This dissertation introduces a new multiscale stochastic finite element method (MSFEM) for determining the mechanical properties of polymer nanocomposites (PNC) consisting of polymers reinforced with single-wall carbon nanotubes (SWCNT). Obviously, reliable characterization of the various properties of nanomaterials such as PNC is indispensable in engineering applications. In this context, it is noted that the results reported in the literature often overestimate the actual mechanical properties of PNC reflecting uncertainty in the assumptions and approximations made. The method proposed herein uses actual experimental characterization information at the nano and micro scales to model the spatial randomness induced by the non-uniform dispersion of SWCNT in polymers, and to determine the mechanical properties of PNC.
First, the proposed method defines a material region and identifies randomness at the nanoscale. Second, it develops a random field model that quantifies the spatial randomness in PNC. Then, the method formulates a Monte Carlo finite element (FE) scheme used to solve a specific elasticity problem. This FE scheme incorporates the effects of the local mechanical properties of both phases in PNC and the size, shape, orientation, agglomeration, and dispersion of SWCNT in polymers.
The developed MSFEM is used in three applications in the dissertation. In the first, tensile test results of two PNC presented in the literature are used to derive estimates of the Young's modulus (YM) and Poisson ratio (PR). The results demonstrate the success of the proposed method in quantifying the effect of the spatial randomness on the mechanical properties of PNC. The second application uses experimental information about nanoindentation (NI) testing to numerically generate NI data which are subsequently used to compute estimates of the overall YM of PNC. The third application addresses the elastic stability of PNC structures. The computed results show the effect of incorporating SWCNT in polymers, as well as of the material randomness on the buckling loads and modes of the PNC structures.
Overall, the proposed MSFEM succeeds in modeling the effect of the spatial randomness on the mechanical properties of PNC by using actual experimental findings, and by efficiently combining information obtained at different length scales.