Eigenstrain and Fourier series for evaluation of elastic local fields and effective properties of periodic composites |
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| Affiliation: | 1. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043 Cassino, FR, Italy;2. Department of Civil Engineering, University of Salerno, via Ponte don Melillo, 84084 Fisciano, SA, Italy;1. Università di Perugia, Civil and Environmental Engineering Dept., Materials Science and Technology, Strada di Pentima 4, 05100 Terni, Italy;2. DIEM Alma Mater Studiorum, Università di Bologna, viale Risorgimento 2, 40136 Bologna, Italy;3. Sapienza Università di Roma, Dept. of Chemical Engineering Materials Environment, via Eudossiana 18, 00184 Roma, Italy;4. Università degli Studi di Camerino, School of Architecture and Design, viale della Rimembranza, 63100 Ascoli Piceno, Italy;1. Faculty of Technology and Metallurgy, RudjerBoskovic 16, 1000, Skopje, Macedonia;2. Department of Chemistry “G.Ciamician”University of Bologna, Via Selmi2, 40126, Bologna, Italy;3. Biocompatibility, Technological Innovations and Advanced Therapies Laboratory - BITTA, Rizzoli Orthopedic Institute, Via di Barbiano 1/10, 40136, Bologna, Italy;1. University Politehnica Bucharest, Splaiul Indepentei 313, Bucharest, Romania;2. ICPE-CA, Bucharest, Romania |
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| Abstract: | The elastic stress and strain fields and effective elasticity of periodic composite materials are determined by imposing a periodic eigenstrain on a homogeneous solid, which is constrained to be equivalent to the heterogeneous composite material through the imposition of a consistency condition. To this end, the variables of the problem are represented by Fourier series and the consistency condition is written in the Fourier space providing the system of equations to solve. The proposed method can be considered versatile as it allows determining stress and strain fields in micro-scale and overall properties of composites with different kinds of inclusions and defects. In the present work, the method is applied to multi-phase composites containing long fibers with circular transverse section. Numerical solutions provided by the proposed method are compared with finite element results for both unit cell containing a single fiber and unit cell with multiple fibers of different sizes. |
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| Keywords: | A. Fibres B. Elasticity C. Micro-mechanics Numerical analysis |
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