Modeling of Nanoindentation Data and Characterization of Polymer Nanocomposites by a Multiscale Stochastic Finite Element Method

This article presents a multiscale stochastic finite element method (MSFEM) for treating Nanoindentation (NI) data and determining the Young's modulus (YM) of polymer nanocomposites (PNC) consisting of polymers reinforced with single-walled carbon nanotubes (SWCNT). The method treats actual NI data as measurements of the local YM of PNC. The variations observed in the local mechanical properties of PNC are used to assess the effect of the non-uniform spatial distribution and dispersion of SWCNT in polymers on the overall mechanical properties. First, the method generates numerically a population of NI data by developing a random field and a multiscale homogenization model and by applying the spectral representation method. Next, the NI data are used in a Monte Carlo finite element (FE) scheme that yields estimates for the overall YM of PNC. The effectiveness of the proposed method in characterizing the mechanical properties of PNC is demonstrated by the agreement of the derived numerical results with pertinent experimental findings.