Adaptive multiscale modeling of polymeric materials with Arlequin coupling and Goals algorithms

In this work, the notion of a posteriori estimation and control of modeling error is extended to large-scale problems in molecular statics. The approaches developed here involve systematic methods for multiscale modeling in which sequences of hybrid particle–continuum models are generated using an adaptive goal-oriented algorithm designed to control modeling error. We focus on a particular class of problems encountered in semiconductor manufacturing in which a molecular model is used to simulate the deformation of polymeric materials used in the fabrication of semiconductor devices. Algorithms are described which lead to a complex molecular model of polymer materials designed to produce an etch barrier, a critical component in imprint lithography approaches to semiconductor manufacturing. The surrogate model involves a combination of the molecular model of the polymer and a coarse-scale model of the polymer as a nonlinear hyperelastic material. This coupled model is based on the so-called Arlequin method. Coefficients for the nonlinear elastic continuum model are determined using numerical experiments on representative volume elements of the polymer model. Furthermore, a simple model of initial strain is incorporated in the continuum equations to model the inherent shrinking of the material. Three-dimensional numerical results demonstrate the effectiveness of the coupled model, the error estimates, and the adaptive modeling procedure.