BEM modeling of wave diffraction in an elastic matrix with nano-heterogeneities

Abstract

This work addresses wave diffraction and scattering in a homogeneous, elastic matrix containing multiple heterogeneities at nano-scale. The source of wave motion is an incident, time harmonic elastic pressure (P) wave propagating through the heterogeneous matrix. The approach followed here is based on a combination of (a) classical elastodynamic theory for the bulk solid, relating the total wave fields with the incident and scattered ones through the superposition principle; (b) non-classical boundary conditions and localized constitutive equations for the matrix-heterogeneity interface in the framework of the GurtinMurdoch surface elasticity theory. The method of solution is the boundary element method using frequency-dependent fundamental solutions for the governing equations of the bulk solid.