Abstract
Based on the surface elasticity theory, the scattering of shear wave (SH-wave) by a cylindrical nano-inclusion with an interface in a right-angle plane is studied using the method of complex variable function. The dynamic stress concentration factor along the interface of inclusion by the SH-wave and scattering cross section are derived and numerically evaluated. The surface effect, the incident wave’s frequency, the shear modulus, and the distances from the center of nano-inclusion to the right-angle boundaries show the different degrees effects on the DSCF. Our results can aid in analyzing the mechanical properties of nonuniform nanocomposites. The proposed method can better solve the scattering problem of the holes/inclusions on noninfinite elastic substrates.
Highlights
It is a classical problem to study the geometric and physical properties of discontinuities in the structures
Consider the boundary conditions of traction free on two straight edges. e scattering wave field satisfying the boundary condition is constructed by using the mirror method. e analytical solutions of displacement fields are expressed by employing the method of wave function expansion and the complex variable function theory. e numerical results of dynamic stress concentration factors about nano-inclusion are illustrated graphically. e effects of surface elasticity on the dynamic stress concentration factor in the matrix material are analyzed. e effects of the frequency of the incident wave and the shear modulus ratio of the nano-inclusion to the matrix and the distances from the center of nano-inclusion to the right-angle boundaries on the DSCF are analyzed
According to the surface elasticity theory, a surface is regarded as negligibly thin membranes that adheres to the matrix without slipping. e classical theory of elasticity is still applicable in the matrix, but the presence of surface stress leads to nonclassical boundary conditions. e equilibrium equations and the isotropic constitutive relations in the matrix are the same as those in the classical theory of elasticity: σij,j ρ zz2tu2i, (24)
Summary
It is a classical problem to study the geometric and physical properties of discontinuities in the structures. Using Gurtin’s surface elasticity theory, Wang et al [16, 17] studied the scattering of the plane wave in the infinite. Mathematical Problems in Engineering nanocomposites with surface effect by the wave functions expansion method. Using the complex variable function theory, Wu [22] discussed the interface effects of SH-waves’ scattering around a cylindrical nano-inclusion. In most practical problems, nanocomposites are finite, and the reflection elastic waves at the edge of the material greatly affect the wave fields. In some cases, it may play an important role. Dynamic stress around a cylindrical nanoinclusion with an interface in a right-angle plane under SHwave is studied within the framework of surface elasticity. Consider the boundary conditions of traction free on two straight edges. e scattering wave field satisfying the boundary condition is constructed by using the mirror method. e analytical solutions of displacement fields are expressed by employing the method of wave function expansion and the complex variable function theory. e numerical results of dynamic stress concentration factors about nano-inclusion are illustrated graphically. e effects of surface elasticity on the dynamic stress concentration factor in the matrix material are analyzed. e effects of the frequency of the incident wave and the shear modulus ratio of the nano-inclusion to the matrix and the distances from the center of nano-inclusion to the right-angle boundaries on the DSCF are analyzed
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