BIEM analysis of a graded nano-cracked elastic half-plane under time-harmonic waves

This work addresses the scattering of time-harmonic waves by a finite, blunt nano-crack in a graded isotropic bulk material with a free surface. The mechanical model is based on classical elastodynamic theory and describes the elastic, isotropic, graded half-plane with quadratically varying material parameters along the depth coordinate. This model is extended to nano-mechanics by using non-classical boundary conditions and localized constitutive equations at the interface between crack and matrix material following the Gurtin-Murdoch surface elasticity theory. The computational technique employed is based on the non-hypersingular traction boundary integral equation method (BIEM) using a closed form Green's function for a half-plane consisting of a functionally graded material (FGM). The dependences of the diffracted and scattered waves and of the local stress concentration fields on key problem parameters such as size and depth of the embedded crack, surface elasticity effects, type and characteristics of the incident wave, and the dynamic interaction phenomenon between the crack and the free-surface boundary are all examined through parametric studies.