A magnetoelectroelastic medium with an elliptical cavity under combined mechanical–electric–magnetic loading

• Published in: Theoretical and applied fracture mechanics Vol. 45; no. 3; pp. 227 - 237
• Main Authors: Zhao, M.H., Wang, H., Yang, F., Liu, T.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.06.2006; Elsevier
• Subjects: Crack; Elliptic cavity; Exact sciences and technology; Exact solution; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Magnetoelectroelastic medium; Physics; Self-consistent method; Solid mechanics; Static elasticity (thermoelasticity...); Strain energy density factor; Structural and continuum mechanics; Self-consistent method; Magnetoelectroelastic medium; Elliptic cavity; Strain energy density factor; Crack; Exact solution; Self consistency; Barium titanates; Modeling; Composite material; Combined load; Ferrite; Infinite medium; Cavity; Magnetic field; Magnetoelastic effect; Surface conditions; Crack array; Magnetostriction; Strain energy; Energy density; Multiaxial load; Electroelasticity; Stroh formalism; Piezoelectric materials; Magnetomechanical properties; Cobalt compound; Electromechanical properties
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/j.tafmec.2006.03.006

The solution for an elliptical cavity in an infinite two-dimensional magnetoelectroelastic medium subject to remotely uniformly applied combined mechanical–electric–magnetic loadings is obtained by using the Stroh formalism and the exact boundary conditions along the surface of the cavity. By letting the minor-axis of the cavity to zero the solution for a crack is deduced. A self-consistent method is proposed to calculate the real crack opening under the combined mechanical–electric–magnetic loadings. The method requires that the crack opening is the minor-axis of the elliptical opening profile. Beside the real crack solution, four different extreme models, i.e., the impermeable crack, permeable crack, electrically impermeable and magnetically permeable crack and electrically permeable and magnetically impermeable crack, are discussed. An expression of the strain energy density factor is derived. Numerical results of the strain energy density at the crack tip are given for a BaTiO 3–CoFe 2O 4 composite with the piezoelectric BaTiO 3 material being the inclusion and the magnetostrictive CoFe 2O 4 material being the matrix. The effects of the proportion of the two phases, permeability of the crack to electric and magnetic fields, the electric and magnetic loadings on the strain energy density factor are discussed.