Overall elastic properties of composites from optimal strong contrast expansion. (1st August 2017)

• Record Type: Journal Article
• Authors: To, Quy-Dong; Nguyen, Minh-Tan; Bonnet, Guy; Monchiet, Vincent; To, Viet-Thanh
• Is Part Of: International journal of solids and structures. Volume 120(2017)
• Page Start: 245
• Page End: 256
• Publication Date: 2017-08-01
• Subjects: Triplet structure factor -- Optimized Neumann series -- Integral equation -- Fourier transform -- Spectral radius; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2017.05.006
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: 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 n th order structure factors are demonstrated.