Dynamic fracture behavior of a nanocrack in a piezoelectric plane

Abstract

AbstractScattering of time harmonic plane waves by a finite blunt nano‐crack in a homogeneous transversely isotropic piezoelectric plane under plane strain conditions is studied. The mechanical model combines: (a) classical elastodynamic theory for the bulk piezoelectric solid, where the total wave comprises both incident and scattered wave field; (b) non‐classical boundary conditions and localized constitutive equation for the interface between the crack and piezoelectric matrix within the frame of the Gurtin‐Murdoch surface elasticity theory. The computational approach uses a non‐hypersingular traction based boundary integral equation method (BIEM) basing on the fundamental solution derived in closed form by Radon transforms. Furthermore, the parametric study is presented which demonstrates the sensitivity of the generalized stress concentration fields near the crack‐tip to the key parameters as the size of the crack, surface properties, coupled nature of the piezoelectricity phenomenon, type and properties of the incident wave such as frequency, wave length and wave propagation direction, dynamic interaction between the crack, incident wave and coupled electro‐elastic continuum.