The Anti-plane Problem Of The Interfacial Inclusion And Crack In Bi-material Half Space

With the rapid development of social economy,the rational use of underground space has attracted wide attention from all walks of life.The safety of underground space is one of the most concerned problems,and there are many influencing factors.Medium defects exist widely in geological structures.When an earthquake occurs,the stress state near the medium defect under the action of seismic waves will directly affect the strength and stability of underground structures,and then threaten people's lives,property and safety.Therefore,it is of great significance to study the stress state near various defects of underground structures and the interaction between defects for the rational design and use of underground space.As the simplest elastic shear wave,the vibration vector and propagation vector of SH wave can be decoupled,which makes it mathematically and physically feasible to study the propagation and scattering of SH wave under complex boundary conditions such as interface,inclusion and crack.Therefore,based on the existing research results,the dynamic anti-plane problem of interface inclusion and interface crack in elastic bi-material half space is systematically studied in this paper.The steady scattering of SH wave by cylindrical inclusion and interface crack is mainly analyzed.The main research contents are as follows:(1)Based on the method of complex variable function,the dynamic anti-plane characteristics of the right-angle domain with a semi-circular inclusion under the action of point source function,i.e.Green function,are studied by using the idea of "mirror image" and the multipolar coordinates moving technology.Through dimensionless parameters and similarity laws obtained by dimensional analysis,the governing equations and boundary conditions of Green's function in corresponding problems are given.Fourier-Hankel wave function expansion method is used to construct scattering waves from a continuation cylinder in a continuation half-space.The standing wave in a continuation cylindrical inclusion is constructed by Fourier-Bessel wave function expansion method.The definite solution conditions are solved by Fourier expansion method,and the numerical calculation format of Green's function is given.Finally,by defining the error function,the correctness of the analytical solution method and the accuracy of the numerical calculation method are analyzed,and the convergence of the obtained Green function in the near and far fields is discussed.(2)Based on the above Green's function solutions,the dynamic anti-plane characteristics of an elastic bi-material half-space with a cylindrical inclusion at the interface under steady SH wave incidence are studied by using dimensional analysis method and wave function expansion method.Through the dimensionless parameters and similarity laws obtained by dimensional analysis,the governing equations and boundary conditions for solving the corresponding problems are given.The scattering of plane waves from a semi-cylindrical inclusion at the interface is solved,and the corresponding numerical matrix format is obtained.Finally,the displacement and stress fields of plane wave,scattered wave and standing wave in interface inclusions in different regions are constructed.The conjunction conditions,definite solution equations and numerical solutions of far and near field problems are discussed.(3)Based on the above-mentioned conjunction model,the interface crack is introduced to study the plane characteristics of an elastic half-space with an interface cylindrical inclusion and an interface crack in bi-material medium under steady SH wave incidence.Through constructing cracks with different depths and lengths by coincidence method,the matrix format for numerical calculation of integral equation can be established.Taking a short crack with a shallow inclusion as an example,the effects of the existence of an interface crack on the dynamic anti-plane characteristics of a interface in bi-material half-space are discussed in detail.This is a comparison of the dimensionless displacement amplitude on the horizontal boundary of half space and the distribution of the dynamic stress concentration factor along the radial and circumferential direction of the outer and inner edges of a cylindrical inclusion with or without a crack.Finally,according to the distribution of stress and the edge stress of the cylindrical inclusion on the bi-material interface,two non dimensional parameters,the number of cracks and debondings are introduced,and the competition relationship between the interface cracking and the inclusion debonding is evaluated.In this paper,based on the frontier of the subject,the dynamic anti-plane steady-state problem in a bi-material half-space subjected to SH waves is systematically and thoroughly studied by using the latest research ideas.The research results provide important theoretical and reference value for earthquake resistance and protection of underground space structures.