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Méthode EF2 et hyperréduction de modèle : vers des calculs massifs à l'échelle micro

Abstract : Model Order Reduction (MOR) methods are used to cope with high computational costs typically involved in parametric analysis of structures requiring a huge number of almost similar simulations. Among them, a so-called hyperreduction method suitable for non-linear mechanical finite element (FE) problems is studied. An objected-oriented approach to deal with it in the framework of a FE software is carried out. The software design takes advantage of a two-level process : a so-called offline computation step in which the reduced model is set up based on collected snapshots of mechanical system states and an online high-speed reduced computation which runs the reduced model. The code design relying on a reduced element is expected to enhance performance, to give a clearer view over the process and to favour code reuse in subsequent developments of the method. Futhermore, the hyperreduction method is reviewed and is deeply improved : vector and tensor bases are introduced to deal with non-scalar fields which arise in non-linear mechanical FE problems and the mechanical balance is ensured in the extrapolation phase. A particular emphasis is placed on the treatment of free and periodic boundary conditions. In this approach, the boundary conditions at the edge of the reduced integration domain are enforced in the reduced balance equations. Numerical toy examples of elasticity fiber/matrix inclusions as well as a full adaptative non-linear simluation are provided to show the capabilities of the implementation. To take into account microstructural behaviors, FE2 methods consist in splitting the computation into two scales. At the micro scale the material constitutive equations are integrated over periodic RVEs. The behavior of the macro structure is carried out by a homogeneized process. A multidimensional hyperreduction method is applied to the massive micro problem composed of the set of the periodic RVEs. A BFGS algorithm is used to update the macro tangent matrices at each integration Gauss point. Some speed-ups are recorded for low dimensional models. However, as the number of degrees of freedom increases, the multidimensional hyperreduction method is proved to be far less efficient to cut computational costs down.
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  • HAL Id : tel-01272193, version 1

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Georges Peyre. Méthode EF2 et hyperréduction de modèle : vers des calculs massifs à l'échelle micro. Mécanique des matériaux [physics.class-ph]. Ecole Nationale Supérieure des Mines de Paris, 2015. Français. ⟨NNT : 2015ENMP0026⟩. ⟨tel-01272193⟩

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