Diffractions of Elastic Waves and Stress Concentration Near a Cylindrical Nano-Inclusion Incorporating Surface Effect

Abstract

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.

Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber

“…Subsequently, Wang [46] investigated the multiple diffraction of plane compressional waves induced by two circular cylindrical holes with surface effects, and addressed the effects of the surface energy and interaction between the two holes on the dynamic stress concentration around the surface of the holes. Using the displacement potential method, Ru et al [47] described the diffraction of elastic waves and the stress concentration near a cylindrical nano-inclusion with surface effect. Zhang et al [48] discussed the diffraction of a plane compressional wave by an array of nano-sized circular holes in an elastic medium.…”

BEM modeling of wave diffraction in an elastic matrix with nano-heterogeneities

“…When the wave first impinges on the inclusion-matrix interface, a reflected wave is generated that propagates back into the matrix, while a refracted wave moves into the inclusion. We define a non-dimensional frequency with respect to the solid matrix material properties as [7] [7]…”

“…Next, the techniques used for solving both static and dynamic problems of solids containing nano-inhomogeneities are as follows: (a) analytical, such as the complex variable technique, see Tian and Rajapakse [4], and the wave function expansion method, see Wang [5], Wang et al [6] and Ru et al [7]; (b) finite element method (FEM), see Wang et al [6]; (c) boundary element method (BEM), see Dong [8], including the complex variable BEM, see Jammes et al [9]. The conclusions, which can be drawn at this stage are as follows: (a) to date, there is a limited number of theoretical and numerical studies for solids on surface effects as seen from the nano-scale; (b) most of the solution techniques that have been developed are semi-analytical, with relatively few papers using the boundary element approach, which is known to be a highly accurate numerical tool.…”

The Method and Software for the Solution of Dynamic Waves Propagation Problem in Elastic Medium

“…The advantage of this method is that it allows approaching the maximum dependence domain of the final and differential equation to the dependence area of the initial differential equation [10][11][12].…”