Investigation of the behavior of a mixed-mode crack in a functionally graded magneto–electro-elastic material by use of the non-local theory

Jamia, Nidhal; El-Borgi, Sami; Rekik, Mahmoud; Usman, Shameem

doi:10.1016/j.tafmec.2014.09.002

Cited by 18 publications

(1 citation statement)

References 40 publications

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“…For the past few years, Zhou et al [31] studied a mode-I crack in functionally graded materials by the non-local theory. 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.…”

Section: Introductionmentioning

confidence: 99%

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

2021

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The paper presents the non-local stress and electric displacement solution of a 3D semi-permeable rectangular crack in infinite orthotropic piezoelectric materials (OPMs). With the help of the generalized Almansi's theorem and 2D Fourier transform, the boundary problem is formulated by three pairs of dual integral equations, and the displacement jumps across the crack surfaces are defined. The Schmidt method is used to solve the dual integral equations. The non-local stress field (NSF) and the non-local electric displacement field (NEDF) along the crack edges are deduced. Numerical results are reported to explain the influence of the size of the rectangular crack, the lattice parameter and the electric permittivity of the air inside the crack on the NSF and the NEDF at the crack edges in OPMs in detail. The present non-local solutions exhibit no stress and electric displacement singularities along the crack edges, and may be benefit future works.

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