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, Dans le chapitre 2, la fabrication additive est mathématiquement décrite comme un problème de couplage multi-physique. Les comportements macroscopiques d'une pièce fabriquée et de son substrat sont découplés en trois aspects : champ thermique, champ mécanique et champ métallurgique. Même si le logiciel ABAQUS est utilisé comme un outil dans nos simulations

, Outre l'équation gouvernante (l'équation de la chaleur avec une condition limite complexe en raison de dépôt du matériau dans la fabrication additive), deux modèles de source de chaleur sont introduits dans l'analyse thermique. Le premier modèle (faisceau gaussien) correspond à un mode de laser transverse fondamental

, Le comportement macroscopique d'une pièce métallique pendant le procédé de la fabrication additive est dominé par l'équation de conservation de la quantité de mouvement, Les équations élasto-plastiques sont combinées au modèle d'écrouissage de Johnson-Cook afin de calculer les contraintes résiduelles

, Pour l'évolution des phases métallurgiques

, austénite cubique centré ?, la martensite cubique centré ?', l'empilement hexagonal compact ?), se comporte différemment selon le procédé thermique, et notamment selon la vitesse de changement de température. Deux modèles de transformation de phase (sans diffusion et avec diffusion), le modèle Koistinen-Marburger (KM) et le modèle modifié Johnson-Mehl-Avrami (JMA) sont brièvement présentés, Le modèle JMA ne peut pas être directement utilisé dans les transformations non-isothermiques de refroidissement ou de réchauffage

, Néanmoins, quelques chercheurs ont proposé des méthodes spécifiques afin de généraliser le modèle