Elastic wave scattering and stress concentration in a finite anisotropic solid with nano-cavities

Abstract

The paper deals with numerical evaluation of the scattered wave and dynamic stress concentration fields in a finite anisotropic solid containing multiple nano-cavities. 2D plane-strain state and in-plane wave motion are assumed. The proposed mechanical model combines classical elastodynamic theory for the bulk general anisotropic solid and the Gurtin–Murdoch theory of surface elasticity assuming localized constitutive equation for the infinitely thin interface between the cavity and the matrix. The developed computational methodology is based on the following: (a) displacement boundary integral equations along existing boundaries using the analytically derived through Radon transform fundamental solution of the equation of motion of the bulk anisotropic solid; (b) non-classical boundary conditions of the Gurtin–Murdoch model along the interface between the matrix and cavities taking into consideration a jump in the stresses as one moves from the bulk material to the cavity due to the presence of surface elasticity; and (c) elastic-viscoelastic correspondence principle. The accuracy of the developed software is proven by comparisons of the obtained results solved by boundary element method and finite element method. A detailed parametric study reveals the sensitivity of the wave field to different key factors such as size, number and configuration of the cavities, surface and bulk material properties.