Influence of non-uniformly periodic distribution of fibers in composites on the stress field and effective shear modulus
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O R I G I NA L PA P E R
Hui-Feng Yang · Cun-Fa Gao
Influence of non-uniformly periodic distribution of fibers in composites on the stress field and effective shear modulus under anti-plane shear
Received: 6 May 2020 / Revised: 11 September 2020 / Accepted: 23 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Based on the complex variable techniques combined with the boundary collocation method, a semianalytical procedure is proposed to explore the anti-plane shear behavior of non-uniformly periodic fibrous composites under uniform remote shear loadings. Specific series with unknown coefficients are introduced to describe the complex potentials of the representative unit cell (RUC) of the composite. The unknown coefficients are determined from the continuity conditions on the interface, the periodic boundary conditions imposed on the edge of the unit cell and the remote loading conditions. Once the complex potentials are determined, the effective moduli of the composite are obtained according to the average-field theory. Extensive numerical examples are provided to investigate the influence of the periodic distribution of the inclusions, the moduli of each component, and the volume fraction of the inclusions on the local stress fields and effective shear moduli of the composite. Numerical results show that the inhomogeneous distribution of the inclusions may induce a continuous area with high equivalent stress in the matrix under certain loadings and material properties of each component. However, we could overcome this disadvantage by changing the components or the periodic arrangement of the inclusions. For the case of a RUC with double inclusions, the two inclusions with the same shear moduli arranged symmetrically in the direction of 45 degrees may induce the transverse isotropy of the composite. Nevertheless, when the two inclusions are horizontally arranged and the volume fraction of the inclusions is large enough (more than 10%), the composite generally shows orthotropic characteristics. 1 Introduction Although there are many kinds of microstructure forms in heterogeneous materials, fibers arrangement in a composite usually has certain periodicity to realize mechanized production. A periodic structure indicates the repeated distribution of unit cells. Theoretically, a periodic structure is an extreme situation in which the microstructures change from complete disorder to a strict arrangement. Based on engineering practices, various natural materials have periodic or nearly periodic microstructures. Therefore, in manufacturing activities, we have been able to control the distribution of fibers in a composite precisely, making it more urgent to understand, from the theoretical point of view, the influence of the periodic arrangement of fibers on the properties of a composite in order to design a perfect composite. H.-F. Yang · C.-F. Gao (B) State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 21
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