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Abstract Based on the complex variable techniques combined with the boundary collocation method, a semi-analytical procedure is proposed to explore the influence of a functionally graded layer on the anti-plane shear behavior of a periodic fibrous composite. The distribution of the inclusions in the matrix is assumed to be periodically uniform so that the composite is represented by a square unit cell with a single inclusion coated with a functionally graded layer. The elastic properties of the functionally graded layer are assumed to vary continuously in the normal direction of the interface so that we may use a group of homogeneous perfectly-bonded sublayers (each having individual elastic constants) to describe approximately the mechanical response of the functionally graded layer to the interaction between it and the surrounding bulk (inclusion and matrix). Specific series with unknown coefficients are introduced to describe the complex potential functions of the representative unit cell of the composite. The unknown coefficients are determined from the continuity conditions on the interface and the periodic boundary conditions imposed on the edge of the unit cell. Once the complex potential functions are determined, the effective moduli of the composite are obtained according to the average-field theory. The effects of the fiber volume fractions, modulus of each component and material gradient parameter of the functionally graded layer on the properties of the composite are discussed via several numerical examples. The results show that whether the modulus of the matrix is larger or smaller than that of the inclusion, one may always design an appropriate material gradient parameter of the functionally graded layer to reduce the equivalent stress concentration around the inclusion. In addition, it is found that the material gradient parameter of the functionally graded layer may have a non-negligible influence on the effective moduli of the composite only when the inclusion is stiffer than the matrix.
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Received: 20 April 2020
Published: 22 February 2021
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2021, Vol. 42 
