Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

Effect of Surface Elasticity on Scattering of Plane P-Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2013 ◽  
Vol 303-306 ◽  
pp. 2656-2660 ◽  
Author(s):  
H. M Wu ◽  
Z. Y. Ou
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Cylindrical Cavity ◽  
Surface Elasticity ◽  
Expansion Method ◽  
P Waves ◽  
Compressional Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

When the characteristic sizes of materials and elements reduce to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of of plane compressional waves (P-waves) by a semi-cylindrical cavity embedded in an elastic half-plane is investigated in this paper. By using the wave function expansion method, we obtain the analytical solutions of elastci fields. The results show that surface energy has a significant effect on the diffractions of P-waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical cavity, the effects of surface elasticity on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2012 ◽  
Vol 627 ◽  
pp. 698-704
Author(s):  
Zhi Ying Ou ◽  
Xiao Wei Liu ◽  
Qiong Deng
Keyword(s):  
Surface Energy ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Fields ◽  
Sh Waves ◽  
Wave Function Expansion Method ◽  
Incident Waves

When the radius of materials and structral devices reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

Surface effect on deformation around an elliptical hole by surface energy density theory

2019 ◽  
Vol 25 (2) ◽  
pp. 337-347
Author(s):  
Liyuan Wang
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Hoop Stress ◽  
Surface Effect ◽  
Plane Deformation ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Elliptical Hole ◽  
External Loading ◽  
Surface Energy Density

The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.

Elastic Energy of Surfaces and Residually Stressed Solids: An Energy Approach for the Mechanics of Nanostructures

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Xiang Gao ◽  
Daining Fang
Keyword(s):  
Surface Energy ◽  
Elastic Energy ◽  
Surface Stress ◽  
Strain Energy ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Small Deformation ◽  
Energy Approach ◽  
Residual Surface Stress ◽  
The Impact

The surface energy plays a significant role in solids and structures at the small scales, and an explicit expression for surface energy is prerequisite for studying the nanostructures via energy methods. In this study, a general formula for surface energy at finite deformation is constructed, which has simple forms and clearly physical meanings. Next, the strain energy formulas both for isotropic and anisotropic surfaces under small deformation are derived. It is demonstrated that the surface elastic energy is also dependent on the nonlinear Green strain due to the impact of residual surface stress. Then, the strain energy formula for residually stressed elastic solids is given. These results are instrumental to the energy approach for nanomechanics. Finally, the proposed results are applied to investigate the elastic stability and natural frequency of nanowires. A deep analysis of these two examples reveals two length scales characterizing the significance of surface energy. One is the critical length of nanostructures for self-buckling; the other reflects the competition between residual surface stress and surface elasticity, indicating that the surface effect does not always strengthen the stiffness of nanostructures. These results are conducive to shed light on the importance of the residual surface stress and the initial stress in the bulk solids.

Diffraction of Plane Compressional Waves by an Array of Nanosized Cylindrical Holes

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Q. F. Zhang ◽  
G. F. Wang ◽  
P. Schiavone
Keyword(s):  
Surface Energy ◽  
Dynamic Stress ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Circular Holes ◽  
Cylindrical Holes ◽  
Effect Of Surface ◽  
Dynamic Stress Concentrations

When the radius of a hole reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the present paper, we consider the diffraction of plane compressional waves by an array of nanosized circular holes in an elastic medium. The effect of surface energy is taken into account through surface elasticity theory. Using the wave expansion method, we derive the corresponding elastic diffraction fields. Dynamic stress concentrations around the holes and the scattering cross section are calculated to address the surface effects on the diffraction phenomena.

Surface/Interface Effect on Dynamic Stress Around a Nanoinclusion in a Semi-Infinite Slab Under Shear Waves

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Xue-Qian Fang ◽  
Le-Le Zhang ◽  
Jin-Xi Liu ◽  
Wen-Jie Feng
Keyword(s):  
Dynamic Stress ◽  
Numerical Solutions ◽  
Shear Waves ◽  
Expansion Method ◽  
Interface Effect ◽  
Image Method ◽  
Dynamic Stress Concentration Factor ◽  
Wave Function Expansion Method ◽  
Infinite Slab ◽  
Incident Waves

This work examines the surface/interface effect on the dynamic stress around a cylindrical nanoinclusion embedded in an elastic semi-infinite slab subjected to antiplane shear waves, and the nanosize effect is considered. The wave function expansion method is employed to express the wave fields in the nanosized structure. The traction free boundary conditions at the three edges of this structure are considered and satisfied by using the image method. The analytical and numerical solutions of the dynamic stress concentration factor around the nanoinclusion are presented. Analyses show that the three edges of the nanosized structure manifest different effects of the dynamic stress around the nanoinclusion. The size effect is also related to the interface properties, the wave frequency of incident waves, and the material properties ratio of the nanoinclusion to matrix. To show the accuracy of the results for certain given parameters, comparison with the existing results is also given.

