Theoretical And Numerical Solutions For Fracture Of Magnetoelectroelastic Materials

Magnetoelectroelasticity that possess strong electromechanical, electromagnetic, magnetomechanical coupling are prime candidates for the development of sensors, transducers, actuators, memory and recording devices, etc. Because of their brittleness, cracks and flaws are inevitably presented in such magnetoelectroelastic materials under the utilizing and manufacturing procedures of intelligent structures and devices. Afterwards, many mechanical researchers have fixed their attentions at the failure of magnetoelectroelastic material weakened by a flaw recently.The research in the dissertation consists of two parts. In the first part, the mode-I Griffith and penny-shaped interfacial cracks in the magnetoelectroelastic material are investigated. In the second part, the various meshless methods are adopted to solve the fracture problem of magnetoelectroelastic materials. The contents of the first and second parts are arranged in the following in detail.Several fracture problems are investigated based on the magnetoelectroelastic coupling.The aim is to obtain the fracture properties of the cracks in the magnetoelectroelastic materials and structures, which will provide a theoretical foundation and technical supports to the design of the magnetoelectroelastic materials and structures.The dynamic response of an interfacial crack between two dissimilar magnetoelectroelastic layers is investigated under magnetic, electrical and mechanical impact loadings. Four kinds of ideal crack-face assumptions, i.e., magnetoelectrically impermeable, magnetically impermeable and electrically permeable, magnetically permeable and electrically impermeable and magnetoelectrically permeable, are adopted separately. The dynamic field intensity factors and energy release rates are derived. The effects of loading combinations and crack configurations especially for the former on the dynamic response are examined according to energy release rate criterion. The numerical results show that, among others, a negative magnetic (or electrical) loading is generally prone to inhibit the crack extension rather than a positive one for a magnetically (or electrically) impermeable interfacial crack.A penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectroelastic loads is investigated under the boundary condition of magnetoelectrically impermeable on the crack surfaces. By using Hankel transform technique, the mixed boundary value problem is firstly reduced to a system of singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The field intensity factors and energy release rate are determined. Numerical results reveal the effects of crack configuration, electric or magnetic loads and material parameters of magnetoelectroelastic layers on crack propagation and growth.The two-dimensional (2D) fracture problem of nonhomogeneous magneto-electro-thermo-elastic materials under dynamically thermal loading is investigated by the meshless local Petrov-Galerkin (MLPG) method. In this MLPG analysis, the moving least squares (MLS) method is adopted to approximate the physical quantities, and the Heaviside step function is taken as a test function. The validity and efficiency of the MLPG method are firstly examined. The crack problem of a nonhomogeneous magneto-electro-thermo-elastic plate is then considered. The materials parameters are assumed to vary in either the height or width direction of the plates. The field intensity factors (FIFs) including the stress intensity factor (SIF), electric displacement intensity factor (EDIF), magnetic induction intensity factor (MIIF) and mechanical mode-I strain energy release rate (MSERR) of the magneto-electro-thermo-elastic materials are computed. The effects of the nonhomogeneous parameters especially the thermal nonhomogeneous parameters on the fracture behavior of crack tips are emphatically evaluated and discussed according the energy release rate criterion.The fracture behaviors of two-dimensional (2-D) planar and axisymmetric problems of magneto-electro-elastic materials are investigated by the method of the meshless local Petrov-Galerkin (MLPG) coupled with finite element method (FEM). In the coupled method, the physical domain is divided into two parts, which are formulated with the MLPG and FEM, respectively. In the MLPG region, the moving least squares (MLS) method is adopted to approximate the physical quantities, and the Heaviside step function is taken as a test function. The interface elements with a novel shape function in present study are introduced. The validity and efficiency of the MLPG/FEM method are verified by the results obtained in the literature. The extended crack open displacements (CODs), especially the field intensity factors (FIFs) of the crack tips for magneto-electro-elastic materials are calculated and analyzed.The crack problem of infinite two-dimensional magnetoelectroelastic solid is studied by means of extended traction boundary element-free method. Using integration by parts an extended traction boundary integral equation that only involves Cauchy singularity is derived. The extended dislocation density on the crack surface is expressed as the combination of the characteristic terms and unknown weight functions, and the radial point interpolation method is adopted to approximate the unknown weight functions. The numerical scheme of the extended traction boundary element-free method is established, and an effective numerical procedure is used to evaluate the Cauchy singular integrals. The FIFs are computed for some selected cracked problems that contain straight, curved and branched cracks, and good numerical results are obtained. The fracture properties of these crack problems are further discussed.