L’´etude des diff´erents mod`eles de la litt´erature fait apparaˆıtre des faiblesses ´evi-dentes pour chacune des contraintes ´equivalentes propos´ees.
Seules nos mesures effectu´ees suivant l’axe D.T. de notre tˆole semblent coh´erentes avec les contraintes ´equivalentes propos´ees dans la litt´erature. Pour les mesures suivant l’axe D.L. de notre tˆole, on ne peut pas faire la part des choses entre les erreurs dues `a nos mesures et celles dues aux mod`eles eux-mˆemes.
Rebondissons : mod´elisons !
En termes de perspectives de mod´elisation, il semble que la d´emarche propos´ee par Pearson et al . va dans la bonne direction et devrait ˆetre g´en´eralis´ee et appliqu´ee directement `a la d´efinition de la contrainte ´equivalente : il faut a priori non seulement int´egrer dans une contrainte ´equivalente la diff´erence des contraintes principales et une contrainte ´equivalente par exemple au sens de Von Mises pour ´eviter de n´egliger l’effet d’une contrainte d’´equibitraction ou d’´equibicompression sur le comportement magn´etique.
Pour prendre en compte la dissym´etrie de comportement entre traction et com-pression, il semble raisonnable d’affiner encore cette approche. Une m´ethode pourrait consister `a int´egrer dans la d´efinition de la contrainte ´equivalente au sens du ma-gn´etisme non seulement les invariants du tenseur des contraintes d’ordre II, mais ´egalement l’invariant du tenseur des contraintes d’ordre III ou les parties positives et n´egatives du tenseur des contraintes.
Par ailleurs, il convient de noter que ce type de mod´elisation doit pouvoir prendre en compte non seulement l’anisotropie induite par le chargement mais aussi l’ani-sotropie initiale toujours non n´egligeable dans les mat´eriaux industriels du g´enie ´electrique. Ce point est d’autant plus d´elicat qu’il est d´esormais prouv´e grˆace `a des mesures Hubert et al. [2002] et des mod`eles d’homog´en´eisation Daniel et al. [2002] qu’une faible texture cristallographique de la tˆole induit des anisotropies des com-portements magn´etique et ´elastique faibles mais une anisotropie du comportement coupl´e importante.
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