Nouvelles approches sans maillage basées sur la méthode des éléments naturels pour la simulation numérique des procédés de mise en forme

La methode des elements finis, bien qu'employee dans la grande majorite des codes de simulation industriels, presente un certain nombre de limitations pour la simulation des procedes de mise en forme, notamment lors de grandes deformations, de la localisation des phenomenes comme c'est le cas pour la formation de bandes de cisaillement ou de fissures. La necessite de reconstruire un maillage verifiant un certain nombre de criteres de qualite entraine des couts de calcul additionnels, ainsi que des problemes de robustesse, particulierement pour les problemes tridimensionnels complexes. Depuis une dizaine d'annees, de nouvelles methodes numeriques, alternatives a la methode des elements finis, ont ete developpees. Ces methodes, appelees methodes sans maillage, construisent une partie ou la totalite de l'approximation entierement a partir du nuage de nœuds. L'objectif de cette these est de developper un certain nombre d'outils numeriques bases sur les concepts precedemment cites affin de mettre au point un logiciel de simulation des procedes permettant de surmonter certaines des difficultes liees a la methode des elements finis. La technique proposee, baptisee methode C-NEM, est une extension de la methode des elements naturels (NEM) dont les ameliorations permettent un traitement plus simple pour l'analyse des procedes. La premiere partie presente la methode et son interet pour les problemes presentant des discontinuites fixes ou mobiles. La deuxieme partie presente des approches permettant de traiter les problemes en grandes deformation avec eventuellement une localisation des phenomenes. La derniere partie illustre la methode au travers d'exemples numeriques.

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