Evaluation of mode III interface cracks in magnetoelectroelastic bimaterials by symplectic expansion

Abstract

The mode III interface crack between two dissimilar magnetoelectroelastic materials is studied by means of symplectic expansion. Four crack surface electromagnetic assumptions, that is, electrically and magnetically permeable, electrically permeable and magnetically impermeable, electrically impermeable and magnetically permeable, and electrically and magnetically impermeable, are taken into account. In the symplectic space, stress, electric displacement, and magnetic induction are found to be the dual variables of the displacement, electric potential, and magnetic potential. The Hamiltonian governing equations that allow the use of the method of separation of variables are formulated by employing the variational principle of mixed energy. Expressions for the mechanical, electric, and magnetic fields are derived explicitly in the series of symplectic eigensolutions with coefficients to be determined by the boundary conditions, and so are the fracture parameters, such as field intensity factors and energy release rates for dissimilar bimaterials. Numerical results are provided to verify the validity of the present method and reveal the influences of the material constants and boundary conditions.

Accurate fracture analysis of electrically permeable/impermeable cracks in one-dimensional hexagonal piezoelectric quasicrystal junction

“…Unlike the classical one-variable Lagrangian system, the fundamental unknowns of the Hamiltonian system are composed of original variables and its dual variables. For the anti-plane fracture analysis, the original variable vector and its dual variable vector can be defined as [44] q…”