Jérémy Lebon

Fat Latin Hypercube Sampling and Efficient Sparse Polynomial Chaos Expansion for Uncertainty Propagation on Finite Precision Models: Application to 2D Deep Drawing Process

In the context of uncertainty propagation, the variation range of random variables may be many oder of magnitude smaller than their nominal values. When evaluating the non-linear Finite Element Model (FEM), simulations involving contact/friction and material non linearity on such small perturbations of the input data, a numerical noise alters the output data and distorts the statistical quantities and potentially inhibit the training of Uncertainty Quantification (UQ) models. In this paper, a particular attention is given to the definition of adapted Design of Experiment (DoE) taking into account the model sensitivity with respect to infinitesimal numerical perturbations. The samples are chosen using an adaptation of the Latin Hypercube Sampling (Fat-LHS) and are required to be sufficiently spaced away to filter the discretization and other numerical errors limiting the number of possible numerical experiments. In order to build an acceptable Polynomial Chaos Expansion with such sparse data, we implement a hybrid LARS+Q-norm approach. We showcase the proposed approach with UQ of springback effect for deep drawing process of metal sheet, considering up to 8 random variables.

A two-pronged approach for the assessment of springback variability for sheet metal forming applications

Springback assessment for sheet metal forming processes is a challenging issue which requires to take into account complex phenomena (physical non linearities and uncertainties). We highlight that the stochastic analysis of metal forming process requires both a high precision and low cost numerical models and propose a two-pronged methodology to address these challenges. The deep drawing simulation process is performed using an original low cost semi-analytical approach based on a bending under tension model with a good accuracy for small random perturbations of the physical and process parameters. The springback variability analysis is performed using an efficient stochastic metamodel, namely a sparse version of the polynomial chaos expansion.

Multi-level modeling for sensitivity assessment of springback in sheet metal forming

In this work, we highlight that sensitivity analysis of metal forming process requires both high precision and low cost numerical models. We propose a two-pronged methodology to address these challenges. The deep drawing simulation process is performed using an original low cost semi-analytical approach based on a bending under tension model (B-U-T) with a good accuracy for small random perturbations of the physical and process parameters. The springback sensitivity analysis is based on the Sobol indices approach and performed using an non intrusive efficient methodology based on the post-treatment of the polynomial chaos coefficients.