We prove some relaxation results in the spirit of Anza Hafsa and Mandallena for integral functionals arising in the study of coherent thermochemical equilibria for multiphase solids. The energy density exhibits an explicit dependence on the deformation gradient and on a vector field representing the chemical composition. The deformation gradient satisfies a determinant type constraint and the chemical composition a constraint on the modulus.
On prouve quelques résultats de relaxation dans le même esprit que Anza Hafsa et Mandallena pour des fonctionnelles intégrales provenant de l'étude de l'équilibre thermochimique pour les solides multiphases. La densité d'énergie considérée dépend du gradient de la déformation ainsi que d'un champ de vecteurs représentant la composition chimique du solide. Le gradient de déformation satisfait une contrainte sur son déterminant et la composition chimique une contrainte sur son module.
Accepted:
Published online:
@article{CRMATH_2009__347_5-6_337_0,
author = {Zappale, Elvira and Zorgati, Hamdi},
title = {Some relaxation results for functionals depending on constrained strain and chemical composition},
journal = {Comptes Rendus. Math\'ematique},
pages = {337--342},
publisher = {Elsevier},
volume = {347},
number = {5-6},
year = {2009},
doi = {10.1016/j.crma.2009.01.024},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.024/}
}
TY - JOUR AU - Zappale, Elvira AU - Zorgati, Hamdi TI - Some relaxation results for functionals depending on constrained strain and chemical composition JO - Comptes Rendus. Mathématique PY - 2009 SP - 337 EP - 342 VL - 347 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.024/ DO - 10.1016/j.crma.2009.01.024 LA - en ID - CRMATH_2009__347_5-6_337_0 ER -
%0 Journal Article %A Zappale, Elvira %A Zorgati, Hamdi %T Some relaxation results for functionals depending on constrained strain and chemical composition %J Comptes Rendus. Mathématique %D 2009 %P 337-342 %V 347 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.024/ %R 10.1016/j.crma.2009.01.024 %G en %F CRMATH_2009__347_5-6_337_0
Zappale, Elvira; Zorgati, Hamdi. Some relaxation results for functionals depending on constrained strain and chemical composition. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 337-342. doi : 10.1016/j.crma.2009.01.024. http://www.numdam.org/articles/10.1016/j.crma.2009.01.024/
[1] Relaxation theorems in nonlinear elasticity, Ann. Inst. H. Poincaré, Volume 25 (2008), pp. 135-148
[2] Direct Methods in the Calculus of Variations, Springer, Berlin, 2008
[3] Convex Analysis and Variational Problems, North-Holland Publishing Company, 1976
[4] The lower quasiconvex envelope of the stored energy function for an elastic crystal, J. Math. Pures Appl., Volume 67 (1988), pp. 175-195
[5] Energy functionals depending on elastic strain and chemical composition, Calc. Var. Partial Differential Equations, Volume 2 (1994), pp. 283-313
[6] Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results, Arch. Rational Mech. Anal., Volume 154 (2000), pp. 101-134
Cited by Sources:
