Volume 7, Issue 4
Bridging Methods for Atomistic-to-continuum Coupling and Their Implementation

Pablo Seleson & Max Gunzburger

Commun. Comput. Phys., 7 (2010), pp. 831-876.

Published online: 2010-07

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  • Abstract

Several issues connected with bridging methods for atomistic-to-continuum (AtC) coupling are examined. Different coupling approaches using various energy blending models are studied as well as the influence that model parameters, blending functions, and grids have on simulation results. We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region. We also show that continuum models are not appropriate for dealing with problems with singular loads, whereas AtC bridging methods yield correct results, thus justifying the need for a multiscale method. We investigate models that involve multiple-neighbor interactions in the atomistic region, particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.

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@Article{CiCP-7-831, author = {Pablo Seleson and Max Gunzburger}, title = {Bridging Methods for Atomistic-to-continuum Coupling and Their Implementation}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {4}, pages = {831--876}, abstract = {

Several issues connected with bridging methods for atomistic-to-continuum (AtC) coupling are examined. Different coupling approaches using various energy blending models are studied as well as the influence that model parameters, blending functions, and grids have on simulation results. We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region. We also show that continuum models are not appropriate for dealing with problems with singular loads, whereas AtC bridging methods yield correct results, thus justifying the need for a multiscale method. We investigate models that involve multiple-neighbor interactions in the atomistic region, particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.09.053}, url = {http://global-sci.org/intro/article_detail/cicp/7657.html} }
TY - JOUR T1 - Bridging Methods for Atomistic-to-continuum Coupling and Their Implementation AU - Pablo Seleson & Max Gunzburger JO - Communications in Computational Physics VL - 4 SP - 831 EP - 876 PY - 2010 DA - 2010/07 SN - 7 DO - http://dor.org/10.4208/cicp.2009.09.053 UR - https://global-sci.org/intro/cicp/7657.html KW - AB -

Several issues connected with bridging methods for atomistic-to-continuum (AtC) coupling are examined. Different coupling approaches using various energy blending models are studied as well as the influence that model parameters, blending functions, and grids have on simulation results. We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region. We also show that continuum models are not appropriate for dealing with problems with singular loads, whereas AtC bridging methods yield correct results, thus justifying the need for a multiscale method. We investigate models that involve multiple-neighbor interactions in the atomistic region, particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.

Pablo Seleson & Max Gunzburger. (1970). Bridging Methods for Atomistic-to-continuum Coupling and Their Implementation. Communications in Computational Physics. 7 (4). 831-876. doi:10.4208/cicp.2009.09.053
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