Wave scattering by nanoheterogeneities embedded in an elastic matrix via BEM

Abstract

In this work, we study elastic wave scattering and diffraction at the nanoscale by multiple heterogeneities such as cavities and inclusions embedded in an otherwise homogeneous elastic matrix. The dynamic loads are the result of pressure and shear waves propagating through the heterogeneous continuum under two-dimensional conditions. The mathematical model used here combines (a) classical elastodynamic theory for the bulk solid, where the total elastic wave field comprises both incident and scattered wave fields, with (b) non-classical boundary conditions and a localized constitutive equation for the matrix–inclusion interfaces within the framework of the Gurtin–Murdoch surface elasticity theory. The computational platform used is the boundary element method (BEM) defined in terms of the frequency-dependent fundamental solution of the governing equations of motion for the bulk solid under time-harmonic conditions. Following development of the BEM for this category of problems, a verification study is conducted to establish its accuracy with the help of benchmark-type examples. Subsequent numerical simulations for the case of multiple cavities and inclusions embedded in an elastic matrix examine the development of the wave fields in the bulk solid, as well as of the dynamic stress concentration factor (DSCF) at the solid-inclusion interfaces, in terms of the following parameters: (a) nanoheterogeneity shape, which directly influences the surface energy; (b) nanoheterogeneity size; (c) ratio of the bulk material properties of the matrix to those of the inclusion; (d) surface properties such as the interfacial constants and the residual interface tension; (e) dynamic interaction between multiple nanoheterogeneities and (f) direction of propagation and frequency content of the incident wave.