  Numerical modeling of viscoelastic properties is critical to developing the
structure-property relationship of polymer nanocomposites. While it is
recognized that the altered polymer region near filler particles, the
interphase, significantly contributes to enhancements of composite properties,
the spatial distribution of interphase properties is rarely considered due to
lack of local property measurements. In recent years, the Atomic Force
Microscopy (AFM) technique has begun to make local property measurements of the
interphase available. In the light of the increasing availability of AFM data,
in this work a new interphase representation for modeling the viscoelastic
properties of polymer nanocomposites is proposed. The proposed interphase
representation disentangles the interphase behavior by two separate components
-- single-body interphase gradient and multi-body compound effect, whose
functional forms are learned via data mining. The proposed interphase
representation is integrated into a Finite Element model, and the effects of
each component of the interphase representations are numerically studied. In
addition, the advantages of the proposed interphase representation are
demonstrated by comparison to a prior simulation work in which only a uniform
effective property of the interphase is considered. Moreover, the proposed
interphase representation is utilized to solve the inverse problem of inferring
spatial distribution of local properties using Bayesian Inference on
experimental data.
