Comptes Rendus
Is incompressible elasticity a conformal field theory?
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 163-169.

In this work, we investigate the theory of linear isotropic incompressible elasticity as a conformal field theory. We calculate the conformal currents, the conservation laws and the balance laws of incompressible elasticity. We investigate the Euler–Lagrange symmetries, variational and divergence symmetries. If the pressure p=0, the conformal group is the symmetry group for homogeneous isotropic linear incompressible elasticity without external forces. The additional symmetry is the special conformal transformation. We also discuss the symmetry breaking terms of special conformal transformations in elasticity.

Dans ce travail, nous examinons la théorie de l'élasticité linéaire incompressible isotrope en tant que théorie conforme. Nous calculons les courants conformes, les lois de conservation et les lois de bilan de l'élasticité incompressible. Nous examinons les symétries d'Euler–Lagrange, ainsi que les symétries variationnelles et les symétries de divergence. Si la pression est nulle, le groupe conforme est le groupe de symétrie pour l'élasticité homogène linéaire isotrope incompressible en l'absence de forces extérieures. La symétrie additionnelle est la transformation spéciale conforme. Nous discutons aussi les termes des transformations spéciales conformes de l'élasticité qui brisent la symétrie.

Published online:
DOI: 10.1016/j.crme.2007.11.006
Keywords: Incompressible elasticity, Conservation laws, Eshelby stress tensor, Conformal field theory
Mot clés : Élasticité incompressible, Lois de conservation, Tenseur des contraintes d'Eshelby, Théorie de champ conforme

Markus Lazar 1; Charalampos Anastassiadis 1

1 Emmy Noether Research Group, Department of Physics, Darmstadt University of Technology, Hochschulstr. 6, 64289 Darmstadt, Germany
@article{CRMECA_2008__336_1-2_163_0,
     author = {Markus Lazar and Charalampos Anastassiadis},
     title = {Is incompressible elasticity a conformal field theory?},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {163--169},
     publisher = {Elsevier},
     volume = {336},
     number = {1-2},
     year = {2008},
     doi = {10.1016/j.crme.2007.11.006},
     language = {en},
}
TY  - JOUR
AU  - Markus Lazar
AU  - Charalampos Anastassiadis
TI  - Is incompressible elasticity a conformal field theory?
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 163
EP  - 169
VL  - 336
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crme.2007.11.006
LA  - en
ID  - CRMECA_2008__336_1-2_163_0
ER  - 
%0 Journal Article
%A Markus Lazar
%A Charalampos Anastassiadis
%T Is incompressible elasticity a conformal field theory?
%J Comptes Rendus. Mécanique
%D 2008
%P 163-169
%V 336
%N 1-2
%I Elsevier
%R 10.1016/j.crme.2007.11.006
%G en
%F CRMECA_2008__336_1-2_163_0
Markus Lazar; Charalampos Anastassiadis. Is incompressible elasticity a conformal field theory?. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 163-169. doi : 10.1016/j.crme.2007.11.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.006/

[1] G. Mack; A. Salam Finite-component field representation of the conformal group, Ann. Phys., Volume 53 (1969), pp. 174-202

[2] G.A. Maugin Material Inhomogeneities in Elasticity, Chapman and Hall, London, 1993

[3] J.K. Knowles; E. Sternberg On a class of conservation laws in linearized and finite elastostatics, Arch. Ration. Mech. Anal., Volume 44 (1972), pp. 187-211

[4] P.J. Olver; P.J. Olver Conservation laws in elasticity. II. Linear homogeneous elastostatics, Arch. Ration. Mech. Anal., Volume 85 (1984), pp. 131-160 (Errata)

[5] S. Li On dual conservation laws in planar elasticity, Int. J. Engrg. Sci., Volume 42 (2004), pp. 1215-1239

[6] R. Kienzler; G. Herrmann Mechanics in Material Space, Springer, Berlin, 2000

[7] J.E. Marsden; T.J.R. Hughes Mathematical Foundations of Elasticity, Dover, New York, 1994

[8] P.J. Olver Applications of Lie Groups to Differential Equations, Springer, New York, 1986

[9] N.H. Ibragimov Transformation Group Applied to Mathematical Physics, Reidel, Dordrecht, 1985

[10] A.O. Barut; R. Raczka Theory of Group Representations and Applications, PWN—Polish Scientific Publishers, Warszawa, 1977

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

Cited by Sources:

Comments - Policy