The diffractions of plane compressional waves (P-wave) and shear waves (SV-wave) by a cylindrical nano-inclusion are investigated in this paper. To account for the surface/interface effect at nanoscale, the surface/interface elasticity theory is adopted in the analysis. Using the displacement potential method, we obtain the solutions for the elastic fields induced by incident P- and SV-waves near a cylindrical nano-inclusion. The results show that surface/interface has a significant effect on the diffractions of elastic waves as the radius of the inclusion shrinks to nanoscale. For incident waves with different frequencies, the effects of interfacial properties on the dynamic stress concentration around the nano-inclusion are discussed in detail.

1.
Wong
,
E.
,
Sheehan
,
P. E.
, and
Lieber
,
C. M.
, 1997, “
Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes
,”
Science
0036-8075,
277
, pp.
1971
1975
.
2.
Davies
,
J. H.
, 1998, “
Elastic and Piezoelectric Fields Around a Buried Quantum Dot
,”
J. Appl. Phys.
0021-8979,
84
, pp.
1358
1365
.
3.
Zhou
,
L. G.
, and
Huang
,
H. C.
, 2004, “
Are Surfaces Elastically Softer or Stiffer
,”
Appl. Phys. Lett.
0003-6951,
84
, pp.
1940
1942
.
4.
Gurtin
,
M. E.
,
Weissmuller
,
J.
, and
Larche
,
F.
, 1998, “
A General Theory of Curved Deformable Interfaces in Solids at Equilibrium
,”
Philos. Mag. A
0141-8610,
78
, pp.
1093
1109
.
5.
Miller
,
R. E.
, and
Shenoy
,
V. B.
, 2000, “
Size-Dependent Elastic Properties of Nanosized Structural Elements
,”
Nanotechnology
0957-4484,
11
, pp.
139
147
.
6.
Shenoy
,
V. B.
, 2002, “
Size-Dependent Rigidities of Nanosized Torsional Elements
,”
Int. J. Solids Struct.
0020-7683,
39
, pp.
4039
4052
.
7.
Sharma
,
P.
,
Ganti
,
S.
, and
Bhate
,
N.
, 2003, “
Effect of Surfaces on the Size-Dependent Elastic State of Nano-Inhomogeneities
,”
Appl. Phys. Lett.
0003-6951,
82
, pp.
535
537
.
8.
Yang
,
F. Q.
, 2004, “
Size-Dependent Effective Modulus of Elastic Composite Materials: Spherical Nanocavities at Dilute Concentrations
,”
J. Appl. Phys.
0021-8979,
95
, pp.
3516
3520
.
9.
Dingreville
,
R.
,
Qu
,
J.
, and
Cherkaoui
,
M.
, 2005, “
Surface Free Energy and Its Effect on the Elastic Behavior of Nano-Sized Particles, Wires and Films
,”
J. Mech. Phys. Solids
0022-5096,
53
, pp.
1827
1854
.
10.
He
,
L. H.
, and
Li
,
Z. R.
, 2006, “
Impact of Surface Stress on Stress Concentration
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
6208
6219
.
11.
Gao
,
W.
,
Yu
,
S. W.
, and
Huang
,
G. Y.
, 2006, “
Finite Element Characterization of the Size-Dependent Mechanical Behaviour in Nanosystems
,”
Nanotechnology
0957-4484,
17
, pp.
1118
1122
.
12.
Chen
,
T. Y.
,
Chiu
,
M. S.
, and
Weng
,
C. N.
, 2006, “
Derivation of the Generalized Young-Laplace Equation of Curved Interfaces in Nanoscaled Solids
,”
J. Appl. Phys.
0021-8979,
100
, p.
074308
.
13.
Wang
,
G. F.
, and
Wang
,
T. J.
, 2006, “
Deformation Around a Nanosized Elliptical Hole With Surface Effect
,”
Appl. Phys. Lett.
0003-6951,
89
, p.
161901
.
14.
Sharma
,
P.
, and
Wheeler
,
L. T.
, 2007, “
Size-Dependent Elastic State of Ellipsoidal Nano-Inclusions Incorporating Surface/Interface Tension
,”
ASME J. Appl. Mech.
0021-8936,
74
, pp.
447
454
.
15.
Tian
,
L.
, and
Rajapakse
,
R. K. N. D.
, 2007, “
Elastic Field of an Isotropic Matrix With a Nanoscale Elliptical Inhomogeneity
,”
Int. J. Solids Struct.
0020-7683,
44
, pp.
7988
8005
.
16.
Ou
,
Z. Y.
,
Wang
,
G. F.
, and
Wang
,
T. J.
, 2009, “
Elastic Fields Around a Nanosized Spheroidal Cavity Under Arbitrary Uniform Remote Loadings
,”
Eur. J. Mech. A/Solids
0997-7538,
28
, pp.
110
120
.
17.
Wang
,
G. F.
,
Feng
,
X. Q.
,
Wang
,
T. J.
, and
Gao
,
W.
, 2008, “
Surface Effects on the Stresses Near a Crack Tip
,”
ASME J. Appl. Mech.
0021-8936,
75
, p.
011001
.
18.
Zhang
,
W. X.
, and
Wang
,
T. J.
, 2007, “
Effect of Surface Energy on the Yield Strength of Nanoporous Materials
,”
Appl. Phys. Lett.
0003-6951,
90
, p.
063104
.
19.
Zhang
,
W. X.
,
Wang
,
T. J.
, and
Chen
,
X.
, 2008, “
Effect of Surface Stress on the Asymmetric Yield Strength of Nanowires
,”
J. Appl. Phys.
0021-8979,
103
, p.
123527
.
20.
Pao
,
Y. H.
, and
Mow
,
C. C.
, 1973,
Diffractions of Elastic Waves and Dynamic Stress Concentrations
,
Crane, Russak & Co., Inc.
,
New York
.
21.
Sinclair
,
A. N.
, and
Addison
,
R. C.
, 1993, “
Acoustic Diffraction Spectrum of a SiC Fiber in a Solid Elastic Medium
,”
J. Acoust. Soc. Am.
0001-4966,
94
, pp.
1126
1135
.
22.
Wang
,
G. F.
,
Wang
,
T. J.
, and
Feng
,
X. Q.
, 2006, “
Surface Effects on the Diffraction of Plane Compressional Waves by a Nanosized Circular Hole
,”
Appl. Phys. Lett.
0003-6951,
89
, p.
231923
.
23.
Wang
,
G. F.
, 2007, “
Diffraction of Plane Compressional Wave by a Nanosized Spherical Cavity With Surface Effects
,”
Appl. Phys. Lett.
0003-6951,
90
, p.
211907
.
You do not currently have access to this content.