The presence of nanoparticles in an elastic solid introduces disturbances that can vary significantly from the ones predicted by classical elasticity. In this study, we were able to determine that nanoscale effects introduced via a coherent interface model can indeed result in complex, non-local displacement and stress fields near the free surface of a substrate. The specific geometry is defined by a spherical nanoparticle near a straight boundary. The system is loaded either through a far-field uniaxial tension or a transformation strain (eigenstrain) in the particle itself. The elastic field can be fully determined using a three-dimensional displacement formulation that incorporates a well-established interface model.
MuraT. Micromechanics of defects in solids. Dordrecht: Martinus Nijhoff, 1987.
2.
SaddMH. Elasticity: theory, applications, and numerics. Oxford: Elsevier, 2005.
3.
CahnJLärchéF. Surface stress and the chemical-equilibrium of small crystals. II. Solid particles embedded in a solid matrix. Acta Metall1982; 30: 51–56.
4.
SharmaPGantiSBhateN. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl Phys Lett2003; 82: 535–537.
5.
ShevchenkoEVTalapinDVKotovNAO’BrienSMurrayCB. Structural diversity in binary nanoparticle superlattices. Nature2006; 439: 55–59.
6.
BenvenisteY. A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. J Mech Phys Solids2006; 54: 708–734.
7.
GurtinMMurdochA. Surface stress in solids. Int J Solids Struct1978; 14: 431–440.
8.
GurtinMWeissmüllerJLärchéF. A general theory of curved deformable interfaces in solids at equilibrium. Philos Mag A1998; 78: 1093–1109.
9.
MohammadiPLiuLPSharmaPKuktaRV. Surface energy, elasticity and the homogenization of rough surfaces. J Mech Phys Solids2013; 61: 325–340.
10.
PovstenkoY. Theoretical investigation of phenomena caused by heterogeneous surface tension in solids. J Mech Phys Solids1993; 41: 1499–1514.
11.
SteigmannDOgdenR. Elastic surface-substrate interactions. Proc R Soc London Ser A; 455: 437–474.
12.
AdamsonAGastA. Physical chemistry of surfaces. New York: Wiley, 1997.
13.
DuanHWangJHuangZKarihalooBL. Eshelby formalism for nano-inhomogeneities. Proc R Soc A2005; 461: 3335–3353.
14.
DuanHWangJHuangZLuoZ. Stress concentration tensors of inhomogeneities with interface effects. Mech Mater2005; 37: 723–736.
15.
HeLLiZ. Impact of surface stress on stress concentration. Int J Solids Struct2006; 43: 6208–6219.
16.
LimCLiZHeL. Size dependent, non-uniform elastic field inside a nano-scale spherical inclusion due to interface stress. Int J Solids Struct2006; 43: 5055–5065.
17.
KushchVMogilevskayaSStolarskiHCrouchS. Elastic interaction of spherical nanoinhomogeneities with Gurtin–Murdoch type interfaces. J Mech Phys Solids2011; 59: 1702–1716.
18.
MiCKourisD. On the significance of coherent interface effects for embedded nanoparticles. Math Mech Solids2014; 19(4): 350–368.
TianLRajapakseRKND. Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity. J Appl Mech2007; 74: 568–574.
23.
ChenTDvorakGJYuCC. Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mech2007; 188: 39–54.
24.
DuanHLWangJHuangZPKarihalooBL. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J Mech Phys Solids2005; 53: 1574–1596.
25.
DuanHLWangJKarihalooBLHuangZP. Nanoporous materials can be made stiffer than non-porous counterparts by surface modification. Acta Mater2006; 54: 2983–2990.
26.
YangF. Size-dependent effective modulus of elastic composite materials: Spherical nanocavities at dilute concentrations. J Appl Phys2004; 95: 3516–3520.
27.
MogilevskayaSGCrouchSLLa GrottaAStolarskiHK. The effects of surface elasticity and surface tension on the transverse overall elastic behavior of unidirectional nano-composites. Compos Sci Technol2010; 70: 427–434.
28.
AvazmohammadiRYangFAbbasionS. Effect of interface stresses on the elastic deformation of an elastic half-plane containing an elastic inclusion. Int J Solids Struct2009; 46: 2897–2906.
29.
JammesMMogilevskayaSCrouchS. Multiple circular nano-inhomogeneities and/or nano-pores in one of two joined isotropic elastic half-planes. Eng Anal Boundary Elem2009; 33: 233–248.
30.
MiCKourisD. Nanoparticles under the influence of surface/interface elasticity. J Mech Mater Struct2006; 1: 763–791.
31.
MiCKourisD. Stress concentration around a nanovoid near the surface of an elastic half-space. Int J Solids Struct2013; 50(18): 2737–2748.
32.
MiCJunSKourisDKimS. Atomistic calculations of interface elastic properties in noncoherent metallic bilayers. Phys Rev B2008; 77: 075425.
33.
TsuchidaENakaharaI. Stress-concentration around a spherical cavity in a semi-infinite elastic body under uniaxial tension. Bull JSME1974; 17: 1207–1217.
34.
ArfkenGWeberH. Mathematical methods for physicists. New York: Elsevier, 2005.
35.
GurtinMMurdochA. Continuum theory of elastic-material surfaces. Arch Ration Mech Anal1975; 57: 291–323.
36.
CallisterW. Materials science and engineering: an introduction. New York: John Wiley & Sons, 2007.
37.
ShenoyV. Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys Rev B2005; 71: 094104.
