A Monte Carlo Finite Element Method for Determining the Young's Modulus of Polymer Nanocomposites using Nanoindentation Data

摘要

This article presents a Monte Carlo finite element method (MCFEM) for determining the Young's modulus (YM) of polymer nanocomposites (PNC) using Nanoindentation (NI) data. The method treats actual NI data as measurements of the local YM of PNC; it further assesses the effect of the non-homogeneous dispersion of carbon nanotubes in polymers on the statistical variations observed in experimental NI data. First the method simulates numerically NI data by developing a random field and a multiscale homogenization model. Subsequently, the MCFEM applies the spectral representation method to generate a population of samples of local YM values. These local values are then used in conjunction with a stochastic finite element scheme to derive estimates for the YM of PNC. The statistical processing of the ensemble of FE solutions yields overall YM values that agree well with corresponding results reported in the literature.