Adaptive Multiscale Modeling of Polymeric Materials

Paul Bauman, University of Texas

An important class of multiscale modeling procedures for nano-systems aim at linking nanoscale and continuum models to reduce the computational effort of mechanical simulations. Continuum models can efficiently capture coarse scale features of the system of interest, but at the expense of the fidelity of the fine scale information. Conversely, molecular or atomistic models can accurately resolve small-scale features, but are computationally intractable for simulating systems of engineering interest. The goal of multiscale models is to exploit the fact that, in many systems, only a small percentage of the material requires fine scale resolution. The primary difficulty of the multiscale approach is the determination of the regions in which the nanoscale and continuum models should be used and modeling the transition between the two. Ideally, the final multiscale model should permit the automatic selection of these regions and control modeling errors to within a user-specified tolerance.

Here, goal-oriented error estimation and adaptive modeling (collectively referred to as the Goals method) is used to study the mechanics of polymer materials within the context of semiconductor manufacturing processes. The Goals methodology is a general framework based upon computing error estimates in a quantity of interest and adaptively selecting the models to be used in the appropriate regions of the domain in order to control the error in the quantity of interest. The method has been successfully applied to several problems in atomistic and molecular modeling. In this presentation, a molecular statics model of a lattice polymer and its correspondence to a class of nonlinear elasticity models will be shown. The Arlequin method will be established within this context, and accompanying solution algorithms discussed. Finally, results of error estimation and adaptive modeling for several quantities of interest will be presented.

Abstract Author(s): Paul T. Bauman