scholarly journals Surface Effect on Diffractions of Elastic Waves and Stress Concentration near a Cluster of Cylindrical Nanoholes Arranged as Quadrate Shape

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ru Yan
Keyword(s):  
Stress Concentration ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Potential Method ◽  
P Wave ◽  
Displacement Potential ◽  
P And Sv Waves

We consider the multiple scattering of elastic waves (P-wave and SV-wave) by a cluster of nanosized cylindrical holes arranged as quadrate shape. When the radius of the holes shrinks to nanometers, the surface elasticity theory is adopted in analysis. Using the displacement potential method and wave functions expansion method, we obtain that the multiple scattering fields induced by incident P- and SV-waves around the holes are derived. The dynamic stress concentration around the holes is calculated to illustrate the effect of surface effects on the multiple scattering of P- and SV-waves.

EFFECTS OF INTERFACE ENERGY ON MULTIPLE SCATTERING OF PLANE COMPRESSIONAL WAVES BY TWO CYLINDRICAL FIBERS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250040 ◽  
Author(s):  
Z. Y. OU ◽  
D. W. LEE
Keyword(s):  
Surface Energy ◽  
Multiple Scattering ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Interface Energy ◽  
Dynamic Mechanical Properties ◽  
Addition Theorem ◽  
Inhomogeneous Materials ◽  
Compressional Waves ◽  
Eigenfunction Expansion Method

The multiple scattering of plane compressional waves by two cylindrical fibers with interface effects is investigated. Based on surface elasticity theory, the wave fields in a nanoscale solid medium can be obtained by applying the eigenfunction expansion method and the Graf's addition theorem. Our results indicate that surface energy significantly affects the diffraction of elastic waves, as the radii of the fibers approach nanometers. The dynamic stress concentration factors at the interfaces between the fibers and the matrix under incident plane compressional waves at different frequencies are examined to determine the effects of surface energy, properties of inhomogeneous materials, and the interaction between fibers in multiple scattering phenomena. These results are helpful in understanding the dynamic mechanical properties of nanocomposites, and the proposed method for investigating the multiple scattering of plane compressional waves can be extended to the case of fiber-reinforced composites.

Dynamic Stress Concentrations Due to Scattering of Elastic SV Waves from a Coated Nanoinclusion with Considerations in the Interfacial Region

2016 ◽  
Vol 33 (3) ◽  
pp. 279-288
Author(s):  
A. R. Ghanei Mohammadi ◽  
P. Hosseini Tehrani
Keyword(s):  
Dynamic Stress ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Interface Energy ◽  
Interfacial Region ◽  
Stress Concentrations ◽  
Wave Function Expansion Method ◽  
Navier Equation ◽  
Stress Concentration Factors ◽  
Elastic Shear

AbstractThe problem of plane elastic shear waves (SV waves) scattering from a circular nanoinclusion surrounded by an inhomogeneous interphase embedded in an elastic matrix is investigated analytically in this paper. An approach is introduced to account for the simultaneous effects of a graded interphase and surface/interface energy based on Gurtin-Murdoch's model of surface elasticity. Using the wave function expansion method, the Navier equation is solved for all three phases (nanofiber-interphase- matrix). Presenting the results in dimensionless manner, Dynamic Stress Concentration Factors (DSCF) for the present problem are obtained and the effects of several parameters on the results are studied in detail. It is understood that taking the effects of both surface/interface and interphase inhomogeneity into account leads to a significant influence on the DSCF results and consequently on the overall dynamic behavior of the nanocomposites.

An Analytic Solution for the Diffraction of Plane P Waves by a Cylindrical Inclusion in Half Space

2011 ◽  
Vol 255-260 ◽  
pp. 2520-2525
Author(s):  
Da Guang Li ◽  
Xue Ping Gao ◽  
Zhang Ying
Keyword(s):  
Half Space ◽  
Analytic Solution ◽  
Incident Angle ◽  
Surface Condition ◽  
Surface Displacement ◽  
Cylindrical Inclusion ◽  
Diffraction Effect ◽  
P Waves ◽  
Plane P Waves ◽  
The Impact

This paper presents an analytic solution for the diffraction of plane P waves by a cylindrical inclusion in half space by Fourier-Bessel wave function expansion method, in which the flat surface of half space is approximated by a large curved surface. The equation can be constructed by the continue boundary and the free surface condition. Based on parametric analysis, the impact of the inclusion on surface displacement amplitude is discussed. It is illustrated that there is large difference of the diffraction characteristics between the hard inclusion and soft inclusion. The displacement response depends strongly on the incident angle and frequency. The diffraction effect can be ignored with large embedded depth of the inclusion.

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