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      On the optimality of the window method in computational homogenization

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      Author
      Temizer, I.
      Wu, T.
      Wriggers, P.
      Date
      2013
      Source Title
      International Journal of Engineering Science
      Print ISSN
      0020-7225
      Volume
      64
      Pages
      66 - 73
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      The window method, where the microstructural sample is embedded into a frame of a homogeneous material, offers an alternative to classical boundary conditions in computational homogenization. Experience with the window method, which is essentially the self-consistent scheme but with a finite surrounding medium instead of an infinite one, indicates that it delivers faster convergence of the macroscopic response with respect to boundary conditions of pure essential or natural type as the microstructural sample size is increased to ensure statistical representativeness. In this work, the variational background for this observed optimal convergence behavior of the homogenization results with the window method is provided and the method is compared with periodic boundary conditions that it closely resembles. © 2013 Elsevier Ltd. All rights reserved.
      Keywords
      Computational homogenization
      Self-consistent scheme
      Thermal conduction
      Computational homogenization
      Faster convergence
      Homogeneous materials
      Macroscopic response
      Micro-structural
      Optimal convergence
      Optimality
      Periodic boundary conditions
      Sample sizes
      Self-consistent scheme
      Thermal conduction
      Window methods
      Boundary conditions
      Optimization
      Homogenization method
      Permalink
      http://hdl.handle.net/11693/21078
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.ijengsci.2012.12.007
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