Homogenization of heat transfer in fibrous composite with stochastic interface defects

Abstract

The main aim of this work is verification how the interface defects appearing frequently in-between the fibres and the matrix affect the effective heat conductivity of fibrous composites. This analysis is provided assuming uncertainty in these defects geometry and frequency, which quite naturally induces randomness in homogenized characteristics of such a composite. Homogenization of this composite is mathematically formulated and numerically implemented using the Finite Element Method (FEM) and also using a combination of triangular and quadrilateral finite elements of the system ABAQUS© with linear approximating functions. Polynomial response functions relating effective conductivity with these defects parameters have been recovered using specific series of the FEM experiments and of traditional formulation of the Least Squares Method. Three different numerical techniques have been employed to determine the basic probabilistic characteristics of the effective heat conductivity – Monte-Carlo simulation, semi-analytical method and also iterative generalized stochastic perturbation technique. Numerical experiments completed assuming Gaussian uncertainties in the interface defects prove their remarkable influence on the homogenized composite. Composite computational model prepared in the system ABAQUS could be next extended towards anisotropic distribution of the fibres within the Representative Volume Element (RVE).