Anisotropic analysis of fibrous and woven materials part 2: Computation of effective conductivity

Micro-scale modeling enables the study of composite material properties at a fundamental level. These properties must be computed at the scale of a representative elementary volume in order to accurately inform macro-scale response simulations. The main focus of this work is to predict the effective thermal conductivity of anisotropic materials based on the three-dimensional reconstruction of their fibrous structure, obtained from X-ray micro-tomography. A computational method that accounts for multiple scales of anisotropy of woven composites is presented, including that of the constituting fibers and tows, and that of woven architectures. The finite volume formulation and implementation based on the Multi-Point Flux Approximation method is detailed. The algorithm was verified against analytical solutions and validated against experiments on both random and woven fibrous samples. In order to apply the method to real materials, the techniques presented in the first part of this study [1] are used to compute the local material orientation, necessary to align the conductivity tensor along the fibers. The method is ultimately used to reverse engineer the orthotropic conductivity of a single carbon fiber by performing parametric studies and comparing against experiments.