Article (Scientific journals)
Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method
Nguyen, Van Dung; Wu, Ling; Noels, Ludovic
2017In Computational Mechanics, 59 (3), p. 483-505
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Keywords :
Computational homogenization; Multiphysics; Boundary conditions; Tangent operator; LIMARC; CECI
Abstract :
[en] This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.
Disciplines :
Mechanical engineering
Materials science & engineering
Author, co-author :
Nguyen, Van Dung  ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Wu, Ling ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Noels, Ludovic  ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method
Publication date :
March 2017
Journal title :
Computational Mechanics
ISSN :
0178-7675
eISSN :
1432-0924
Publisher :
Springer Science & Business Media B.V., New York, United States - New York
Volume :
59
Issue :
3
Pages :
483-505
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
Name of the research project :
The authors gratefully acknowledge the financial support from F.R.SF. N.R.S. under the project number PDR T.1015.14. Computational resources have been provided by the supercomputing facilities of the Consortium des Equipements de Calcul Intensif en Federation Wallonie Bruxelles (CECI) funded by the Fond de la Recherche Scientifique de Belgique (FRS-FNRS).
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
CÉCI - Consortium des Équipements de Calcul Intensif [BE]
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