Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

Abstract

PurposeThe paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.Design/methodology/approachThe fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.FindingsDifferent from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.Originality/valueAccording to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

Non‐local stress and electric displacement solution of a 3D semi‐permeable rectangular crack in infinite orthotropic piezoelectric materials

“…Meanwhile, the non-local theory have been extended to solve the mixed-mode crack problem in a functionally graded magneto-electro-elastic material [32]. Liu et al [33][34][35] analyzed the non-local theory solution of 3D rectangular crack in orthotropic elastic medium and piezoelectric materials. Shi et al [36] established a fully coupled 2D magneto-electro-thermo-elastic (METE) theory with non-local and surface effects.…”