Effective elastic properties of composites with randomly distributed thin rigid fibres

The aim of the work is to analyse the effective elastic properties of composites with randomly distributed thin rigid fibres. The matrix is linear-elastic, homogenous and isotropic, and the fibres are perfectly connected to the matrix. Two-dimensional models of composites are analysed using the boundary element method (BEM). The method requires division of fibres and external boundaries of the plate into boundary elements. The boundary quantities are interpolated using quadratic shape functions. The direct solutions are: displacements and tractions along the external boundaries, displacements of fibres and interaction forces between the fibres and the matrix. Three numerical examples are presented in the paper: a single fibre in a circular disc, uniformly distributed parallel fibres and randomly distributed and oriented fibres in a square plate. The influence of distribution and orientation of fibres on effective Young’s moduli, Poisson’s ratios and Kirchhoff’s moduli is analysed. The examples demonstrate the accuracy and efficiency of the method.