Dynamic BEM analysis of elastic anisotropic nano‐sheet with surface imperfections and cavities

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Abstract
The paper considers elastic anisotropic nano‐sheet with nanotopography and containing embedded nanocavities under time‐harmonic in‐plane wave motion. The mechanical model is based on the classical elastodynamic theory for the anisotropic bulk solid and the nonclassical boundary conditions along its boundary derived by Gurtin and Murdoch. A localized constitutive equation for the half‐plane boundary is considered in the frame of surface elasticity theory. The computational tool is an efficient direct displacement boundary element method (BEM) based on the frequency‐dependent elastodynamic fundamental solution for elastic generally anisotropic material. To show the versatility of the proposed methodology, wave propagation in an elastic anisotropic heterogeneous nano‐sheet with nanorelief presented by hill‐canyon nanotopography is studied. The simulations illustrate the dependence of the wave field on the material anisotropy, on the surface elasticity properties, on the nanorelief peculiarities, on the nanocavities existence and their dynamic interaction, and on the incident wave characteristics. The obtained results reveal the potential of the developed mechanical model based on the boundary integral equations in the frame of surface elasticity theory to produce highly accurate results by using strongly reduced discretization mesh in comparison with the domain‐based methods.

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