13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Fracture Analysis of Particulate MEE Materials Using a Domain-Independent Interaction Integral Method Hongjun Yu1,3,*, Linzhi Wu2,* 1 Institute of Applied Mathematics, Harbin Institute of Technology, Harbin 150001, China 2 Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, China 3 School of Civil Engineering, Harbin Institute of Technology, Harbin 150001, China * Corresponding author: yuhongjun@hit.edu.cn (Hongjun Yu); wlz@hit.edu.cn (Linzhi Wu) Abstract This paper first introduces an expanded tensor notation to express the basic relations of magneto-electro-elastic (MEE) media and then, derives a domain formulation of the interaction integral on the basis of the expanded tensor notation for computing the intensity factors (IFs). The present interaction integral does not require material properties to be differentiable and moreover, it is domain-independent for material interfaces, which may make the interaction integral to become one of the most promising techniques in analyzing the crack problems of MEE composites. Then, the numerical implementation of the interaction integral combined with the extended finite element method (XFEM) is introduced. Using this method, the crack problems of a particulate MEE plate are studied. Keywords Magneto-electro-elastic (MEE), Crack, Interaction integral, Intensity factors (IFs), Extended finite element method (XFEM) 1. Introduction Magneto-electro-elastic (MEE) materials have drawn significant interest in several engineering fields as a class of important functional materials, such as magnetic field probes, electronic packaging, actuators, waveguides, sensors, phase investors, transducers. However, a great drawback of MEE materials is their inherent brittleness and low fracture toughness. Generally, these materials may fail prematurely in service due to some defects arising during the manufacturing process and thus, it is of practical significance to learn the fracture feature of MEE materials. Liu et al. [1] studied Green's functions for a cracked MEE body. Wang and Mai [2] obtained a general two-dimensional (2D) solution of the MEE fields around the crack tip. Gao et al. [3] derived an explicit solution in closed form for the intensity factors (IFs) and electro-magnetic fields inside a crack in MEE media. After that, considerable theoretical research works were carried out on the fracture problems of MEE materials. However, most of the theoretical research works restrict MEE media to be infinite and only a few simple configurations can be solved. Therefore, numerical techniques are usually employed in actual fracture analyses of MEE materials. Among numerical methods, the interaction integral has generated a great interest for its convenience in decoupling mechanical stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF). The interaction integral was proposed by Stern et al. [4] to decouple mechanical mode-I and mode-II SIFs on the basis of the J-integral by a superposition of two admissible states. Recently, the interaction integral was extended to solve the IFs of piezoelectric (PE) media [5] and those of MEE media [6]. For MEE materials, the interaction integral published previously has a shortcoming that is it requires the material properties to be differentiable. Generally, MEE materials are a category of composites composed of PE and PM phases, and the interfaces between constituent phases may reduce their reliability since the interfaces generally act as sources of failures in service. Therefore, the interfaces can not be ignored when the fracture behaviors of MEE composites are concerned. Fortunately, Yu et al. [7] have developed a new interaction integral for PE solids which is domain-independent for material interfaces. This point brings a great convenience to the fracture analysis of the composites with
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