A new integral equation formulation of two-dimensional inclusion–crack problems |
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| Institution: | 1. Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China;2. School of Mechanical Engineering, Yonsei University, Seoul 120-749, Korea;1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China;1. Institute of Microstructure and Properties of Advanced Materials, Beijing University of Technology, Beijing 100022, PR China;2. Institute of Laser Engineering, Beijing University of Technology, Beijing, 100022, PR China;1. School of Mechanical and Aerospace Engineering, Nanyang Technological University of Singapore, 50 Nanyang Avenue, Singapore 639798, Singapore;2. Infineon Technologies Pte Ltd, 8 Kallang Sector, Singapore 349282, Singapore |
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| Abstract: | A new integral equation formulation of two-dimensional infinite isotropic medium (matrix) with various inclusions and cracks is presented in this paper. The proposed integral formulation only contains the unknown displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks. In order to solve the inclusion–crack problems, the displacement integral equation is used when the source points are acting on the inclusion–matrix interfaces, whilst the stress integral equation is adopted when the source points are being on the crack surfaces. Thus, the resulting system of equations can be formulated so that the displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks can be obtained. Based on one point formulation, the stress intensity factors at the crack tips can be achieved. Numerical results from the present method are in excellent agreement with those from the conventional boundary element method. |
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