Research Article
Adaptive generalized mathematical homogenization framework for nanostructured materials
Jacob Fish,
Aiqin Li,
Fazel Yavari,
Corresponding Author
Jacob Fish
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.Search for more papers by this authorAiqin Li
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
Search for more papers by this authorFazel Yavari
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
Search for more papers by this authorJacob Fish,
Aiqin Li,
Fazel Yavari,
Corresponding Author
Jacob Fish
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.Search for more papers by this authorAiqin Li
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
Search for more papers by this authorFazel Yavari
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
Search for more papers by this authorAbstract
We present an adaptive generalized mathematical homogenization (AGMH) framework for modeling nanostructured materials with evolving defects at a finite temperature. By this approach molecular dynamics model is employed in the vicinity of defects whereas constitutive equation-free continuum model is used away from the defects. The proposed framework consists of the following salient features: (i) a constitutive law-free cohesive element whose behavior is modeled by the atomistic representative volume element (ARVE) and (ii) a dislocation detection band embedded in the ARVE aimed at detecting dislocations passing from or into the interior of the nanograins. These features of the model are critical to studying deformation of nanocrystals where only a small portion of the problem domain requires molecular resolution. Copyright © 2010 John Wiley & Sons, Ltd.
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