Application of P.O.D. and D.E.P.O.D. model reduction methods to semi-thick sheet metal forming
Résumé
Model reduction allows transforming a high-dimensional model into a very low-dimensional approximation, which makes it possible to significantly decrease the computational time while preserving the physics of the problem. In this paper, it is applied to a metal forming process, the semi-thick sheet bulging test, where computing time can be quite significant when using the associated inverse analysis. The problem is characterized by large deformations, development of instability, implicit velocity / pressure formulation and unstructured meshes of tetrahedrons. A Proper Orthogonal Decomposition (POD) is implemented in the commercial software Forge®. The proposed reduced order model (ROM) involves a reduced basis for both velocity and pressure fields to account for the incompressibility constraint. The ROM by POD allows reducing the number of unknowns to less than 12 while keeping the results accuracy and precisely predicting the sheet instability development. The ROM remains accurate for a wide range of material parameters variations. The DEPOD approach allows further extending the ROM validity range, through the information of additional snapshots in the vicinity of the initial ones
Domaines
Matériaux
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