. =-i-?, , 1111.

, ) ) ? mnpq : I ? 1111 , I ? 1112 , I ? 1122 , I ? 2211 , I ? 1211 et des termes symétriques : I ? 1222 = I ? 2212 et en remplaçant les expressions des déformations ? 11 = ??e x11

, ) )) 2 + ? 2 I ? 1212

, La relation A.4 peut être réécrite sous la forme ci-dessous

, De cette dernière équation (A.6), nous déduisons les intégrales I 1222 , I 2222 , I 1212 : I 1222 = 6? 2 I ? ? mnpq

C. Multiphysics, Après nous avons interpolé les solutions v qui sont fonction de d. Ceci nous permet d'obtenir la première et la deuxième intégrale de A.2, évaluées sur les bords des fissures avec le même logiciel Comsol Multiphysics pour une valeur donné de d. Ces calculs ont été effectués pour une vingtaine valeurs de d variant de 0 à 1 et les résultats interpolés par des fonctions polynomiales, Nous avons résolu les problèmes de cellules pour différentes valeurs de la variable d'endommagement d données

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