Variational eigenstrain multiscale finite element method

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 17-20, 2004, Pages 1803-1824

  Li, Shaofan ^a   Gupta, Anurag ^a   Liu, Xiaohu ^a   Mahyari, Morteza ^a  

^a 109 McLaughlin Hall   (United States)

Author keywords

Adaptive finite element method; Eigenstrain method; Homogenization; Multiscale simulation; Variational multiscale method

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; DISCRIMINATORS; FINITE ELEMENT METHOD; NUMERICAL ANALYSIS; THEOREM PROVING;

SUBSCALE FINITE ELEMENT METHOD; VARIATIONAL EIGENSTRAIN MULTISCALE METHOD;

COMPOSITE MICROMECHANICS;

FINITE ELEMENT METHOD; HOMOGENIZATION;

EID: 1842736765     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.042     Document Type: Article

References (18)

1. Adams R.A. Sobolev Spaces 1975 Academic Press New York, San Francisco, London
2. Brenner S.C. Scott L.R. The Mathematical Theory of Finite Element Methods 1994 Springer-Verlag New York
3. Eshelby J.D. The elastic field outside an ellipsoidal inclusion Proc. R. Soc. Lond. A 252 1957 561-569
4. Eshelby J.D. Elastic inclusions and inhomogeneities Sneddon I.N. Hill R. Progress in Solid Mechanics vol. 2 1961 89-140 North-Holland Amsterdam
5. Guedes J.M. Kikuchi N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods Comput. Methods Appl. Mech. Engrg. 83 1990 143-198
6. Hughes T.J.R. The Finite Element Method 1987 Prentice-Hall Englewood Cliffs, New Jersey
7. Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Engrg. 127 1995 387-401
8. Hughes T.J.R. Stewart J. A space-time formulation for multiscale phenomena J. Comput. Appl. Math. 74 1996 217-229
9. Hughes T.J.R. Feijoo G.R. Mazzei L. Quincy J.-B. The variational multiscale method--a paradigm for computational mechanics Comput. Methods Appl. Mech. Engrg. 166 1998 3-24
10. Krajcinovi D. Damage Mechanics 1996 Elsevier Amsterdam, New York
11. Mura T. Micromechanics of Defects in Solids 1987 Martinus Nijhoff Publishers Dordrecht
12. Renardy M. Rogers R.C. An Introduction to Partial Differential Equations 1993 Springer-Verlag New York, Berlin
13. Sanchez-Palencia E. Non-homogeneous media and vibration theory Lecture Notes in Physics vol. 127 1980 Springer-Verlag Berlin
14. Somigliana C. Sopra l'equilibrio di un corpo elastico isotropo Il Nuo. Ciem. 1886 17-19
15. Tanaka K. Mori T. Note on volume integrals of the elastic field around an ellipsoidal inclusion J. Elast. 2 1972 199-200
16. Timoshenko S.P. Goodier J.N. Theory of Elasticity third ed. 1970 McGraw-Hill New York
17. Tong P. Mei C.C. Mechanics of composite of multiple scales Comput. Mech. 9 1992 195-201
18. Willis L.J. Variational and related methods for the overall properties of composites Adv. Appl. Mech. 21 1981 1-78