Dynamic response of elastic anisotropic solid with nanoinclusions

Abstract

AbstractThe finite elastic anisotropic solid with multiple elastic isotropic/anisotropic nanoinclusions of arbitrary shape, size, number and geometrical configuration subjected to time‐harmonic or transient loads is examined under plane strain conditions. The proposed mechanical model is based on a hybrid usage of elastodynamic theory for the bulk elastic anisotropic solid under non‐classical boundary conditions (BC), supplemented with a localized constitutive equation for the solid‐nanoinclusion interface in the framework of the Gurtin‐Murdoch theory of surface elasticity. The developed and verified numerical scheme for solution of the transient problem is based on the hybrid usage of direct and inverse Fourier transform (FFT), boundary element method (BEM) in conjunction with closed form frequency dependent fundamental solution of elastodynamic equation for anisotropic materials. The proposed model is flexible, numerically efficient and has virtually no limitations regarding the type of material anisotropy, nanoinclusions’ shape, size, number and geometrical configuration. The numerical results show a marked dependence of the wave fields on the surface elasticity effects, on the size, number and position of the nanoinclusions, on the type of material anisotropy, on the type and properties of the dynamic load, on the mutual interactions between nanoinclusions and between them and the external solid's boundary.