First online: 07 October 2010 ... Fiber-reinforced Epoxy Composite Cyclic Loading. Computational Homogenization Macro-scale Stress. Tangent Stiffness Tensor Dual Solution ... Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential ... Commun Math Sci 8(3):671â695.
Original Paper Archives of Computational Methods in Engineering December 2010, Volume 17, Issue 4, pp 373-391 First online: 07 October 2010
Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions H. Lamari , A. Ammar , P. Cartraud , G. Legrain , F. Chinesta , F. Jacquemin
Abstract Computational homogenization is nowadays one of the most active research topics in computational mechanics. Different strategies have been proposed, the main challenge being the computing cost induced by complex microstructures exhibiting nonlinear behaviors. Two quite tricky scenarios lie in (i) the necessity of applying the homogenization procedure for many microstructures (e.g. material microstructure evolving at the macroscopic level or stochastic microstructure); the second situation concerns the homogenization of nonlinear behaviors implying the necessity of solving microscopic problems for each macroscopic state (history independent nonlinear models) or for each macroscopic history (history dependant nonlinear models). In this paper we present some preliminary results concerning the application of Proper Generalized Decompositions—PGD—for addressing the efficient solution of homogenization problems. This numerical technique could allow to compute the homogenized properties for any microstructure or for any macroscopic loading history by solving a single but highly multidimensional model. The PGD allows circumventing the so called curse of dimensionality that mesh based representations suffer. Even if this work only describes the first steps in a very ambitious objective, many original ideas are launched that could be at the origin of impressive progresses.
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About this Article Title Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions Journal Archives of Computational Methods in Engineering Volume 17, Issue 4 , pp 373-391 Cover Date 2010-12 DOI 10.1007/s11831-010-9051-4 Print ISSN 1134-3060 Online ISSN 1886-1784 Publisher Springer Netherlands Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Appl.Mathematics/Computational Methods of Engineering Industry Sectors Aerospace Automotive Engineering Authors H. Lamari (1) A. Ammar (2) P. Cartraud (1)
G. Legrain (1) F. Chinesta (3) F. Jacquemin (4) Author Affiliations 1. GeM, UMR CNRS-Centrale de Nantes-Université de Nantes, 1 rue de la Noe, BP 92101, 44321, Nantes cedex 3, France 2. Arts et Métiers ParisTech, 2 boulevard du Ronceray, BP 93525, 49035, Angers cedex 01, France 3. EADS Corporate Foundation International Chair, GeM, UMR CNRS-Centrale de Nantes-Université de Nantes, 1 rue de la Noe, BP 92101, 44321, Nantes cedex 3, France 4. GeM, UMR CNRS-Centrale de Nantes-Université de Nantes, 58, rue Michel Ange, BP 420, 44606, Saint Nazaire cedex, France
