Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems

International Journal of Solids and Structures

Volumn 42, Issue 13, 2005, Pages 3833-3851

  Zhang, X ^a   Sharma, P ^a  

^a UNIVERSITY OF HOUSTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPOSITE MATERIALS; CONTINUUM MECHANICS; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; GRANULAR MATERIALS; LIQUID CRYSTALS; STRAIN; STRESS ANALYSIS; TENSORS;

COUPLE STRESSES; EIGENSTRAINS; NANO-INCLUSIONS; NON-LINEAR HOMOGENIZATION;

INCLUSIONS;

EID: 13544263609     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.12.005     Document Type: Article

References (48)

1. E.C. Aifantis Update on a class of gradient theories Mechanics of Materials 35 2003 259 280
2. Bilby, B.A., Miller, K.J., Willis, J.R., 1984. IUTAM/IFC/ICM Symposium on Fundamentals of Deformation and Fracture (Sheffield, England, 2-5 April 1984, Eshelby Memorial Symposium), Cambridge University Press, Cambridge
3. R.C. Cammarata Surface and interface stress effects in thin films Progress in Surface Science 46 1 1994 1 38
4. Y. Chen, J.D. Lee, and A. Eskandarian Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation International Journal of Engineering Science 41 1 2003 61 83
5. Y. Chen, J.D. Lee, and A. Eskandarian Atomistic viewpoint of the applicability of microcontinuum theories International Journal of Solids and Structures 41 2004 2085
6. Z.Q. Cheng, and L.H. He Micropolar elastic fields due to a spherical inclusion International Journal of Engineering Science 33 3 1995 389 397
7. Z.Q. Cheng, and L.H. He Micropolar elastic fields due to a circular cylindrical inclusion International Journal of Engineering Science 35 7 1997 659 668
8. W.J. Drugan micromechanics-based variational estimates for a higher-order nonlocal constitutive equation and optimal choice of effective moduli for elastic composites Journal of the Mechanics and Physics of Solids 48 2000 1359
9. A.C. Eringen Microcontinuum Field Theories. I: Foundations and Solids 1999 Springer-Verlag New York
10. C. Eringen Nonlocal Continuum Field Theories 2002 Springer-Verlag New York
11. C. Eringen, and D.G.B. Edelen International Journal of Engineering Science 10 3 1972 233
12. J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion and related problems Proceedings of the Royal Society of London A A241 1957 376 396
13. J.D. Eshelby The elastic field outside an ellipsoidal inclusion Proceedings of the Royal Society of London A A252 1959 561 569
14. N.A. Fleck, and J.W. Hutchinson A reformulation of strain gradient plasticity Journal of the Mechanics and Physics of Solids 49 10 2001 2245 2271
15. G.W. Gibbons, and B.F. Whiting Newtonian gravity measurements impose constraints on unification theories Nature 291 1981 636
16. M.Y. Gutkin Nanoscopics of dislocation and disclinations in gradient elasticity Reviews on Advanced Material Science 1 2000 27 60
17. M.Y. Gutkin, and E.C. Aifantis Screw dislocation in gradient elasticity Scripta Materialia 35 1996 1353
18. O.D. Kellogg Foundation of Potential Theory 1953 Dover New York
19. H. Kleinert Gauge Fields in Condensed Matter vol. 2 1989 World Scientific 9971-50-210-0
20. W.T. Koiter Couple stresses in the theory of elasticity. I and II Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen (B) 67 1964 17 44
21. J.A. Krumhansl Mechanics of generalized continua E. Kroner 1968 Springer Verlag Berlin 298
22. I. Kunin Quantum mechanical formalism in classical wave propagation problems International Journal of Engineering Science 20 2 1982
23. I. Kunin On foundations of the theory of elastic media with microstructure International Journal of Engineering Science 22 8-10 1983
24. K. Markov, and L. Preziosi Heterogeneous media: micromechanics modeling methods and simulations 2000 Birkhauser Verlag Switzerland
25. K. Markov On the inhomogeneity problem in micropolar elasticity Theoretical and Applied Mechanics 3 1979 52 59
26. R.E. Miller, and V.B. Shenoy Size-dependent elastic properties of nanosized structural elements Nanotechnology 11 3 2000 139 147
27. G.W. Milton Theory of Composites 2001 Cambridge University Press
28. R.D. Mindlin Micro-structure in linear elasticity Archive for Rational Mechanics and Analysis 16 1964 51 78
29. R.D. Mindlin Second gradient of strain and surface-tension in linear elasticity International Journal of Solids and Structures 1 1965 417 438
30. R.D. Mindlin, and H.F. Tiersten Effects of couple-stresses in linear elasticity Archive for Rational Mechanics and Analysis 11 1962 615
31. T. Mura Micromechanics of Defects in Solids 1987 Martinus Nijhoff Hague, Netherlands
32. T. Mura, H.M. Shodja, and Y. Hirose Inclusion problems Applied Mechanics Review 49 10 1996 S118 S127 part 2
33. S. Nemat-Nasser, and M. Hori Micromechanics: Overall Properties of Heterogeneous Solids 1999 Elsevier Science Publishers
34. H. Nozaki, and M. Taya Elastic fields in a polyhedral inclusion with uniform eigenstrains and related problems Journal of Applied Mechanics 68 2001 441
35. P. Ponte Castañeda Journal of the Mechanics and Physics of Solids 40 1992 1757
36. A.C.E. Reid, and R.J. Gooding Inclusion problem in a two-dimensional nonlocal elastic solid Physical Review B 46 1992 6045
37. C.Q. Ru, and E.C. Aifantis A simple approach to solve boundary-value problems in gradient elasticity Acta Mechanica 101 1993 59 68
38. P. Sharma, and A. Dasgupta Scale-dependent average elastic fields of spherical and cylindrical inhomogeneities in micropolar medium and overall properties Physical Review B 66 2002 2241XX
39. P. Sharma, and S. Ganti Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies Journal of Applied Mechanics 71 2004 663
40. Sharma, P., Ganti, S., in press. Elastic gauge-fields of screw dislocations in dispersive (nonlocal) crystalline solids: length scale interactions. Proceedings of the Royal Society of London A
41. P. Sharma, S. Ganti, and N. Bhate Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities Applied Physics Letters 82 4 2003 535 537
42. Sharma, P., Wheeler, L., submitted for publication
43. Y. Shibutani, V. Vitek, and J.L. Bassani Nonlocal properties of inhomogeneous structures by linking approach of generalized continuum to atomistic model International Journal of Mechanical Sciences 40 2-3 1998 129 137
44. S. Torquato Random Heterogeneous Materials: Microstructure and Macroscopic Properties 2001 Springer-Verlag New York
45. R.A. Toupin Elastic materials with couple stresses Archive for Rational Mechanics and Analysis 11 1962 385
46. R. Wang Acta Mechanica 85 3-4 1990 131
47. G.J. Weng M. Taya H. Abe Micromechanics and Inhomogeneity: The Toshio Mura Anniversary Volume 1990 Springer-Verlag
48. F. Yang, A.C.M. Chong, D.C.C. Lam, and P. Tong Couple stress based strain gradient theory for elasticity International Journal of Solids and Structures 39 10 2002 2731 2743