Effect of Stochastic Nanotube Waviness on the Elastic and Thermal Properties of Nanocomposites by Fiber Embedment in Finite Elements

In this paper the impact of entangled and non-straight fibers in the determination of the effective elastic and thermal properties of polymer nanocomposite (PNC) is addressed. Most of the models in recent studies assume nanotubes to be well dispersed straight fibers. Nonetheless, experiments reveal that nanotube formation become wavy during the manufacturing process, due to their high aspect ratio and low bending stiffness. In the paper an attempt to model the behavior of entangled fibers is made and the influence of morphological parameters is investigated. First, an approach to generate random microstructures is developed. Then, using an embedded fiber finite element (EFFE) approach, the effective properties are computed for each of the random microstructures. This approach requires only a regular grid for the finite element (FE) mesh, circumventing the requisite computationally costly and human labor intensive mesh refinement of ordinary FE in order to capture the local morphology of the composite material. The EFFE approach is used in conjunction with an appropriately modified Monte Carlo procedure to derive statistics of the computed effective physical properties; several of these numerical results are found in good agreement with related experimental data.