Abstract
We review some recent developments in the coupling of atomistic and continuum models based on the blending of the two models in a bridge region connecting the other two regions in which the models are separately applied. We define four such models and subject them to patch and consistency tests. We also discuss important implementation issues such as: the enforcement of displacement continuity constraints in the bridge region; and how one defines, in two and three dimensions, the blending function that is a basic ingredient in the methods.
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References
Badia, S., et al.: A Force-Based Blending Model for Atomistic-to-Continuum Coupling. Inter. J. Multiscale Comput. Engrg. (to appear)
Badia, S., et al.: On Atomistic-to-Continuum (AtC) Coupling by Blending. SIAM J. Multiscale Modeling and Simulation (submitted)
Belytschko, T., Xiao, S.: Coupling Methods for Continuum Model with Molecular Model. Inter. J. Multiscale Comput. Engrg. 1, 115–126 (2003)
Belytschko, T., Xiao, S.: A Bridging Domain Method for Coupling Continua with Molecular Dynamics. Comp. Meth. Appl. Mech. Engrg. 193, 1645–1669 (2004)
Ciarlet, P.: The finite element method for elliptic problems. SIAM, Philadelphia (2002)
Fish, J., et al.: Concurrent AtC Coupling Based on a Blend of the Continuum Stress and the Atomistic Force. Comp. Meth. Appl. Mech. Engrg. (to appear)
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© 2008 Springer-Verlag Berlin Heidelberg
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Badia, S., Bochev, P., Gunzburger, M., Lehoucq, R., Parks, M. (2008). Bridging Methods for Coupling Atomistic and Continuum Models. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_2
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DOI: https://doi.org/10.1007/978-3-540-78827-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78825-6
Online ISBN: 978-3-540-78827-0
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