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

SUMMARYIn 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...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2014-02, Vol.97 (6), p.395-422
Main Authors: Kerfriden, P., Ródenas, J. J., Bordas, S. P.-A.
Format: Article
Language:English
Subjects:
Computation
computational homogenisation
constitutive relation error
error estimation
Mechanics
model order reduction
Physics
proper orthogonal decomposition
Structural mechanics
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Summary:SUMMARYIn 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. Copyright © 2013 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4588