Theoretical And Numerical Study On Fracture Of Magnetoelectroelastic Media

In this doctoral dissertation, fracture model and quantitative analysis method of piezoelectric material and magnetoelectroelastic material are investigated. Based on the PS (Polarization Saturation) model in the piezoelectric media, the fracture behaviors of the magnetoelectroelastic media with the Strip Electric-Magnetic Polarization Saturation (SEMPS) are discussed, including their analytical solutions and numerical methods or results. After that, the effect of mechanical, electric and magnetic loadings on the fracture behaviors is displayed. The main works are as follows:(1) By using the dislocation theory and the concept of electric dislocation, the local stress intensity factor and local J-intergal in the PS model are expressed by the conventional dislocation and electric dislocation, which is essential to extend the PS model to the SEMPS case in the magnetoelectroelastic media.(2) The concept of magnetic dislocation is proposed by extending the electric dislocation. After that, the magnetic potential discontinuity penetrated the spatial region surrounded by the crack face is expressed by the continuous distribution of magnetic dislocation. The extended dislocation theory of fracture of the magnetoelectroelastic media is studied.(3) Basic equations and approach to the study of the Strip Electric-Magnetic Polarization Saturation (SEMPS) are obtained for the fracture behavior of magnetoelectroelastic media, where the electric field in the strip electric yielding zone ahead of the crack tip is equal to the saturation electric displacement, while the magnetic induction in the strip magnetic yielding zone is equal to the saturation magnetic induction. By using the extended Stroh formalism and the extended dislocation modeling of a crack, the analytical solution of SEMPS for the Griffith crack problem under the electrically and magnetically impermeable boundary condition in a magnetoelectroelastic medium is obtained. The sizes of the electric yielding zone and the magnetic yielding zone, the extended intensity factors and the local J-integral are obtained. The effect of the combined mechanical-electric-magnetic loadings on the local J-integral is studied. The results show that the sizes of these two saturation zones are dependent on material constants, the size of crack, the applied mechanical-electric-magnetic loadings, as well as on the saturation electric displacement and the saturation magnetic induction. However, the local J-integral has nothing to do with the saturation electric displacement and the saturation magnetic induction.(4) The Hybrid Extended Displacement Discontinuity-Fundamental Solution Method (HEDD-FSM) of the PS model of a crack in a piezoelectric medium is proposed. In this HEDD-FSM, the solution is expressed approximately by a combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack and on the electric yielding zone. The unknown constants in the solutions are determined by letting the approximated solution satisfy the prescribed conditions on the boundary of the domain, on the crack face and on the electric yielding zone. One key step of this method is choosing a suitable virtual boundary, which circles the real zone boundary. The efficiency and the accuracy of the HEDD-FS method are verified on fracture analysis of finite elastic media and infinite piezoelectric media. The obtained results exhibit that the numerical data on the basis of the HEDD-FS method for the case of finite elastic media agree well with the analytical solution. When the media becomes large enough or infinite, the numerical results of PS model on the basis of the HEDD-FS method for the case of infinite piezoelectric media also agree well with the analytical solution. In such case, the proposed numerical method is acceptable and reliable.(5) By using the HEDD-FS method, the PS model of a crack is studied quantitatively in finite piezoelectric media under the electrically impermeable boundary condition and electrically semi-permeable boundary condition.(6) The SEMPS model of a crack are studied in infinite magnetoelectroelastic media under the electrically and magnetrically impermeable boundary condition by using the extended displacement discontinuity (EDD) method, which could be used to study fracture of SEMPS model under other boundary condition.