A micromechanical approach of nonlocal modeling for media with periodic microstructures

Mechanics Research Communications

Volumn 35, Issue 1-2, 2008, Pages 126-133

  Yuan, Xi ^a   Tomita, Yoshihiro ^b   Andou, Tomoaki ^a  

^a Astom R and D   (Japan)

^b KOBE UNIVERSITY   (Japan)

Author keywords

Homogenization; Micromechanics; Nonlocal modeling

Indexed keywords

BOUNDARY VALUE PROBLEMS; NUMERICAL METHODS; PERIODIC STRUCTURES; PROBLEM SOLVING;

MACROSCOPIC BEHAVIORS; NONLOCAL MODELING; PERIODIC MICROSTRUCTURE;

MICROMECHANICS;

EID: 37349030205     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechrescom.2007.07.004     Document Type: Article

References (23)

1. Aifantis E.C. On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. 106 (1984) 326-330
2. Bakhvalov N., and Panasenko G. Homogenization: Averaging Processes in Periodic Media (1989), Kluwer Academic Publishers, The Netherland
3. Berglund K. Structural models of micropolar media, Mechanics of Micropolar media. In: Brulin, and Hsieh R.K.T. (Eds). Cism Lecture Notes (1982), World Scientific, Singapore pp. 35-86
4. Bigoni D., and Drugan W.J. Analytic derivation of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech. 74 (2007) 741-753
5. Boutin C. Microstructural effects in elastic composites. Int. J. Solid Struct. 33 (1996) 1023-1051
6. Bouyge F., Jasiuk I., and Ostoja-Starzewski M. A micromechanically based couple-stress model of an elastic two-phase composite. Int. J. Solid Struct. 38 (2001) 1721-1735
7. Cosserat E., and Cosserat F. Theorie des corps deformables (1909), Hermann, Paris
8. Eringen A.C. Theory of Micropolar Elasticity. In: Liebowitz H. (Ed). Frature 2 (1968), Academic Press, New York pp. 662-729
9. Eringen A.C. Nonlocal continuum mechanics based on distributions. Int. J. Eng. Sci. 44 (2006) 141-147
10. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiments. Acta Metall. Mater. 42 (1994) 475
11. Forest S. Mechanics of generalized continua: construction by homogenization. J. Phys. IV (1998) 39-48
12. Forest S., and Sab K. Cosserat overall modeling of heterogeneous materials. Mech. Res. Commun. 25 (1998) 449-454
13. Gambin B., and Kröner E. Higher-order terms in the homogenized stress-strain relation of periodic elastic media. Phys. Stat. Sol. 151b (1989) 513-519
14. Gray W.G., and Lee P.C.Y. On the theorems for local volume averaging of multiphase systems. Int. J. Multiphase Flow 3 (1977) 333-340
15. Koiter W.T. Couple-stress in the theory of elasticity. Koninkliike Nederlandse Akademie van Wetenschappen B-29 (1964) 17-44
16. Kouznetsova V., Geers M.G.D., and Brekelmans W.A.M. Multi-scale constitutive modeling of heterogeneous materials with gradient-enhanced computational homogenization scheme. Int. J. Num. Meth. Eng. 54 (2002) 1235-1260
17. Mindlin R.D. Microstructure in linear elasticity. Arch. Ration. Mech. Anal. 16 (1965) 51-78
18. Slattery J.C. Momentum, Energy, and Mass Transfer in Continua (1972), McGraw-Hill
19. Smyshlyaev V.P., and Cherednichenko K.D. On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media. J. Mech. Phys. Solid 48 (2000) 1325-1357
20. Suquet P.M. Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia E., and Zaoui A. (Eds). Homogenization Techniques for Composite Media (1986), Springer-Verlag
21. Toupin R.A. Elastic materials with couple stress. Arch. Ration. Mech. Anal. 11 (1962) 385-414
22. Van der Sluis O., Vosbeck P.H.J., Schreurs P.J.G., and Meijer H.E.H. Homogenization of heterogeneous polymers. Int. J. Solid Struct. 36 (1999) 3193-3214
23. Yuan X., and Tomita Y. A nonlocal model of materials with microstructure base on asymptotic homogenization method. Mater. Sci. Res. Int. 7 (2001) 82-89