Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error

Kerfriden, Pierre ORCID: https://orcid.org/0000-0002-7749-3996, Ródenas, J. J. and Bordas, Stephane Pierre Alain ORCID: https://orcid.org/0000-0001-8634-7002 2014. Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error. International Journal for Numerical Methods in Engineering 97 (6) , pp. 395-422. 10.1002/nme.4588

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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 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords:	model order reduction; error estimation; computational homogenisation; proper orthogonal decomposition; constitutive relation error
Publisher:	John Wiley & Sons
ISSN:	0029-5981
Funders:	EPSRC, European Research Council (ERC), EU FP7
Date of First Compliant Deposit:	30 March 2016
Last Modified:	16 Nov 2024 21:45
URI:	https://orca.cardiff.ac.uk/id/eprint/52130

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