On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media

Journal of the Mechanics and Physics of Solids

Volumn 48, Issue 6, 2000, Pages 1325-1357

  Smyshlyaev, V P ^a   Cherednichenko, K D ^a  

^a University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; ELASTICITY; VARIATIONAL TECHNIQUES;

HOMOGENIZED EQUATIONS; PERIODICITY CELL; STRAIN GRADIENT THEORIES;

STRAIN RATE;

EID: 0033902368     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(99)00090-3     Document Type: Article

References (22)

1. Aifantis E.C. On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol. 106:1984;326-330.
2. Bakhvalov, N.S., Panasenko, G.P., 1984. Homogenization: Averaging Processes in Periodic Media. Nauka, Moscow (in Russian). English translation in: Mathematics and its Applications (Soviet Series) 36, Kluwer Academic Publishers, Dordrecht-Boston-London.
3. Bensoussan A., Lions J.-L., Papanicolaou G.C. Asymptotic Analysis for Periodic Structures. 1978;North-Holland, Amsterdam.
4. Boutin C. Microstructural effects in elastic composites. Int. J. Solids and Structures. 33:1996;1023-1051.
5. Cherednichenko, K.D., Smyshlyaev, V.P. 1999. On full asymptotic expansion of the solutions of non-linear periodic rapidly oscillating problems. Isaac Newton Institute for Mathematical Sciences. Preprint NI99028-SMM.
6. Cosserat E., Cosserat F. Theorie des corps deformables. 1909;Hermanns, Paris.
7. Drugan W.J., Willis J.R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids. 44:1996;497-524.
8. Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42:1994;475.
9. Fleck N.A., Hutchinson J.W. Strain gradient plasticity. Hutchinson J.W., Wu T.Y. Advances in Applied Mechanics. vol. 33:1997;295-361 Academic Press, New York.
10. Jikov V.V., Kozlov S.M., Oleinik O.A. Homogenization of Differential Operators and Integral Functionals. 1994;Springer-Verlag, Berlin, Heidelberg.
11. Luciano, R., Willis, J.R., 2000a. Bounds on non-local effective relations for random composites loaded by configuration-dependent body force. J. Mech. Phys. Solids, to appear.
12. Luciano, R., Willis, J.R., 2000b. Micromechanical non-local constitutive relations for heterogeneous materials, in preparation.
13. Mindlin R.D. Microstructure in linear elasticity. Arch. Ration. Mech. Anal. 16:1965;51-78.
14. Sanchez-Palencia, E., 1980. Nonhomogeneous media and vibration theory. Lecture Notes in Physics 127.
15. Shu J.Y., Fleck N.A. The prediction of size effect in micro-indentation. Int. J. Solids Structures. 35:1998;1363-1383.
16. Smyshlyaev V.P., Fleck N.A. Bounds and estimates for linear composites with strain gradient effects. J. Mech. Phys. Solids. 42:1994;1851-1882.
17. Smyshlyaev V.P., Fleck N.A. Bounds and estimates for the overall plastic behaviour of composites with strain gradient effects. Proc. R. Soc. Lond. A. 451:1995;795-810.
18. Smyshlyaev V.P., Fleck N.A. The role of strain gradients in the grain size effect for polycrystals. J. Mech. Phys. Solids. 44:1996;465-495.
19. Toupin R.A. Elastic materials with couple stresses. Arch. Ration. Mech. Anal. 11:1962;385-414.
20. Triantafyllidis N., Bardenhagen S. The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models. J. Mech. Phys. Solids. 44:1996;1891-1928.
21. Willis J.R. Variational and related methods for the overall properties of composites. Yih C.-S. Advances in Applied Mechanics. vol. 21:1981;1-78 Academic Press, New York.
22. Willis J.R. The overall elastic response of composite materials. J. Appl. Mech. 50:1983;1202-1209.