The area contraction and expansion for a nano-void under four different kinds of loading

Archive of Applied Mechanics

Volumn 81, Issue 9, 2011, Pages 1323-1331

  Yi Feng, Hu ^a   Chen, Yi Heng ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Area contraction; M integral; Nano hole; Neutral loading point; Surface effect

Indexed keywords

AREA CONTRACTION; M-INTEGRAL; NANO-HOLE; NEUTRAL LOADING POINT; SURFACE EFFECT;

EXPANSION; SURFACE TENSION; SURFACES; TENSILE STRESS;

LOADING;

EID: 80052506866     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-010-0489-5     Document Type: Article

References (22)

1. Hui, T., Chen, Y.-H.: The M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. ASME J. Appl. Mech. 77, 021019-1-9 (2009)
2. Hui, T., Chen, Y.-H.: The two state M-integral for a nano inclusion in plane elastic materials. ASME J. Appl. Mech. 77, 024505-1-5 (2009)
3. Ortiz, M.: Nanomechanics of defects in solids. Adv. Appl. Mech. 36, 2-79 (1999)
4. Miller, R. E., Shenoy, V. B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139-147 (2000)
5. Shenoy, V. B.: Size-dependent rigidities of nanosized torsional elements. Int. J. Solids Struct. 39, 4039-4052 (2002) (Pubitemid 34842361)
6. Gurtin, M. E., Weissmuller, J., Larché, F.: A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A 78, 1093-1109 (1988)
7. Sharma, P., Ganti, S.: Interfacial elasticity corrections to size-dependent strain-state of embedded quantum dots. Phys. Status Solidis B, 19. 234, R10-R12 (2002) (Pubitemid 36027880)
8. Sharma, P., Ganti, S.: Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies. ASME J. Appl. Mech. 71, 663-671 (2004) (Pubitemid 40122560)
9. Sharma, P., Ganti, S., Bhate, N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82, 535-537 (2003)
10. Lim, C. W., Li, Z. R., He, L. H.: Size-dependent, non-uniform elastic field inside a nano-scale spherical inclusion due to interface stress. Int. J. Solids Struct. 43, 5055-5065 (2006) (Pubitemid 44061809)
11. Tian, L., Rajapakse, R. K. N. D.: Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity. ASME J. Appl. Mech. 74, 568-574 (2007) (Pubitemid 47154039)
12. Mogilevskaya, S. G., Crouch, S. L., Stolarski, H. K.: Multiple interacting circular nano-inhomogeneitieswith surface/interface effects. J. Mech. Phys. Solids 56, 2298-2327 (2008)
13. Yang, F. Q.: Size-dependent effective modulus of elastic Composite Materials: Spherical nanocavities at dilute concentrations. J. Appl. Phys. 95, 3516-3520 (2004)
14. Duan, L. H., Wang, J., Huang, Z. P., Karihaloo, B. L.: Size-dependent effective elastic constants of solids containing nanoinhomogeneities with interface stress. J. Mech. Phys. Solids 53, 1574-1596 (2005) (Pubitemid 40644971)
15. Marian, J., Knap, J., Ortiz, M.: Nanovoid deformation in aluminum under simple shear. Acta Mater 53, 2893-2900 (2005)
16. Knowles, J. K., Sternberg, E.: On a class of conservation laws in linearized and finite elastostatics. Arch. Rat. Mech. Anal. 44, 187-211 (1972)
17. Budiansky, B., Rice, J. R.: Conservation laws and energy-release rates. ASME J. Appl. Mech. (40), 201-203 (1973)
18. Herrmann, A. G., Herrmann, G.: On energy release rates for a plane crack. ASME J. Appl. Mech. 48, 525-528 (1981) (Pubitemid 12457095)
19. Chen, F. H. K., Shield, R. T.: Conservation laws in elasticity of the J-integral type. Zeitschrift Fuer AngewandteMathematik Und Physik 28, 1-22 (1977)
20. Chen, Y.-H.: M-integral analysis for two-dimensional solids with strongly interacting cracks, Part I. In an infinite brittle sold. Int. J. Solids Struct. 38, 3193-3212 (2001) (Pubitemid 32257375)
21. Chen, Y.-H.: M-integral analysis for two-dimensional solids with strongly interacting cracks, Part II. In the brittle phase of an infinite metal/ceramic biomaterial. Int. J. Solids Struct. 38, 3213-3232 (2001) (Pubitemid 32257376)
22. Chen, Y.-H.: Advances in Conservation Laws and Energy Release Rates. Kluwer Academic Publishers, The Netherlands (ISBN 1402005008) (2002)