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

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Smelser, R., Epstein, M., & Germain, P. (2020). The method of virtual power in the mechanics of continuous media I : Second-gradient theory. Mathematics And Mechanics Of Complex Systems. https://doi.org/doi:10.2140/memocs.2020.8.153
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Faculty, 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. Authored by Paul Germain, translated by Marcelo Epstein and Ronald E. Smelser.

Details
Title

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

Author(s)

Smelser, Ronald
Epstein, Marcelo
Germain, Paul

UNC Charlotte Affiliate Type

Faculty

Extent

1 online resource

Date Created

2020

Genre

articles

Resource Type

text

Abstract

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. Authored by Paul Germain, translated by Marcelo Epstein and Ronald E. Smelser.

Subjects--Topics

Continuum mechanics
Mechanics

Is Part Of

Mathematics and mechanics of complex systems

Language

English

Published Version (Please cite this version)

doi:10.2140/memocs.2020.8.153

Publisher's Version

https://doi.org/10.2140/memocs.2020.8.153

Permalink

http://hdl.handle.net/20.500.13093/work:1088

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