Abstract
For equilibrium states of elastic materials some general formulae of conservation type have been established in recent papers by Knowles and Sternberg and by Green. It is shown that these results arise naturally from the application of standard integral identities to an energy-momentum tensor first introduced into elastostatics by Eshelby. A duality is exhibited between the energy-momentum tensor and the Cauchy stress which leads directly to inverse deformation relations for elastic solids due originally to Shield.
Résumé
Knowles et Sternberg et Green ont récemment établi des formules générales du genre conservation pour des etats d'équilibre dans des matières élastiques. On démontre que ces résultats découlent naturellement de l'application des identités intégrales standard à un tenseur d'énergie-moment qui a été introduit dans l'élastostatique pour la première fois par Eshelby. On montre qu'il existe une dualité entre le tenseur d'energiemoment et le tenseur de contraintes de Cauchy qui mène directement à des relations inverses de déformation pour des solides élastiques que Shield fut le premier à obtenir.
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Chadwick, P. Applications of an energy-momentum tensor in non-linear elastostatics. J Elasticity 5, 249–258 (1975). https://doi.org/10.1007/BF00126989
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DOI: https://doi.org/10.1007/BF00126989