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Anti-Plane Fracture Problems in Magnetoelectroelastic Materials

Author: LiGang
Tutor: WangBaoLin
School: Harbin Institute of Technology
Course: Applied Mathematics
Keywords: Magnetoelectroelastic materials Magnetoelectroelasticity Energy release rate Intensity factor
CLC: O346.1
Type: Master's thesis
Year: 2008
Downloads: 45
Quote: 0
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Abstract


Magnetoelectroelastic materials made of piezoelectric/piezomagnetic materials can exhibit a significant magneto electric effect. They have good prospect in information technology, non-destructive testing, new material technology, new intelligent materials and structure, and many other high-tech fields. In recent years, the study of correlative mechanical behavior in magnetoelectroelastic materials has attracted more theoretical emphases, and gradually become a hotspot topic of mechanics, material science and physics.At present, the research results of mechanical behaviors in Magneto- electroelastic materials are very abundant.This paper mainly considers the anti-plane crack problems （only out-of-plane displacement and in-plane electric fields and in-plane magnetic inductions） in magnetoelectroelastic materials subjected to mechanical-electro-magnetic loads.The contents include the following parts:Under the mechanical-electro-magnetic loads, the complex fuction knowledge is used to obtain the analytic complex functions and give the corresponding analytic expressions. The result shows that the strain, electric and magnetic field strengths are uniform and vary with the shape of inclusion.The deduced analytic expressions are used to study the mechanical, electric and magnetic fields inside the elliptical inclusion. The changes of the corresponding stress, electric displacement and magnetic induction are analyzed when the region of elliptical inclusion approaches a crack. The result shows that the strain, electric and magnetic field strengths have not the imaginary parts and have only components parallel to x2 axis.The deduced analytic expressions are used to study the mechanical, electric and magnetic fields along the interface. The changes of the corresponding stress, electric displacement and magnetic induction are analyzed when the the region of elliptical inclusion approaches a crack. The result shows that the strain, electric and magnetic field strengths equal the remote applied strain, electric and magnetic field strengths, respectively. Based on the definition of the energy and energy release rate, the expressions are presented. When the region of elliptical inclusion approaches a crack, energy and energy release rate approach zeroes. The derived expressions are used to study the mechanical, electric and magnetic fields at the crack tip, give the expressions of the intensity factors, and give the relations between the intensity factors and energy release rate. The result shows that the electric and magnetic loadings have a great influence on the energy release rate.According to the results in this thesis, the study of the crack in the magnetoelectroelastic materials is similar to that in piezoelectric materials. However, this paper studies the problem for the most general case, which is more practical and applicable. The results in this thesis provide the theoretical models for the study of numerical analysis on the crack in Magnetoelectro- elastic materials.

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory
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