Multiscale homogenization of n-component composites with semi-elliptical random interface defects |
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| Institution: | 1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;2. Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw, Poland;3. Department of Higher Mathematics and Mechanics, Engels Institute of Technology (Branch), Saratov State Technical University, Saratov Region, Ploschad Svobodi 17, 413100 Engels, Russian Federation;4. Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov, Russian Federation;1. School of Mechatronic Engineering, Northwestern Polytechnical University, Xi''an 710072, China;2. Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi''an 710072, China;3. Institute of Printing and Packaging Engineering, Xi''an University of Technology, Xi''an 710048, China;1. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy;2. Extreme Computing Research Center, Computer Electrical and Mathematical Sciences & Engineering Department, King Abdullah University of Science and Technology, Saudi Arabia;1. Corporate Sector Research and Advance Engineering, Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen, Germany;2. Chair for Continuum Mechanics, Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Kaiserstr. 10, 76131 Karlsruhe, Germany |
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| Abstract: | Effective elastic characteristics of periodic multicomponent composite materials with random interface defects are studied in the paper. The defects are assumed to be semi-elliptical and lying with major semi axes along the interfaces, where minor and major semi-axes as well as the defects number are given as input random variables. The homogenization approach has a multiscale character—some algebraic approximation is used first to calculate effective elastic parameters of the interphase including all defects located at the same interface. Equations for interphase random elastic parameters are obtained using MAPLE symbolic mathematics in conjunction with probabilistic generalized perturbation method. A different homogenization method is applied at the micro scale, where the cell problem is solved numerically using the Finite Element Method (FEM) program. Since the composites considered exhibit random variations of both elastic properties and the interface defects, the overall homogenized characteristics must be obtained as random quantities, which is realized on the micro scale by the Monte-Carlo simulation. The proposed interface defects model obeys the porosity effects resulting from the nature of some matrices in engineering composites as well as the interface cracks appearing as a result of composites ageing during static or fatigue fracture. |
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