| Reference : A model order reduction approach to construct efficient and reliable virtual charts i... |
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| Engineering, computing & technology : Multidisciplinary, general & others | |||
| Computational Sciences | |||
| http://hdl.handle.net/10993/15807 | |||
| A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation | |
| English | |
| [fr] Réduction de modèle pour la construction efficace et robuste d'abaques virtuelles pour l'homogénisation | |
| [de] Ein Modellreduktion Ansatz zur effizienten und zuverlässigen virtuellen Abaqus in Homogenisierung konstruieren | |
| Kerfriden, Pierre [] | |
| Goury, Olivier [] | |
| Khac Chi, Hoang [] | |
Bordas, Stéphane  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >] | |
| 15-Jun-2014 | |
| Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics | |
| Yes | |
| Yes | |
| International | |
| 17th U.S. National Congress on Theoretical and Applied Mechanics Michigan State University | |
| 15-20 June 2014 | |
| USACM | |
| Michigan | |
| United States of America | |
| [en] model reduction ; virtual charts ; homogenisation | |
| [en] Computational homogenisation is a widely spread technique to calculate the overall properties
of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2]. Indeed, it relies on fewer assumptions than analytical or semi-analytical homogenisation approaches and can be used to coarse-grain a large range of micro-mechanical models. However, this accuracy comes at large computational costs, which prevents computational homogenisation from being used routinely in optimisation, even in the context of linear elastic materials. Indeed, a unit cell problem has to be solved for each microscopic distribution of interest in order to obtain the corresponding homogenised material constants. In the context of nonlinear, time-dependant problem, the computational effort becomes even greater as computational homogenisation requires solving for the time-evolution of the microstructure at every point of the macroscopic domain. In this paper, we propose to address these two issues within the unified framework of projection-based model order reduction (see for instance [3, 4, 5, 6]). The smoothness of the solution of the unit cell problem with respect to parameter or time variations is used to create a reduced order model with very few degrees of freedom, hence reducing the computational burden by orders of magnitude. [1] Tarek J. Zohdi and Peter Wriggers. Introduction to Computational Micromechanics, volume 20 of lecture notes in applied and computational mechanics. Springer, 2005. [2] M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans. Multi-scale computational homogenization: Trends and challenges. J. Computational Applied Mathematics, 234(7):2175–2182, 2010. [3] D.B.P. Huynh G. Rozza and A.T. Patera. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Archives of Computational Methods in Engineering, 15(3):229–275, 2008. [4] D. Amsallem and C. Farhat. An Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity. AIAA Journal, 46(7):1803–1813, 2008. [5] P. Kerfriden, P. Gosselet, S. Adhikari, and S.P.-A. Bordas. Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 200(5- 8):850–866, 2011. [6] P. Kerfriden, J.-C. Passieux, and S.P.-A. Bordas. Local/global model order reduction strategy for the simulation of quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 89(2):154–179, 2011. [7] M. Barrault, Y. Maday, N.C. Nguyen, and A.T. Patera. An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de Math´ematiques, 339(9):667–672, 2004. | |
| Researchers ; Professionals ; Students ; Others | |
| http://hdl.handle.net/10993/15807 | |
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