Experiments and theory in strain gradient elasticity

Journal of the Mechanics and Physics of Solids

Volumn 51, Issue 8, 2003, Pages 1477-1508

  Lam, D C C ^a   Yang, F ^a,b   Chong, A C M ^a   Wang, J ^a,b   Tong, P ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b SOUTHWEST JIAOTONG UNIVERSITY   (China)

Author keywords

A. Strain gradient effects; B. Constitutive behavior; Beams; C. Mechanical testing; Elastic material

Indexed keywords

BENDING (DEFORMATION); CANTILEVER BEAMS; ELASTICITY; MECHANICAL TESTING; STRESSES;

STRAIN-GRADIENT EFFECTS;

STRAIN;

EID: 0038721068     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(03)00053-X     Document Type: Article

References (24)

1. Albrecht T.R., Akamine S., Carver T.E., Quate C.F. Microfabrication of cantilever for the atomic force microscope. J. Vacuum Sci. Technol. A-Vacuum Surf. Films. 8:1990;3386-3396.
2. Bashir R., Gupta A., Neudeck G.W., McElfresh M., Gomez R. On the design of piezoresistive silicon cantilevers with stress concentration regions for scanning probe microscopy applications. J. Micromech. Microeng. 10:2000;483-491.
3. Carr D.W., Craighead H.G. Fabrication of nanoelectromechanical systems in single crystal silicon using silicon on insulator substrates and electron beam lithography. J. Vacuum Sci. Technol. B. 15:1997;2760-2763.
4. Chong A.C.M., Lam D.C.C. Strain gradient plasticity effect in indentation hardness of polymers. J. Mater. Res. 14:1999;4103-4110.
5. Craighead H.G. Nanoelectromechanical systems. Science. 290:2000;1532-1535.
6. Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advances in Applied Mechanics, Vol. 33. Academic Press, New York, pp. 295-361.
7. Fleck N.A., Hutchinson J.W. A reformulation of strain gradient plasticity. J. Mech. Phys. Solids. 49:2001;2245-2271.
8. Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W. Strain gradient plasticity. theory and experiments Acta Metall. Mater. 42:1994;475-487.
9. Gao H.J., Huang Y., Nix W.D., Hutchinson J.W. Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids. 47:1999;1239-1263.
10. Koiter W.T. Couple stresses in the theory of elasticity. I and II. Proc. K. Ned. Akad. Wet. (B). 67:1964;17-44.
11. Lam D.C.C., Chong A.C.M. Indentation model and strain gradient plasticity law for glassy polymers. J. Mater. Res. 14:1999;3784-3788.
12. Ma Q., Clarke D.R. Size dependent hardness of silver single crystals. J. Mater. Res. 10:1995;853-863.
13. Manias E., Chen J., Fang N., Zhang X. Polymeric micromechanical components with tunable stiffness. Appl. Phys. Lett. 79:2001;1700-1702.
14. Menard K.P. Dynamic Mechanical Analysis: a Practical Introduction. 1999;CRC Press, Boca Raton, FL.
15. Mindlin R.D. Micro-structure in linear elasticity. Arch. Rational Mech. Anal. 16:1964;51-78.
16. Mindlin R.D. Second gradient of strain and surface tension in linear elasticity. Int. J. Solids Struct. 1:1965;417-438.
17. Mindlin R.D., Tiersten H.F. Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal. 11:1962;415-448.
18. Nix W.D. Mechanical properties of thin films. Metall. Trans. A. 20:1989;2217-2245.
19. O'Malley R.E. Singular Perturbation Methods for Ordinary Differential Equations. 1991;Springer, New York.
20. Poole W.J., Ashby M.F., Fleck N.A. Micro-hardness of annealed and work-hardened copper polycrystals. Scripta Metall. Mater. 34(4):1996;559-564.
21. Stelmashenko N.A., Walls M.G., Brown L.M., Milman Y.V. Microindentations on W and Mo oriented single crystals. an STM study Acta Metall. Mater. 41(2):1993;2855-2865.
22. Stölken J.S., Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Metall. Mater. 46:1998;5109-5115.
23. Toupin R.A. Elastic materials with couple stresses. Arch. Rational Mech. Anal. 11:1962;385-414.
24. Yang F., Chong A.C.M., Lam D.C.C., Tong P. Couple stress Based Strain gradient theory for elasticity. Int. J. Solids Struct. 39:2002;2731-2743.