the basis of his publications (1825–1848). This emphasizes the original approach of Piola who favoured a direct projection on the material configuration (where material particles are “labelled”), this yielding the now well known Piola–Kirchhoff stresses in the so-called Piola format of continuum mechanics. Piola is a follower of Lagrange and Poisson, much more than of Cauchy. But he established the connection of his equations with those of the more familiar Euler–Cauchy format (expressed in the actual configuration) of elasticity. Kirchhoff, much more known than Piola because of his renowned works in electricity, spectroscopy and thermo-chemistry, also contributed to the same format as Piola, hence his name attached to that of Piola. The works of Piola acquired a well deserved recognition and an excellent range of applications with the expansion of nonlinear elasticity, the modern theory of material inhomogeneities and the notion of configurational forces.

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Notes

  1. 1.

    A microfilm copy of the memoirs of 1836 and 1845 was kindly provided to us in 1991 by the Municipal Library of Modena during our stay as a visiting professor of the Italian CNR in Pisa.

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  1. Institut Jean Le Rond d’Alembert, Université Pierre et Marie Curie, Paris Cedex 05, France

    Gérard A. Maugin

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Maugin, G.A. (2014). Piola and Kirchhoff: On Changes of Configurations. In: Continuum Mechanics Through the Eighteenth and Nineteenth Centuries. Solid Mechanics and Its Applications, vol 214. Springer, Cham. https://doi.org/10.1007/978-3-319-05374-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-05374-5_4

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