Time-domain Singular Integral Equation Method For Dynamic Fracture Of2D Piezoelectric/Magneto-electro-elastic Materials

It is the rapidly developing science and technology that play an important role in the material and mechanical industry. The appearance of intelligent materials like piezoelectric materials and magnet-electroelastic materials especially give a booming impetus to intelligent material manufacturings. However, despite the better and better skills, the cracks in the materials are still inevitable. These defects do great harm to the structures, what’s worse, once suffered dynamic loads, the structures will be damaged quickly and easily. That’s really a challenge for fracture mechanical researchers. Since there are a lot of difficulties in numerical and theoretical to solve the dynamic fracture problems, only a few studies have been conducted on this issue. So far, most of fracture analysis of piezoelectric/magnetoelectric materials are carried out only considering static loading. The analytical solutions for dynamic fracture analysis are limited to a specific geometry and loading configuration. Actually, the shape of cracks and the arbitrariness of the spatial distribution of cracks have a big difference. Due to the mutual interaction between multiple cracks tending to reduce the strength of the structures, the research of multiple cracks has also important practical value. In this paper, the research objects are cracked piezoelectric and magnetoelectroelastic materials, and numerical method are applied for analysis the dynamic response of cracks under impact loading. The main contribution of this paper are as follows:1. For a single crack in two dimensional infinite piezoelectric material, a Cauchy type singular integral equations are established according to the known Green’s function. By using the properties of the fundamental solutions and the main-part method, the singular field vicinity of the crack tips are obtained. In the numerical part, the quadrature formula of Lubich and Gauss Chebyshev formula are applied to approximate the integral equations. The numerical results of typical examples are analyzed and compared with those obtained.2. For multiple non-intersection cracks subjected to impact loading, singular integral equations are formed, and numerical method are applied to solve the equations. Computational program are developed, and kinds of numerical results are obtained. The effect of geometric distribution of cracks on dynamic stress intensities are shown in the graphs. For intersection cracks, boundary integral equations are also established. Besides, the variation of singular index at the intersection point are shown.3. The above numerical method of piezoelectric materials are extended to fracture analysis of magneto-electro-elastic materials. Singular integral equations are established, and the singular stress filed near the crack tips are obtained. Then, numerical results are calculated to analyze the variation of dynamic stress intensity factors when crack is subjected to the mechanical, electrical and magnetic impact loading under different crack boundary conditions.4. Singular boundary integral equations are also built for arbitrary oriented cracks acted upon impact loading in magneto-electro-elastic materials. Then the integral equations are discretized by numerical methods and several numerical results are obtained. The effect of configuration of cracks on variation of dynamic stress intensities are discussed at the last part.