The elastic energy-momentum tensor

✍ Scribed by J. D. Eshelby

• Publisher: Springer Netherlands
• Year: 1975
• Tongue: English
• Weight: 814 KB
• Volume: 5
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00126994

✦ Synopsis

The application to continuum mechanics of the general methods of the classical theory of fields is advocated and illustrated by the example of the static elastic field. The non-linear theory of elasticity is set up in the most convenient form (Lagrangian coordinates and stress tensor). The appropriate energy-momentum tensor is derived, and it is shown that the integral of its normal component over a closed surface gives the force (as the term is used in the theory of solids) on defects and inhomogeneities within the surface. Other topics discussed are Giinther's and related integrals, symmetrization of the energy-momentum tensor, and the Eulerian formulation. Some further extensions, existing and potential, are indicated.

RI~SUMI~

On signale les avantages de l'application h la m6chanique des milieux continus des m6thodes de la th6orie classique des champs. A titre d'example la th6orie de l'61asticit6 est construite sous la forme la plus convenable cette fin (coordon6es de Lagrange, composantes de tension de Boussinesq). On d6duit ensuite le tenseur d'6nergie-impulsion dont l'int6grale de la composante normale 6tendue sur une surface ferm6e donne la force (comme on l'entend en th6orie des solides) agissant sur les d6faults dans son int6rieur. On discute aussi quelques int6grales semblables, entr'elles celles de Giinther, la sym6trisation du tenseur d'6nergie-impulsion et la formulation en coordon6es d'Euler. On r6capitule par conclure certains autres r6sultats d6j~t connus, tout en indiquant quelques extensions possibles.