Multiple Scattering Of Elastic Waves By Eccentric Cylindrical Core-shell Structures At Nanoscale

The problem of stress concentration has always been a hot topic for scholars,ranging from circular hole to inclusion,from full space to half space.The wave function solution satisfying the boundary conditions is constructed to solve the elastic wave scattering problem with relatively simple structure,but some important factors are often ignored,such as the eccentric structure model,surface defects and the interference phenomenon in the matrix.At the same time,with the development of science and technology,nano-scale materials will show different properties from macro materials.Among them,core-shell composites can be made from engineering materials and carbon nanotubes,because they show better properties than single materials,people pay more attention to them.Therefore,it is of great practical significance to study the propagation of elastic waves in nano core-shell composites.In summary,based on surface elasticity and wave theory,a new interface mechanics model is proposed in this paper,which mainly considers the multiple scattering problem of eccentric cylindrical core-shell structure with ideal/non ideal interface in nanoscale.By using the wave function expansion method and Graf addition formula,combined with the generalized Young-Laplace equation,the boundary conditions related to the surface effect of the eccentric cylindrical core-shell structure at the nanometer scale are obtained,and the boundary problem of wave equation is transformed into solving a set of infinite algebraic equations;In order to obtain the dynamic stress concentration factor(DSCF)around the interface of eccentric cylindrical core-shell structure at nanometer scale,the infinite series in the equations are truncated accurately and the Maple software is used for numerical calculation;Finally,the related factors affecting DSCF and their changing rules were presented by graphical method.The problems studied are not only applicable to the study of composite nanomaterials and nanomaterials,but also deepen people's understanding of new nano core-shell structure composites,which enriches the study of surface elasticity theory.The main contents of this paper are as follows:(1)Firstly,the wave function expressions related to radius and angle are obtained by using the wave function expansion method.Then,the multipolar coordinate transformation between the inner domain and the outer domain is carried out by using the multipolar coordinate moving technique.The multiple scattering of plane compressional waves(P waves)by eccentric cylindrical core-shell structure with ideal interface in nanoscale is studied by using the orthogonal normalization of trigonometric function.(2)The linear elastic model is used to simulate the non-ideal interface,and the displacement discontinuity and stress continuity are assumed.The boundary conditions at the surface/interface at the nanometer scale are obtained by using the generalized Young-Laplace equation.The multiple scattering of the plane compression wave(P wave)from the eccentric cylindrical core-shell structure with the non-ideal interface at the nanometer scale is further studied.The results show that the surface effect,eccentricity,shear modulus ratio(hard and soft inclusion)and spring constant have significant influence on the dynamic stress concentration factor for the multiple scattering problem of eccentric cylindrical core-shell structure at nanometer scale.