Electro-magneto-elastic analysis of a piezoelectromagnetic strip with a finite crack under longitudinal shear

The singular stress, electric and magnetic fields in a piezoelectromagnetic strip containing a Griffith crack under longitudinal shear are obtained by the theory of linear piezoelectromagneticity. The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip. Fourier transforms are used to reduce the mixed boundary value problems of the crack, which is assumed to be either impermeable or permeable, to dual integral equations. The solution of the dual integral equations is then expressed in terms of Fredholm integral equations of the second kind. Expressions for strains, stresses, electric fields, electric displacements, magnetic fields and magnetic inductions in the vicinity of the crack tip are derived. For the impermeable crack, the electric field intensity factor (EFIF) and the magnetic field intensity factor (MFIF) depend on the edge loading conditions, whereas, the EFIF and MFIF for the permeable crack are always zero. The results obtained show that the width of the strip have significant influence on the field intensity factors and the energy release rates.