On reflected interactions in elastic solids containing inhomogeneities |
| |
| Institution: | 1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA;2. Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903, USA;1. Institute of Mechanics, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39016 Magdeburg, Germany;2. Department of Civil, Environmental and Geo-Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis, MN 55455, USA;1. Department of Wind Energy, Technical University of Denmark, Risø Campus, Frederiksborgvej 399, Building 228, 4000 Roskilde, Denmark;2. Department of Management and Engineering, University of Padova, Stradella S. Nicola, 3, 36100 Vicenza, Italy;1. School of Civil Engineering, Central South University, Changsha, 410083, PR China;2. Key Laboratory of Mechanics on Environment and Disaster in Western China, The Ministry of Education of China, Lanzhou University, Lanzhou, 730000, PR China;3. Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000, PR China;4. Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan, 430023, PR China;5. Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ, 08903, USA |
| |
| Abstract: | Interactions in linear elastic solids containing inhomogeneities are examined using integral equations. Direct and reflected interactions are identified. Direct interactions occur simply because elastic fields emitted by inhomogeneities affect each other. Reflected interactions occur because elastic fields emitted by inhomogeneities are reflected by the specimen boundary back to the individual inhomogeneities. It is shown that the reflected interactions are of critical importance to analysis of representative volume elements. Further, the reflected interactions are expressed in simple terms, so that one can obtain explicit approximate expressions for the effective stiffness tensor for linear elastic solids containing ellipsoidal and non-ellipsoidal inhomogeneities. For ellipsoidal inhomogeneities, the new approximation is closely related to that of Mori and Tanaka. In general, the new approximation can be used to recover Ponte Castañeda–Willis׳ and Kanaun–Levin׳s approximations. Connections with Maxwell׳s approximation are established. |
| |
| Keywords: | Effective elastic properties Elastic interactions Reflected interactions Thermodynamic limit Integral equations |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
