Extended-PGD Model Reduction for Nonlinear Solid Mechanics Problems Involving Many Parameters

Pierre Ladevèze (1) , Charles Paillet (1) , David Néron (1)

1 LMT - Laboratoire de Mécanique et Technologie

Reduced models and especially those based on Proper Generalized Decomposition (PGD) are decision-making tools which are about to revolutionize many domains. Unfortunately, their calculation remains problematic for problems involving many parameters, for which one can invoke the “curse of dimensionality”. The paper starts with the state-of-the-art for nonlinear problems involving stochastic parameters. Then, an answer to the challenge of many parameters is given in solid mechanics with the so-called “parameter-multiscale PGD”, which is based on the Saint-Venant principle.

Domaines: Mécanique des structures [physics.class-ph]; Mécanique [physics.med-ph]

Pierre Ladevèze, Charles Paillet, David Néron. Extended-PGD Model Reduction for Nonlinear Solid Mechanics Problems Involving Many Parameters. Advances in Computational Plasticity, pp.201-220, 2017, ⟨10.1007/978-3-319-60885-3_10⟩. ⟨hal-01926425⟩