Paper published in a book (Scientific congresses, symposiums and conference proceedings)
Advances in error estimation for homogenisation
Alves Paladim, Daniel; Kerfriden, Pierre; Moitinho de Almeida, José Paulo et al.
2015In 13th U.S. National Congress on Computational Mechanics
 

Files


Full Text
Presentation-expanded.pdf
Publisher postprint (604.7 kB)
Download
Annexes
Presentation.odp
(409.51 kB)
Request a copy

All documents in ORBilu are protected by a user license.

Send to



Details



Keywords :
micromechanics; error estimation; homogenisation
Abstract :
[en] In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this obstacle by representing them as a random a field. Under this framework, it is possible to quantify the accuracy of the surrogate model (the homogenised model) in terms of first moments of the energy norm and quantities of interest. This work builds on the seminal work of [1]. The methodology here presented rely on the Constitutive Relation Error (CRE) which states that a certain measures of the primal and dual surrogate model upper bound the exact error. The surrogate model, in agreement with homogenisation, is deterministic. This property exploited to obtain bounds whose computation is also deterministic. It is also shown that minimising the CRE in the set of homogenisation schemes leads us to an optimal surrogate that is closely related to the classical Voigt and Reuss models. Numerical examples demonstrate that the bounds are easy and affordable to compute, and useful as long as the mismatch between he diffusion coefficients of the microstructure remain small. In the case of high mismatch, extensions are proposed, through the introduction of stochastic surrogate models.. [1]Romkes, Albert, J. Tinsley Oden, and Kumar Vemaganti."Multi-scale goal-oriented adaptive modeling of random heterogeneous materials." Mechanics of materials 38.8(2006): 859-872.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Alves Paladim, Daniel;  Cardiff University
Kerfriden, Pierre;  Cardiff University
Moitinho de Almeida, José Paulo;  Universidade de Lisboa
Chevreuil, Mathilde;  Université de Nantes > GeM
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
yes
Language :
English
Title :
Advances in error estimation for homogenisation
Publication date :
July 2015
Event name :
13th U.S. National Congress on Computational Mechanics
Event place :
San Diego, United States - California
Event date :
from 27-07-2015 to 30-07-2015
Main work title :
13th U.S. National Congress on Computational Mechanics
Focus Area :
Computational Sciences
European Projects :
FP7 - 289361 - INSIST - Integrating Numerical Simulation and Geometric Design Technology
Funders :
CE - Commission Européenne [BE]
Available on ORBilu :
since 26 November 2015

Statistics


Number of views
120 (5 by Unilu)
Number of downloads
90 (2 by Unilu)

Bibliography


Similar publications



Contact ORBilu