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Autre Publication Scientifique Année : 2019

Model reduction technique for nonlinear problems Application to structures under large number of cycles loads and to simulations with variability

Méthode de réduction de modèles en non-linéaire Application aux structures soumises à un grand nombre de cycles de charges et aux simulations avec variabilité

Résumé

Numerous engineering problems, despite the impressive progress of computational simulation techniques, remain intractable today. POD (Proper Orthogonal Decomposition), RB (Reduced Basis), PGD (Proper General Decomposition) [1, 2, 3] and other model reduction methods are leading to a new generation of high-performance computational tools which provide solutions to engineering problems which are inaccessible to standard codes based on classical and well-established numerical techniques. During this seminar we will present the advantages of the PGD model reduction method coupled with a dedicated solver for the treatment of nonlinear problems. A first application will concern the use of these methods combined with a two-time-multiscale approach that consists in computing the quantities of interest only at particular predefined cycles called the "nodal cycles"’ and using a suitable interpolation to estimate their evolution at the intermediate cycles [4, 5]. The proposed framework is exemplified for a structure subjected to cyclic loading, where, combined to visco-plasticity, damage is considered to be isotropic and micro-defect closure effects are taken into account. The combination of these techniques leads to a "digital twin" that allows creating virtual S-N curves for large number of cycles. The second framework that will be presented is the one of taking into account parametric variability [6, 7, 8]. The main idea is that, when considering a parametric study, the reduced model generated for some previous sets of parameters is reused and enriched if needed for a new set all along the parametric study. The basis can be viewed as a set of modes adapted to the loadings and the physics of the phenomenon and is in our cases of small size, which enables light weight calculation. The gain of the strategy for studying the influence of material variability will be exemplified on some 3D examples with large numbers of degrees of freedom. References [1] M. Barrault, Y. Maday, N.C. Nguyen, A.T. Patera. An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Mathematique, Vol 339(9), 667–672, 2004. [2] M.D. Gunzburger, J.S. Peterson, J.N. Shadid. Reduced-order modeling of time-dependent pdes with multiple parameters in the boundary data. Computer Methods in Applied Mechanics and Engineering 196(4-6), 1030–1047, 2007. [3] F. Chinesta, P. Ladevèze, E. Cueto. A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engi- neering, 18(4), 395–404, 2011. [4] D. Néron, M. Bhattacharyya, A. Fau, U. Nackenhorst, P. Ladevèze, A LATIN-based model reduction approach for the simulation of cycling damage, Computational Mechanics, 62(4), 725-743, 2017. [5] D. Néron, M. Bhattacharyya, A. Fau, U. Nackenhorst, P. Ladevèze, A multi-temporal scale model reduction approach for the computation of fatigue damage, Computer Methods in Applied Mechanics and Engineering 340, 630 - 656, 2018, [6] C. Heyberger, P.-A. Boucard, D. Néron, A rational strategy for the resolution of parametrized problems in the PGD framework. Computer Methods in Applied Mechanics and Engineering 259, 40-49. 2013 [7] D. Néron, P.-A. Boucard, N. Relun, Time-space PGD for the rapid solution of 3D nonlinear parametrized problems in the many-query context. International Journal for Numerical Methods in Engineering 103.4, 275-292, 2015 [8] M.Vitse, D.Néron, P.-A.Boucard, Dealing with a nonlinear material behavior and its variability through PGD models: Application to reinforced concrete structures, Finite Elements in Analysis and Design 153, 22-37, 2019
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hal-02132611 , version 1 (17-05-2019)

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  • HAL Id : hal-02132611 , version 1

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Pierre-Alain Boucard. Méthode de réduction de modèles en non-linéaire Application aux structures soumises à un grand nombre de cycles de charges et aux simulations avec variabilité. 2019. ⟨hal-02132611⟩
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