Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

International Journal of Solids and Structures

Volumn 44, Issue 11-12, 2007, Pages 3738-3755

  Yu, Wenbin ^a   Tang, Tian ^a  

^a Utah State University   (United States)

Author keywords

Anisotropic; Heterogeneous; Homogenization; Unit cell; VAMUCH; Variational asymptotic method

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; HOMOGENIZATION METHOD; MATHEMATICAL MODELS; NUMERICAL METHODS; PARAMETER ESTIMATION;

HETEROGENEOUS MATERIALS; UNIT CELLS; VAMUCH; VARIATIONAL ASYMPTOTIC METHOD;

MICROMECHANICS;

EID: 33947610195     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.10.020     Document Type: Article

References (34)

1. Aboudi J. A continuum theory for fiber-reinforced elastic-visoplastic composites. International Journal of Engineering Science 20 5 (1982) 605-621
2. Aboudi J. Micromechanical analysis of composites by the method of cells. Applied Mechanics Reviews 42 7 (1989) 193-221
3. Aboudi J., Pindera M.J., and Arnold S.M. Linear thermoelastic higher-order theory for periodic multiphase materials. Journal of Applied Mechanics 68 (2001) 697-707
4. Accorsi M.L., and Nemat-Nasser S. Bounds on the overall elastic and instantaneous elastoplastic moduli of periodic composites. Mechanics of Materials 5 3 (1986) 209-220
5. Banerjee B., and Adams D.O. On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method. International Journal of Solids and Structures 41 2 (2004) 481-509
6. Banks-Sills L., Leiderman V., and Fang D. On the effect of particle shape and orientation on elastic properties of metal matrix composites. Composites Part B: Engineering 28B (1997) 465-481
7. Bensoussan A., Lions J., and Papanicolaou G. Asymptotic Analysis for Periodic Structures (1978), North-Holland, Amsterdam
8. Berdichevsky V.L. On averaging of periodic systems. PMM 41 6 (1977) 993-1006
9. Berdichevsky V.L. Variational-asymptotic method of constructing a theory of shells. PMM 43 4 (1979) 664-687
10. Christensen R.M. Mechanics of Composite Materials (1979), Wiley-Interscience, New York
11. Dvorak G.J., and Bahei-El-Din Y.A. Elastic-plastic behavior of fibrous composites. Journal of Mechanics and Physics of Solids 27 (1979) 51-72
12. Guedes J.M., and Kikuchi N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element method. Computer Methods in Applied Mechanics and Engineering 83 (1990) 143-198
13. Hashin Z. Analysis of composite materials-a survey. Applied Mechanics Review 50 (1983) 481-505
14. Hashin Z., and Shtrikman S. A variational approach to the theory of the elastic behaviour of polycrystals. Journal of Mechanics and Physics of Solids 10 (1962) 343-352
15. Hill R. The elastic behavior of crystalline aggregate. Proceedings of the Physical Society of London A65 (1952) 349-354
16. Hill R. Theory of mechanical properties of fibre-strengthened materials-iii. Self-consistent model. Journal of Mechanics and Physics of Solids 13 (1965) 189-198
17. Hollister S.J., and Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Computational Mechanics (1992)
18. Kunin I. Theory of Elastic Media with Microstructure Vol. 1 and 2 (1982), Springer Verlag, Berlin
19. Manevitch L.I., Andrianov I.V., and Oshmyan V.G. Mechanics of Periodically Heterogeneous Structures (2002), Springer, Berlin
20. Milton G.W. Bounds on the electromagnetic, elastic and other properties of two component composites. Physics Review Letters 46 8 (1981) 542-545
21. Murakami H., and Toledano A. A higher-order mixture homogenization of bi-laminated composites. Journal of Applied Mechanics 57 (1990) 388-396
22. Paley M., and Aboudi J. Micromechanical analysis of composites by the generalized cells model. Mechanics of Materials 14 (1992) 127-139
23. Postma G.W. Wave propagation in a stratified medium. Geophysics 20 (1955) 780
24. Sun C.T., and Vaidya R.S. Prediction of composite properties from a representative volume element. Composites Science and Technology 56 (1996) 171-179
25. Walker K.P., Freed A.D., and Jordan E.H. Accuracy of the generalized self-consistent method in modeling the elastic behavior of periodic composite properties of unidirectional fiber-reinforced composites and their sensitivity coefficients. Philosophical Transactions of the Royal Society of London A345 (1993) 545-576
26. Williams T.O. A three-dimensional, higher-order, elasticity-based micromechanics model. International Journal of Solids and Structures 42 (2005) 971-1007
27. Williams T.O. A two-dimensional, higher-order, elasticity-based micromechanics model. International Journal of Solids and Structures 42 (2005) 1009-1038
28. Yu W. A variational-asymptotic cell method for periodically heterogeneous materials. Proceedings of the 2005 ASME International Mechanical Engineering Congress and Exposition (2005), ASME, Orlando, Florida
29. Yu W., and Hodges D.H. An asymptotic approach for thermoelastic analysis of laminated composite plates. Journal of Engineering Mechanics 130 5 (2004) 531-540
30. Yu W., and Hodges D.H. A simple thermopiezoelastic model for composite plates with accurate stress recovery. Smart Materials and Structures 13 4 (2004) 926-938
31. Yu W., and Hodges D.H. Mathematical construction of an engineering thermopiezoelastic model for smart composite shells. Smart Materials and Structures 14 1 (2005) 43-55
32. Yu W., Hodges D.H., and Volovoi V.V. Asymptotic construction of Reissner-like models for composite plates with accurate strain recovery. International Journal of Solids and Structures 39 20 (2002) 5185-5203
33. Yu W., Hodges D.H., and Volovoi V.V. Asymptotic generalization of Reissner-Mindlin theory: accurate three-dimensional recovery for composite shells. Computer Methods in Applied Mechanics and Engineering 191 44 (2002) 5087-5109
34. Yu W., Hodges D.H., Volovoi V.V., and Cesnik C.E.S. On Timoshenko-like modeling of initially curved and twisted composite beams. International Journal of Solids and Structures 39 19 (2002) 5101-5121