Vol. 8, No. 2, 2020

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The method of virtual power in the mechanics of continuous media, I: Second-gradient theory

Paul Germain

Vol. 8 (2020), No. 2, 153–190

The systematic application of the definition of internal forces, by means of the virtual power produced in a class of virtual motions, leads to a consistent mathematical representation of stresses and strains in any given mechanical model. It is thus possible to write the statical and dynamical equations and to state well posed boundary value problems. The second-gradient theory, presented here by way of example, can be developed without any ambiguity. An essential distinction is drawn between intrinsic and classical stresses so as to avoid certain issues of interpretation. It is shown that all the results of classical linear elasticity can be immediately extended to the case of second-gradient elastic media. The constitutive equations of nonlinear elasticity are also formulated.

Translated by Marcelo Epstein and Ronald E. Smelser

Received: 16 December 2018
Revised: 25 June 2019
Accepted: 17 August 2019
Published: 19 May 2020
†Paul Germain
Institut de Mécanique théorique et appliquée
Université de Paris VI