Coupling of atomistic and continuum simulations using a bridging scale decomposition

By Gregory J. Wagner, Wing Kam Liu. 2003

703 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/2356f2b52a9d9a4b4baec9b0cf500cd2360768de

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

A mathematical framework of the bridging scale method (2006, methodology): “Besides simplifying considerably the original derivations in Reference [1], we further identify two error sources in this method.”
A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids (2007, methodology): “Among them are the coupled length scale method [1, 2], the bridging method [3, 4], the bridging domain method [5, 6], the method coupling atomistic and discrete dislocation plasticity [7], and the homogenization [8].”
Multiscale aggregating discontinuities: A method for circumventing loss of material stability (2008, methodology): “Engng 2008; 73:869–894 DOI: 10.1002/nme It could be argued that the proposed method offers little advantage over concurrent analysis at different scales, such as in Xiao and Belytschko [44], Wagner and Liu [45] or Karpov et al. [46], and this argument cannot be dismissed lightly.”
Bridging the scales in nano engineering and science (2006, methodology): “Formulation of absorbing inter- faces include damping (Broughton et al., 1999), Langevin equation (Wagner & Liu, 2003), precomputing exact absorbing boundary conditions for harmonic potentials (Cai et al., 2000), approximating exact absorbing boundary conditions and calibrating coefficients to…”
A bridging domain method for coupling continua with molecular dynamics (2004, methodology): “As in [7,8], the molecular displacements are modeled as the sum of a coarse scale (represented by finite element interpolants) and a fine scale.”
On the L2 and the H1 couplings for an overlapping domain decomposition method using Lagrange multipliers (2007, methodology): “Examples of multiscale modelling approaches for linking atomistic with macroscopic continuum models, are the handshake methods of Rudd and Abraham [18–20], the bridging-domain method of Belytschko [21, 22] and the bridging scale method [23].”
A two-scale model of granular materials (2012, methodology): “For this purpose we introduce a decomposition of the particle displacements into a coarse and a fine scale part like it is used in the Bridging Scale Method [28] to couple atomic and continuum simulations.”
Multi-scale micromorphic theory for hierarchical materials (2007, methodology): “To overcome this issue, the bridging scale method (Wagner and Liu, 2003; Kadowaki and Liu, 2004) can be used to split the computation among several domains, and therefore, use several time steps according to the level of resolution.”
A bridging scale method for granular materials with discrete particle assembly – Cosserat continuum modeling (2011, methodology): “Based on the bridging scale method (BSM) initially presented in nano mechanics [1,2], a new version of the BSM that couples discrete particle assembly modeling using the discrete element method (DEM) and Cosserat continuum modeling using the finite element method (FEM) at both micro–macro scale leve”
Coarse‐graining of multiscale crack propagation (2010, background): “For example, in Abraham et al. [19] and Khare et al. [20], the atomistic and quantum domains are embedded in a continuum domain, and in Xiao and Belytschko [21] and Wagner and Liu [22], atomistic domains are embedded in continuum domains.”
A surface Cauchy–Born model for nanoscale materials (2006, background): “Methods for both quasistatic [27–29] and dynamic coupling of atomistics and continua [30–40] have been proposed.”