Periodic unfolding and homogenization. (English. Abridged French version) Zbl 1001.49016

Summary: A novel approach to periodic homogenization is proposed, based on an unfolding method, which leads to a fixed domain problem (without singularly oscillating coefficients). This method is elementary in nature and applies to cases of periodic multi-scale problems in domains with or without holes (including truss-like structures).


49J45 Methods involving semicontinuity and convergence; relaxation
74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
Full Text: DOI


[1] Allaire, G., Homogenization and two-scale convergence, SIAM J. math. anal., 23, 1482-1518, (1992) · Zbl 0770.35005
[2] Allaire, G.; Briane, M., Multiscale convergence and reiterated homogenization, Proc. roy. soc. Edinburgh sect. A, 126, 297-342, (1996) · Zbl 0866.35017
[3] Arbogast, T.; Douglas, J.; Hornung, U., Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. math. anal., 21, 823-836, (1990) · Zbl 0698.76106
[4] Casado-Díaz, J., Two-scale convergence for nonlinear Dirichlet problems in perforated domains, Proc. roy. soc. Edinburgh, sect. A, 130, 249-276, (2000) · Zbl 0977.35019
[5] Casado-Díaz, J.; Luna-Laynez, M.; Martı́n, J.D., An adaptation of the multi-scale methods for the analysis of bery thin reticulated structures, C. R. acad. sci. Paris, Série I, 332, 223-228, (2001) · Zbl 0984.35017
[6] J. Casado-Dı́az, M. Luna-Laynez, J.D. Martı́n, Homogenization of nonhomogeneous monotone operators in thin reticulated structures: a multi-scale method, to appear
[7] Cioranescu, D.; Donato, P., An introduction to homogenization, Oxford lecture series in math. appl., 17, (1999), Oxford University Press
[8] A. Ene, J. Saint Jean Paulin, On a model of fractured porous media, Publication Dép. Math. Université de Metz 2 (1996)
[9] Defranceschi, A.; Dal Maso, G., Correctors for the homogenization of monotone operators, Differential integral equations, 3, 6, 1151-1166, (1990) · Zbl 0733.35005
[10] G. Griso, Analyse asymptotique de structures réticulées. Thèse Université Pierre et Marie Curie (Paris VI), 1996
[11] Griso, G., Thin reticulated structures, (), 161-182 · Zbl 0845.35009
[12] Nguetseng, G., A general convergence result for a functional related to the theory of homogenization, SIAM J. math. anal., 20, 608-629, (1989) · Zbl 0688.35007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.