Scattering Of SH Wave With Nano-inhomogeneous Defect

In the mechanical structure,there are many kinds of geometric or physical discontinuities such as defects or technological holes/inclusions.When the structure bears the dynamic load represented by elastic wave,the displacement and stress in the structure will be redistributed.At present,many scholars have studied the defect body under various models,but mainly focused on the macro scale,the research on nano defect body is relatively less.When the material scale reaches nanometer or smaller,the surface/interface effect will have a significant impact on the mechanical behavior of the material.Therefore,it is very important to determine the distribution of dynamic stress near the defects for the optimal design of nano materials.In this paper,based on the existing research results,the scattering of shear wave(SH wave)by nano inhomogeneous defects embedded in different models is studied by using wave function expansion method and complex function theory combined with surface elasticity theory.Firstly,the displacement potential function of the incident wave,the scattered wave and the refracted wave fields are given in combination with the wave theory.And then the corresponding stress fields with unknown coefficients are obtained according to the classical elastic theory.Secondly,based on the surface elasticity theory,the boundary conditions at the boundary of the nano-non-homogeneous body are given.Then according to the orthogonality of the trigonometric function,the unknown coefficients are solved by numerical simulation using Maple software to obtain the stress field.Finally,the effects of various factors on dynamic stress concentration factor(DSCF)and radial stress under different models are discussed based on numerical results.Focusing on the basic idea mentioned above,this paper systematically studies the following:(1)Research on the scattering of SH wave by nano cylindrical hole/inclusion in an infinite elastic bodyThe theory of complex variable function is used to study the scattering of SH wave by nano cylindrical hole/inclusion.Firstly,the incident,scattered,and refracted wave fields are given according to the wave equation.Secondly,considering the surface effect,the boundary conditions at the nanoscale are given,and the infinite algebraic equations with unknown coefficients are solved.The analytical solutions of the stress fields are obtained by the orthogonality of the trigonometric function.Finally,the effects of surface effect,wave number and inclusion hardness on the dynamic stress concentration factor and radial stress around the hole/inclusion are analyzed by numerical simulation.(2)Research on the scattering of SH wave by nano arc-shaped hole/inclusion on a half plane boundaryThe wave function expansion method is used to study the scattering of incident plane SH wave by nano arc-shaped hole/inclusion on a half plane boundary.Combining the classical elastic theory and the surface elasticity theory,the analytical solution of the semi-circular stress field and the infinite algebraic equations of the general arc stress field are obtained by the orthogonality of the trigonometric function.Finally,the effects of surface effect,incident angle,arc depth and inclusion hardness on the dynamic stress concentration factors around the hole/inclusion are analyzed by an example.(3)Research on the scattering of SH wave by cylindrical nano-inclusion in a right-angled planeUsing the wave function expansion method,the complex function theory and multi-pole coordinate movement technology,the scattering of SH wave by cylindrical nano-inclusion in a right-angled plane is studied.Firstly,the free field in a right-angled plane is given.Secondly,the scattering and refraction fields in the right-angled plane are established by the mirror method.The total wave fields in the same coordinate system are given by the Graf addition formula.Then,the surface elasticity theory is used to obtain the stress boundary condition and the displacement continuous condition,and the infinite algebraic equations with unknown coefficients in the scattering and refraction wave functions are established.Finally,the numerical solutions of the stress fields are obtained by the orthogonality of the trigonometric function.The numerical results show that surface effect significantly affects DSCF when the inclusion shrinks to nanoscale.At the same time,the influence of the incident wave number,the hardness of the inclusion,and the distance from the center of the nano-inclusion to the right-angle boundary on the dynamic stress concentration factor around the cylindrical inclusion are analyzed.(4)Research on the scattering of SH wave in the arc-shaped elastic nano-inclusion at the corner point of right-angled planeUsing the wave function expansion method,combined with classical elasticity theory and surface elasticity theory,the scattering of the incident plane SH wave in the arc-shaped nano-inclusion at the corner point of right-angled plane is discussed.The analytical solution of the stress field is obtained by the orthogonality of the trigonometric function.Finally,the effects of surface effect,wave number and incident angle on the dynamic stress concentration factor around the arc are discussed by numerical simulation.(5)Research on the scattering of SH wave around an arbitrary shape nano-hole/inclusion in an infinite elastic bodyThe complex wave function theory and conformal transformation method are used to discuss the scattering of SH wave by arbitrary-shaped nano-hole/inclusion.The arbitrary shaped hole/inclusion is transformed into a circular hole/inclusion by conformal transformation,and then the incident,scattering and the refractive wave function in the circular hole/inclusion are given.Then the stress boundary condition and displacement continuity condition at the hole/inclusion interface are also given according to the surface elasticity theory,and the infinite algebraic equations with unknown coefficients corresponding to scattering and refracted waves are obtained,which are solved by the orthogonality of trigonometric function.Finally,through numerical simulation,as a special case,the effects of wave number,the ratio of the minor and major axes of an ellipse,inclusion hardness and surface effect on the DSCF around circular,elliptical and square holes/inclusions are discussed.