model order reduction; Constitutive relation error; error estimation; Computational homogenisation; homogenisation; Proper orthogonal decomposition
Abstract :
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 nite 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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Kerfriden, Pierre; Cardiff University > Institute of Mechanics and Advanced Materials > Lecturer
Ródenas, Juan-José
Bordas, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Language :
English
Title :
Certification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error
Publication date :
February 2014
Journal title :
International Journal for Numerical Methods in Engineering
ISSN :
1097-0207
Publisher :
Wiley, Chichester, United Kingdom
Volume :
97
Issue :
6
Pages :
395-422
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
European Projects :
FP7 - 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
Funders :
CER - Conseil Européen de la Recherche [BE] CE - Commission Européenne [BE]
