Theoretical Investigations On Mechanical Behavior Of Fracture And Stability For Some Advanced Electromagnetic Materials And Structures

Due to their unique properties and potential background of applications in engineering, the fracture behavior, instability and other mechanical properties of the electromagnetic materials have become the basic problems in applications and design. This thesis mainly aims at the advanced materials which arouse worldwide attentions recently, such as superconductor, dielectric elastomer, magnetoelectroelastic and functionally graded materials. Based on the Magneto-Electro-Elastic coupling properties, the fracture behavior, instability and other mechanical behavior in electromagnetic materials are investigated.Firstly, the stress distribution, the magnetostriction and the crack problem in the superconductor are analyzed. Accroding to the elasticity theory, the stress induced by the flux pinning and the non-superconducting inclusions in the bulk superconductors are analyzed. The stress distribution in the superconductor and the effects of elastic moduli and volume fraction on the magnetostriction in the superconducting composite are discussed. In addition, based on a simple assumption in which the effect and disturbance of the crack on the shielding current and the magnetic field are neglected. The Bean and Kim model are adopted. Using the basic knowledge of the fracture mechanics, the crack problems in the rectangular and cylindrical superconductors are discussed, respectively. The variations of the stress intensity factors are considered in the magnetization process of zero-field cooling (ZFC) and field cooling (FC). When the magnetic field reduction process is different, the variations of the stress intensity factors are different, and there are differences between the results obtained from the Bean model and the Kim model.Secondly, the instability and viscoelastic problems in the dielectric elastomer have been taken into account. During the process of inflation of the balloon which subject to the electric field, the Maxwell stress model is used to discuss the instability problem in the dielectric elastomer balloon. The results show that the failure-modes in the dielectric balloon are related to the material properties and the loading history. In addition, using the linear perturbation analysis, the instability problem is discussed in the dielectric elastomer, and the critical stretch values are obtained at different electrical field. It is found that the instability in the dielectric elastomer are dependent of the material parameter. Based on the tensor analysis and the finite element method, the viscoelastic behavior subject to the electric field is obtained in the dielectric elastomer. The numerical resuts agree well with the theoretical results. We further show the creep of the dielectric elastomer subject to a constant electrical field and the strain history of the dielectric elastomer subjected to a cyclic electrical load.Finally, the crack problems in the functionally graded materials and the magnetoelectroelastic materials are discussed. Using the Fourier transform method, a singular integral equation for a static crack in the functionally graded materials is obtained, and the equation can be solved numerically. The results obtained show the effects of nonhomogeneity constant, relative crack length and thickness ratio on the stress intensity factor. For the transient crack problem in the magnetoelectroelastic materials, the Laplace transform and inversion are employed to reduce the problem to singular integral equations for the impermeable crack. Numerical results are shown graphically to illustrate the effects of relative loading parametersκD andκB, and the crack configuration on the dynamic behavior of the crack in the magnetoelectroelastic strip. The results indicate that the electric and magnetic impact play a great role in the transient fracture behavior.