Reference : Certification of projection-based reduced order modelling in computational homogenisa...
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
Certification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error
Kerfriden, Pierre [Cardiff University > Institute of Mechanics and Advanced Materials > > Lecturer]
Ródenas, Juan-José []
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
International Journal for Numerical Methods in Engineering
Yes (verified by ORBilu)
United Kingdom
[en] model order reduction ; error estimation ; homogenisation
[en] 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.
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