Pilotage du chargement en formulation X-FEM: application aux lois cohésives

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/28/21/ANNEX/r_22HF3P0A.pd

Propagation 3D de fissures cohésives X-FEM

International audienceUne stratégie innovante d'étude quasi-statique de problèmes de propagation de fissures a été proposée dans Code_Aster, couplant des modèles de zones cohésives et la méthode des éléments finis étendus (XFEM). Elle a été validée sur des benchmarks issus de la littérature, pour la plupart des expériences réalisées sur des éprouvettes de béton. La capacité de la méthode à prédire des trajets de fissurations complexes pour des problèmes tridimensionnels a ainsi été illustrée. Une extension à la dynamique a été réalisée et validée pour les trajets de fissurations droits, les premiers résultats sur trajets courbes étant prometteurs

A projection-based reduced-order model for parametric quasi-static nonlinear mechanics using an open-source industrial code

We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code aster. Model order reduction aims to lower the computational cost of engineering studies that involve the simulation to a costly high-fidelity differential model for many different parameters, which correspond, for example to material properties or initial and boundary conditions. We develop an adaptive algorithm based on a POD-Greedy strategy, and we develop an hyper-reduction strategy based on an element-wise empirical quadrature in order to speed up the assembly costs of the reduced-order model by building an appropriate reduced mesh. We introduce a cost-efficient error indicator which relies on the reconstruction of the stress field by a Gappy-POD strategy. We present numerical results for a three-dimensional elastoplastic system in order to illustrate and validate the methodology

Projection-based model order reduction for prestressed concrete with an application to the standard section of a nuclear containment building

We propose a projection-based model order reduction procedure for the ageing of large prestressed concrete structures. Our work is motivated by applications in the nuclear industry, particularly in the simulation of containment buildings. Such numerical simulations involve a multi-modeling approach: a three-dimensional nonlinear thermo-hydro-visco-elastic rheological model is used for concrete; and prestressing cables are described by a one-dimensional linear thermo-elastic behavior. A kinematic linkage is performed in order to connect the concrete nodes and the steel nodes: coincident points in each material are assumed to have the same displacement. We develop an adaptive algorithm based on a Proper Orthogonal Decomposition (POD) in time and greedy in parameter to build a reduced order model (ROM). The nonlinearity of the operator entails that the computational cost of the ROM assembly scales with the size of the high-fidelity model. We develop an hyper-reduction strategy based on empirical quadrature to bypass this computational bottleneck: our approach relies on the construction of a reduced mesh to speed up online assembly costs of the ROM. We provide numerical results for a standard section of a double-walled containment building using a qualified and broadly-used industrial grade finite element solver for structural mechanics (code$\_$aster)