MATEC Web Conf.
Volume 318, 20207th International Conference of Materials and Manufacturing Engineering (ICMMEN 2020)
|Number of page(s)||6|
|Published online||14 August 2020|
A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM
Université Paris-Saclay, ENS Paris-Saclay, CNRS, LMT Laboratoire de Mécanique et Technologie, 94235, Cachan, France.
2 Mechanical Engineering Department, Laboratory of Manufacturing Technology & Machine Tools, International Hellenic University, GR-62124 Serres Campus, Greece.
Parametric simulations of thermomechanical metal forming processes still remain computational costly and difficult due to inherent strong non-linearities. To this end, Reduced Order Models (ROMs) are introduced to decrease the computational time in large scale models and provide near-optimal solutions in acceptable times. ROMs based on the Proper Orthogonal Decomposition (POD) are usually capable of accurately reproducing the dynamics of high-fidelity FEM simulations and offer the potential for near real-time analysis. However, ROMs are not robust with respect to parameter changes and must often be rebuilt for each parameter variation. This work aims to interpolate ROM POD basis associated with a limited number of training points on Grassmann manifolds, so as to obtain a robust ROM corresponding to a target parameter. A novel Space-Time (ST) POD basis interpolation, where the reduced spatial and time basis are separately interpolated on Grassmann manifolds, is proposed. Good correlations of the ROM ST models with respect to their associated high-fidelity FEM counterpart simulations are found. Hence, application of the ROM adaptation method for near real-time metal forming simulations using off-line computed ROM POD databases can be possible.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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