Asymptotic homogenisation in linear elasticity. Part I: Mathematical formulation and finite element modelling

Computational Materials Science

Volumn 45, Issue 4, 2009, Pages 1073-1080

  Pinho da Cruz, J ^a   Oliveira, J A ^a   Teixeira Dias, F ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Asymptotic expansion homogenisation; Composite materials; Finite element method; Formal mathematics; Localisation; Periodic microstructure

Indexed keywords

ASYMPTOTIC EXPANSION HOMOGENISATION; EQUILIBRIUM STATE; FINITE ELEMENT MODELLING; FORMAL MATHEMATICS; LINEAR ELASTICITIES; LINEAR ELASTICITY PROBLEMS; LOCALISATION; MATHEMATICAL BASIS; MATHEMATICAL EQUATIONS; MATHEMATICAL FORMULATIONS; MECHANICAL BEHAVIOURS; MICRO-STRUCTURAL; PERIODIC MICROSTRUCTURE; PHYSICAL PHENOMENON; STRESS AND STRAINS; STRUCTURAL COMPONENTS;

ASYMPTOTIC ANALYSIS; COMPOSITE MATERIALS; COMPOSITE MICROMECHANICS; ELASTICITY; EQUATIONS OF STATE; MICROSTRUCTURE;

FINITE ELEMENT METHOD;

EID: 67349214608     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2009.02.025     Document Type: Article

References (18)

1. Guedes J.M., and Kikuchi N. Computer Methods in Applied Mechanics and Engineering 83 2 (1990) 143-198
2. S.D. Poisson, Second Mémoire sur la Théorie du Magnétisme, Académie Royale des Sciences de l'Institut de France 5 (1824) 488-533.
3. Maxwell J.C. A Treatise on Electricity and Magnetism (1873), Clarendon Press, Oxford, United Kingdom
4. Rayleigh J.W. Philosophical Magazine 34 (1892) 481-502
5. Spagnolo S. Annali della Scuola Normale Superiore di Pisa 22 (1968) 571-597
6. Sanchez-Palencia E. Compte-rendus de l'Académie des Sciences, série A-B 271 (1970) A1129-A1132
7. De Giorgi E., and Spagnolo S. Bollettino della Unione Matematica Italiana 8 (1973) 391-411
8. Bensoussan A., Lions J.L., and Papanicolaou G. Asymptotic Analysis for Periodic Structures (1978), North-Holland, Amesterdam, Netherlands
9. Sanchez-Palencia E. Non-homogeneous media and vibration theory. Lectures Notes in Physics vol. 127 (1980), Springer-Verlag, Berlin, Germany
10. Murat F., and Tartar L. H-Convergence. In: Cherkaev A., and Kohn R. (Eds). Topics in the Mathematical Modelling of Composite Materials, Series Progress in Nonlinear Differential Equations and their Applications vol. 31 (1997), Birkhäuser, Boston, United States of America 21-43
11. Dal Maso G. An Introduction to Γ-Convergence (1993), Birkhäuser, Boston, United States of America
12. Cioranescu D., and Donato P. An Introduction to Homogenization. Oxford Lecture Series in Mathematics and Its Applications vol. 17 (1999), Oxford University Press, Oxford, United Kingdom
13. J. Sanchez-Hubert, E. Sanchez-Palencia, Introduction aux Méthodes Asymptotiques et à l'Homogénéisation - Application à la Mécanique des Milieux Continus, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, France, 1992.
14. K. Terada, Global-Local Modeling for Composites by the Homogenization Method, Ph.D. Thesis, University of Michigan, Michigan, United States of America, 1996.
15. L. Tartar, Quelques Remarques sur l'Homogénéisation, Functional Analysis and Numerical Analysis, in: Proceedings of the Japan-France Seminar 1976, Japan Society for the Promotion of Science, 1978, pp. 469-482.
16. Nguetseng G. SIAM Journal of Mathematical Analysis 20 3 (1989) 608-629
17. P.W. Chung, Computational Methods for Multi-Scale/Multi-Physics Problems in Heterogenous/Composite Structures, Ph.D. Thesis, University of Minnesota, Minnesota, United States of America, 1999.
18. Chung P.W., Tamma K.K., and Namburu R.R. Composites Part A 32 (2001) 1291-1301