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Piola and Kirchhoff: On Changes of Configurations

  • Gérard A. MauginEmail author
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Part of the Solid Mechanics and Its Applications book series (SMIA, volume 214)

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.

Keywords

Continuum mechanics Finite strains Piola–Kirchhoff stresses Cauchy–Green tensors Principle of virtual work Elasticity 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut Jean Le Rond d’AlembertUniversité Pierre et Marie CurieParis Cedex 05France

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