A penny-shaped crack in an infinite linear transversely isotropic medium subjected to uniform anti-symmetric heat flux: Closed-form solution

• The problem of a penny-shaped crack with uniform anti-symmetric heat flux applied over upper and lower surfaces of the crack in transversely isotropic magneto-electro-thermo-elastic medium is investigated.
• We obtain the complete [explicit closed-form] solution to the problem for the first time via potential theory method.
• The solutions to the similar problems in transversely isotropic thermopiezoelectric, thermopiezomagnetic, thermoelastic materials are also presented as degenerated cases.

The problem of a penny-shaped crack subjected to anti-symmetric uniform heat flux in an infinite transversely isotropic magneto-electro-thermo-elastic medium is investigated. Although we start our derivations in magneto-electro-thermo-elastic medium, the solution presented in this paper is also applicable for linear transversely isotropic thermopiezoelectric, thermopiezomagnetic, thermoelastic materials. Previous researchers obtained the closed-form solution to the similar problem in crack plane. In regards to full-space solution, they expressed it in multiple integration or line integrals involving Bessel functions. In this article, the authors find that the full-space solution could be in terms of the explicit elementary functions via potential theory method developed by Fabrikant. What's more, the closed form solutions in all kinds of linear transversely isotropic medium can serve as benchmarks for future numerical studies of multiphase composites.