Surrogate POD models for building forming limit diagrams of parameterized sheet metal forming applications

Hamdaoui, M.; Le Quilliec, Guénhaël; Breitkopf, Piotr; Villon, Pierre
May 2013
AIP Conference Proceedings;May2013, Vol. 1532 Issue 1, p607
Academic Journal
The aim of this work is to present a surrogate POD (Proper Orthogonal Decomposition) approach for building forming limit diagrams at minimum cost for parameterized sheet metal formed work-pieces. First, a Latin Hypercube Sampling is performed on the design parameter space. Then, at each design site, displacement fields are computed using the popular open-source finite element software Code_Aster. Then, the method of snapshots is used for POD mode determination. POD coefficients are interpolated using kriging. Furthermore, an error analysis of the surrogate POD model is performed on a validation set. It is shown that on the considered use case the accuracy of the surrogate POD model is excellent for the representation of finite element displacement fields. The validated surrogate POD model is then used to build forming limit diagrams (FLD) for any design parameter to assess the quality of stamped metal sheets. Using the surrogate POD model, the Green-Lagrange strain tensor is derived, then major and minor principal deformations are determined at Gauss points for each mesh element. Furthermore, a signed distance between the forming limit curve in rupture and the obtained cloud of points in the plane ([variant_greek_epsilon]2, [variant_greek_epsilon]1) is computed to assess the quality of the formed workpiece. The minimization of this signed distance allows determining the safest design for the chosen use case.


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