Reference : A model order reduction approach to construct efficient and reliable virtual charts i...
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation
[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 mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics
17th U.S. National Congress on Theoretical and Applied Mechanics Michigan State University
15-20 June 2014
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
FP7 ; 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery

File(s) associated to this reference

Fulltext file(s):

Open access
Proceedings.pdfPublisher postprint2.11 MBView/Open

Additional material(s):

File Commentary Size Access
Open access
US.pdf8.97 MBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.