Usually the homogenization process used to determine the macroscopic mechanical fields from knowledge of the microscale geometry and the corresponding local fields is based on the development of localization (sometimes also called concentration) relations. The aim of this paper is to deal with the application of such relations in an opposite way, to deduce the local fields from the macroscopic ones, and their improvement when some basic hypotheses of the homogenization technique are no longer valid.
SuquetP.Plasticité et homogénéisation. Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris 6, 1982.
2.
KruchS.Comportement global des matériaux composites viscoélastiques. PhD Thesis, Université Pierre et Marie Curie, Paris 6, 1988.
3.
KruchS.ForestS.Computation of coarse grain structures using a homogeneous equivalent mediumJ. Phys. IV, 1998, 8, 197–205.
4.
FeyelF.Application du calcul parallèle aux modèles à grand nombre de variables internes. PhD Thesis, Ecole Nationale Supérieure des Mines de Paris, 1998.
5.
DvorakG.Transformation field analysis of inelastic composite materialsProc. R. Soc. Lond., 1992, A437, 311–327.
6.
DvorakG.Bahei-El-DinY.WafaA.Implementation of the transformation field analysis for inelastic composite materialsComputational Mechanics, 1994, 14, 201–228.
7.
ChabocheJ. L.KruchS.MaireJ. F.PottierT.Towards a micromechanics based inelastic and damage modeling of compositesInt. J. Plasticity, 2001, 17 (4), 411–439.
KruchS.CarrereN.ChabocheJ.L.Fatigue damage analysis of unidirectional metal matrix compositesInt. J. Fatigue, 2006, 28, 1420–1425.
10.
Sanchez PalenciaE.Non-homogeneous media and vibration theory. Lecture notes in physics, Vol. 127, 1980 (Springer-Verlag, Berlin).
11.
BoutinC.Microstructural effects in elastic compositesInt. J. Solids Structs, 1996, 33 (7), 1023–1051.
12.
ChabocheJ. L.FeyelF.On the multiscale analysis of composite structures by using a FE2 technique and fibre-matrix damage mechanics. In Workshop on Continuous Damage and Fracture, Cachan, France, 2000.
13.
DumontetH.Homogénéisation et effets de bords dans les matériaux composites. Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris 6, 1990.
14.
BuannicN.CartraudP.Higher-order effective modeling of periodic heterogeneous beams. II. Derivation of the proper boundary conditions for the interior asymptotic solutionInt. J. Solids Structs, 2001, 38, 7163–7180.
15.
ForestS.Homogenization methods and the mechanics of generalized continua - Part 2Theoret. Appl. Mechanics, 2002, 28–29, 113–143.
16.
KouznetsovaV.Computational homogenization for the multi-scale analysis of multi-phase materials. PhD Thesis, Technische Universiteit Eindhoven, 2002.
