International audienceThis paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modeling elastoplastic materials in transient dynamics. At each time step, the refinement is automatic and starts with the calculation of the solution on a coarse mesh. Then, an error indicator is used to control the accuracy of the solution and a finer localized mesh is created where the user prescribed accuracy is not reached. A new calculation is performed on this new mesh using the non linear ``Full Approximation Scheme'' (FAS) multigrid strategy. Applying the error indicator and the refinement strategy recursively, the optimal mesh is obtained. This mesh verifies the error indicator on the whole structure. The multigrid strategy is used for two purposes. First, it optimizes the computational cost of the solution on the finest localized mesh. Second, it ensures information transfer amongst the different hierarchical meshes. A standard time integration scheme is used and the mesh is reassessed at each time step

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This contribution proposes to model thixoforming processes using the eXtended Finite Element Method (X-FEM). The X-FEM is very suitable for modeling forming processes with complex tool geometries as the mesh does not need to conform with the boundary of the structure. Even if the use of the X-FEM helps to describe the boundary position, the mesh still deforms when the structure is stressed. To avoid mesh distortions that appear in large deformation analysis, an Arbitrary Lagrangian Eulerian formulation is used (ALE) [3].

This paper presents an adaptive strategy dedicated to non-linear transient dynamic problems. The spatial mesh is optimized to ensure the accuracy of the solution. Beginning from a coarse mesh, an error indicator is used to estimate the discretization error and new elements are created where the prescribed accuracy is not reached. A localized multigrid solver is used and the strategy is applied recursively until the local mesh size ensures that the discretization error is less than the prescribed accuracy. The spatial mesh is recreated at each time step.