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C. Annexe and . Cqicui, Intégral, uf- La combinaison des relations (C-2) et (C-5) permet de calculer le terme sous le signe intégrale (C-1): c,j"G jn, pp.5-6

. La-dérivée-d, ordre 4 de R est donnée par: R,noo* --zk, p.7

. Compte-tenu-de, on écrit (C-8) sous la forme suivante: ol*(,)=# ?h{i t, p.10

. Le-fait-d, avoir écrit la dérivée seconde par rapport à xn et x-à I'extérieur de I'intégrale est licite puisque I'intégration s'effectue sur V' (sous entendu Ç1

C. Annexe, Calcul de l'Intésrale uh

L. Relation, C-1) s'écrit alors sous la forme suivante: rh ,-\- gl+vç, ôrrr,rXnX uil'"(r)=-;Ël(-Ë+2ff) 0(r'), p.16

. Partir-desquels, Ie (x) possède trois formes différentes: sur [0,1], x Ko (x) Io (x) = -x ln(x) sur [1,12], x Ko (x) Io (x) = -1, \2 sur [12,X], x Ko (x) Io (*) = l

J. Xdx-oï and J. Ro, Io (x) dx X+- P

. Finalement, la déformation thermique macroscopique est nulle El

D. Annexe, Calcul des Déformations Inélastiques Macroscopiques On utilise I'une des propriétés de la fonction de Dirac qui permet de passer d'une intégrale de volume à une intégrale surfacique

. Annexe-s, Références biblio graphique s tll R.dewi t, Theory of Disctinations: III. Continuous and Discrete Disclinations in Isotropic Elasticity, J.Res'Nat'Bur'Stand'(U'S)Phys. and Chem, vol.774, issue.3, pp.359-368, 1973.

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. Au-cours-de-la, (,lnponements des matériaux, il est difficile d'ignorer les processus inévcrsibles. Ce sont des processus taisent intervenir des déformations inélastiques ou anélastiques s'accompagnant d'une dissipation intrinsèque pro

. Pratiquenrenf, tout phénornène inélastique ou anélastique esr lié à la propagation de défauts