Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 120, Issue -, Pages 245-256Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2017.05.006
Keywords
Triplet structure factor; Optimized Neumann series; Integral equation; Fourier transform; Spectral radius
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Funding
- National Foundation for Science and Technology Development (NAFOSTED) [107.02-2016.05]
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In this paper, we propose a new systematic procedure of estimating elastic properties of composites constituted of two phases, matrix and inclusions. A class of integral equations based on eigenstrain (or eigenstress) with the matrix as reference material is constructed with an explicit form in Fourier space. Each integral equation belonging to this class can yield estimates of the overall elastic tensor via Neumann series expansion. The best estimates and series are selected based on the convergence rate criteria of the series, i.e the spectral radius must be minimized. The optimized series is convergent for any finite contrast between inclusions and matrix. Applying the optimized series and the associated estimates to different microstructures yields very satisfying results when compared with the related full solution. For the case of a random distribution of spherical inclusions, exact relations between the elastic tensor and nth order structure factors are demonstrated. (C) 2017 Elsevier Ltd. All rights reserved.
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