Réduction dimensionnelle pour la simulation de la fatigue des métaux

Abstract : In order to take account of fatigue cracks initiation and growth, it is necessary to know the history of the various mechanical quantities in fatigue initiation site. This requires knowledge of the stabilized cyclic mechanical states. From a numerical approach, numerical simulation of polycrystalline aggregates with conventional resolution methods are only carried out for a few cycles. This work presents the development of accelerated numerical methods to reduce the computation time of the Finite Element method in the case of numerical simulation of polycrystalline aggregates under cyclic loading. The first idea is to keep a constant stiffness matrix during overall simulation in order to get just one single factorization to carry out. An algorithm has been proposed in this sense with an incremental and non incremental resolution. The second proposal is based on the use of a model reduction method coupled with the finite element method to solve space/time problem. The PGD has been selected. This method allows to decouple spatial and time coordinates and the displacement fields are computed for a certain number of modes. Two possibilities have been proposed to implement the PGD method in the context of plasticity. The third proposal is to use an a priori adaptative approach based on the use of APR strategy to solve a reduced order model in terms of number of degrees of freedom. An incremental adaptive strategie has been proposed in order to master the quality of the reduced-basis for a certain time steps. Four possibilities of using the APR method have been proposed. The applicability and the performance of the different methods have been first analyzed on a conventional three-dimensional elastoplastic problem with a spherical defect, then on the scale of the microstructure with numerical simulation of polycrystalline aggregates under cyclic elasto-visco-plastic loading. The analyzes have shown that the macroscopic and mesoscopic mechanical responses of the model reduction methods are very close to the incremental method. The simulation time has been reduced by the different methods. The time gains are more significant by increasing the size of the meshes and the non-linearity of the problem. Nevertheless, the idea of keeping a constant stiffness matrix with the incremental method has enabled more CPU time saving at the microstructural scale.
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Mohamed Aziz Nasri. Réduction dimensionnelle pour la simulation de la fatigue des métaux. Mécanique des matériaux [physics.class-ph]. Ecole nationale supérieure d'arts et métiers - ENSAM, 2017. Français. ⟨NNT : 2017ENAM0016⟩. ⟨tel-01533317⟩

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