Comptes Rendus
Configurational forces as dissipative mechanisms: a revisit
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 126-131.

A variational argument is used to obtain a necessary and sufficient condition for interpreting the work done by configurational forces as the net dissipation. This condition is the Euler–Lagrange equation associated with the variational integral. We use this simple proposition to re-interpret classical results and also gain insight into recently obtained configurational forces in the stress space.

Un argument variationnel est utilisé pour obtenir une condition nécessaire et suffisante permettant d'interpréter le travail effectué par les forces configurationnelles comme une dissipation nette. Cette condition est l'équation d'Euler–Lagrange associée à l'intégrale variationnelle. Nous utilisons cette proposition simple pour ré-interpréter des résultats classiques et aussi approfondir l'interprétation de forces configurationnelles récemment définies dans l'espace des contraintes.

Published online:
DOI: 10.1016/j.crme.2007.11.004
Keywords: Computational solid mechanics, Dissipative mechanisms, Variational integral
Mot clés : Mécanique des solides numérique, Mécanismes dissipatifs, Intégrale variationnelle

Anurag Gupta 1; Xanthippi Markenscoff 2

1 Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
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Anurag Gupta; Xanthippi Markenscoff. Configurational forces as dissipative mechanisms: a revisit. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 126-131. doi : 10.1016/j.crme.2007.11.004.

[1] J.D. Eshelby The continuum theory of lattice defects (F. Seitz; D. Turnbull; X. Markenscoff; A. Gupta, eds.), Solid State Physics, vol. 3, Academic Press, New York, 1956, pp. 79-144 (For a complete set of papers by J.D. Eshelby see, Collected Works of J.D. Eshelby: Mechanics of Defects and Inhomogeneities, 2006, Springer)

[2] J.R. Rice A path-independent integral and the approximate analysis of strain concentrations by notches and cracks, Journal of Applied Mechanics, Volume 35 (1968), pp. 379-386

[3] H.D. Bui Fracture Mechanics: Inverse Problems and Solutions, Springer, 2006

[4] G. Gioia; M. Ortiz Delamination of compressed thin films, Advances in Applied Mechanics, vol. 33, 1997, pp. 119-192

[5] E. Fried; M.E. Gurtin A unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain boundaries and epitaxy, Advances in Applied Mechanics, vol. 40, 2004, pp. 5-177

[6] M. Peach; J.S. Koehler The forces exerted on dislocations and the stress fields produced by them, Physical Review, Volume 80 (1950) no. 3, pp. 436-439

[7] W. Heidug; F.K. Lehner Thermodynamics of coherent phase transformations in non-hydrostatically stressed solids, Pure and Applied Geophysics, Volume 123 (1985), pp. 91-98

[8] J.K. Knowles; E. Sternberg On a class of conservation laws in linear and finite elastostatics, Archive for Rational Mechanics and Analysis, Volume 44 (1972), pp. 187-211

[9] B.E. Pobedrja A new formulation of the problem in mechanics of a deformable solid body under stress, Soviet Mathematics Doklady, Volume 22 (1980) no. 1, pp. 88-91

[10] B.E. Pobedria; T. Holmatov On the existence and uniqueness of solutions in the elasticity theory problem with stresses, Vestnik Moskovskogo Universiteta, Seriya 1 (Matematika Mekhanika), Volume 1 (1982), pp. 50-51

[11] S. Li; A. Gupta; X. Markenskoff Conservation laws of linear elasticity in stress formulations, Proceedings of Royal Society London A, Volume 461 (2005), pp. 99-116

[12] E. Reissner On a variational principle for finite elastic deformations, Journal of Mathematical Physics, Volume 32 (1953) no. 2–3, pp. 129-135

[13] I.M. Gelfand; S.V. Fomin Calculus of Variations, Dover, 2000

[14] E. Noether Invariante variationsprobleme, Göttinger Nachrichten (Mathematisch-physikalische Klasse), Volume 2 (1918), pp. 235-257 (Transl.: Transport Theory Statistical Physics, 1, 1971, pp. 186-207)

[15] J.D. Eshelby The elastic energy-momentum tensor, Journal of Elasticity, Volume 5 (1975), pp. 321-335

[16] B.E. Pobedrya; D.V. Georgievskii Equivalence of formulations for problems in elasticity theory in terms of stresses, Russian Journal of Mathematical Physics, Volume 13 (2006) no. 2, pp. 203-209

[17] V. Kucher; X. Markenscoff; M. Paukshto Some properties of the boundary value problem of linear elasticity in terms of stresses, Journal of Elasticity, Volume 74 (2004) no. 2, pp. 135-145

[18] R.A. Adams Sobolev Spaces, Academic Press, New York, 1975

[19] X. Markenskoff; A. Gupta Configurational balance laws for incompatibility in stress space, Proceedings of Royal Society London A, Volume 463 (2007), pp. 1379-1392

[20] E. Kröner Continuum theory of defects (R. Balian et al., eds.), Les Houches, Session 35, 1980, Physique des défauts, North-Holland, New York, 1981, pp. 215-315

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