Anti-plane analysis on a finite crack in a one-dimensional hexagonal quasicrystal strip |
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| Institution: | 1. College of Science, China Agricultural University, Beijing 100083, PR China;2. College of Engineering, China Agricultural University, Beijing 100083, PR China;3. Sinomatech Wind Power Blade Co., Ltd, Beijing 100092, PR China;4. Civil and Environmental Engineering School, University of Science and Technology Beijing, Beijing 100083, PR China;5. Institute of Mechanics, University of Kassel, 34125 Kassel, Germany;1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China;2. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China;3. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China;4. Soft Matter Research Center (SMRC), Zhejiang University, Hangzhou, 310027, China;1. School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China;2. Henan Key Engineering Laboratory for Anti-fatigue Manufacturing Technology and School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China;3. Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada;1. Department of Engineering Mechanics, Southeast University, Nanjing 210096, Jiangsu, PR China;2. Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, United States;3. School of Civil Engineering, Southwest Forestry University, Kunming 650224, Yunnan, PR China;1. College of Science, China Agricultural University, Beijing 100083, China;2. College of Engineering, China Agricultural University, Beijing 100083, China;3. Department of Civil Engineering, University of Akron, Akron, OH 44325-3905, USA |
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| Abstract: | The anti-plane fracture problem for a finite crack in a one-dimensional hexagonal quasicrystal strip is analyzed. By using Fourier transforms, the mixed boundary value problems are reduced to the dual integral equations. The solution of the dual integral equations is then expressed by the complete elliptic integrals of the first and the third kinds. The expressions for stress, strains, displacements and field intensity factors of the phonon and phason fields near the crack tip are obtained exactly. The path-independent integral derived by a conservation law equals the energy release rate, which can be used as a fracture criterion for a mode III fracture problem. |
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| Keywords: | Quasicrystal Finite crack Fourier transform Stress intensity factor Energy release rate |
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