Closed-form field in an infinite space of transversely isotropic multiferroic composite medium with an elliptical or penny-shaped crack: 3D exact analysis

This paper studies the mode I problem of an elliptical or penny-shaped crack contained in an infinite space of multiferroic composite material with transverse isotropy. Closed-form analytical solutions and numerical results are presented in this work in a systematic way. The crack is postulated to be either electrically/magnetically permeable or impermeable. For the first time, boundary integro-differential equations, corresponding to the crack with different magneto-electric properties, are established using the generalized method of potential theory in conjunction with the static general solutions. For four physical cases, closed-form coupled magneto-electro-elastic field variables in the space are explicitly obtained. Crack surface displacement, generalized stress intensity factor and crack compliance matrix generalized from the rock mechanics all turn out to be an intrinsic combination of a material factor and a geometrical factor. The weak and strong interactions in multiferroic composite media are exhaustively accounted for. The obtained analytical solutions may serve as benchmarks for numerous forthcoming simplified and numerical studies.