Title : Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error Language : English Author, co-author : Kerfriden, P. [School of Engineering Cardiff University The Parade, CF243AA Cardiff UK] Ródenas, J. J. [Centro de Investigacíon de Tecnología de Vehículos (CITV) Universitat Poliècnica de València E-46022-Valencia Spain] Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >] Publication date : 2013 Journal title : International Journal for Numerical Methods in Engineering Peer reviewed : Yes (verified by ORBilu ) Audience : International ISSN : 00295981 Keywords : [en] Computational homogenisation ; Constitutive relation error ; Error estimation ; Model order reduction ; Proper orthogonal decompositionAbstract : [en] SUMMARY: In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model. © 2013 John Wiley & Sons, Ltd.Funders : ERC Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/10040 DOI : 10.1002/nme.4588 Framework Programme / European Project : FP7 ; 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery 
[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
