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

Paul T. Bauman, J. Tinsley Oden*, Serge Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)799-818
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Issue number5-8
StatePublished - Jan 15 2009
Externally publishedYes


  • Adaptive modeling
  • Arlequin coupling
  • Error estimation
  • Goals algorithms
  • Multiscale modeling

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mechanics


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