Effective elastic properties of composites with randomly distributed thin rigid fibres
- PDF / 2,075,858 Bytes
- 15 Pages / 595.276 x 790.866 pts Page_size
- 86 Downloads / 201 Views
O R I G I NA L
Piotr Fedelinski
Effective elastic properties of composites with randomly distributed thin rigid fibres
Received: 30 January 2020 / Accepted: 18 August 2020 © The Author(s) 2020
Abstract 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. Keywords Composite · Rigid fibre · Effective property · Homogenization · Representative volume element · Boundary element method
1 Introduction The stiffness and strength of composites can be increased by using thin fibres as reinforcement. Modelling of such composites can be significantly simplified, assuming that the fibres are perfectly rigid. This assumption can be applied to fibres that are much stiffer than the matrix surrounding them and is now often used to analyse composites reinforced with nanofibres. Overall effective elastic properties of composites can be obtained using various homogenization methods (see, for example, the handbooks by Nemat-Nasser and Hori [1], Mura [2] and Qu and Cherkaoui [3]). Analytical methods are usually used to analyse single rigid fibres in the infinite domain and computational methods for composites with multiple fibres. Dundurs and Markenscoff [4] applied the method of Green’s function to thin rigid inclusions perfectly attached to the elastic matrix loaded by concentrated forces, dislocations and a concentrated couple to determine stress fields. Li and Ting [5] used the Stroh formalism and Fredholm integral equations to analyse displacement and stress fields for a rigid or an elastic line inclusion in an anisotropic elastic infinite plate uniformly loaded at infinity. Hu et al. [6] analysed the influence of rigid-line fibres and a bi-material interface on stress intensity factors at crack tips using integral equations. Pingle et al. [7] derived the solutions for the rigid-line inclusions using the duality principle. The method was applied to analysis of stresses in the neighbourhood of a fibre and the composite compliance. Gorbatikh et al. [8] studied the influence of stress intensity factors at the tips of rigid fibres on effe
Data Loading...
