Singularity characteristic analyses for magneto-electro-elastic V-notches

• Linear singularity eigen-equation for MEE V-notch is established.
• Iterative solution for the transcendental eigen-equation is avoided.
• Singularities for plane and anti-plane MEE V-notches are considered.
• Singularity order and eigen-angular function can be yielded simultaneously.

Due to the material or geometrical discontinuities, the stress, electric displacement and magnetic induction may become theoretically infinite and singular at the vertexes of magneto-electro-elastic (MEE) V-notches, where the mechanical failure or dielectric breakdown may initiate from. Based on the assumption of the asymptotic expansions of the physical fields near the vertex, the characteristic differential equations with respect to the singularity order are derived from the equilibrium equations and Maxwell equations. After a set of variable replacement, these non-linear differential equations are transformed into the linear ones. The traditional iterative method for solving the transcendental equation is avoided. The mechanical, electric and magnetic boundary conditions together with interfacial continuity conditions are also expressed by the combination of the singularity order and characteristic angular functions. The singularity characteristic analyses for MEE V-notches are transformed into a problem of solving characteristic ordinary differential equations with variable coefficients. The singularity orders and characteristic angular functions can be derived by introducing the interpolating matrix method to solve the established characteristic equations. Herein, the singularities for the in-plane and anti-plane MEE V-notches are respectively investigated. The influence of the poling direction on the singularities of MEE V-notches is discussed. The role of the volume fraction of the BaTiO3 inclusions on the singularities of MEE V-notches is studied. The obtained results can be used to design MEE products for reducing the singularity induced by the V-notch.