Predictive multiscale theory for design of heterogeneous materials

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Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “Among the recent works, we can mention the method of Guidault et al. [36] based on the LATIN method and domain decomposition concepts; the multigrid method proposed in [61]; the method of Cloirec et al. [13] based on Lagrange multipliers; the multiscale projection method of Belytschko et al. [10, 44”
Multiscale modeling and characterization of granular matter: From grain kinematics to continuum mechanics (2011, methodology): “Another similar multiscale method is the recently proposed virtual power domain decomposition (Liu and McVeigh, 2008), which has been used to do concurrent and hierarchical simulations in solids with heterogeneities at multiple scales.”
Statistical volume element method for predicting microstructure–constitutive property relations (2008, methodology): “By intelligently combining the use of these single scale methods, various multiscale methods have been developed to compute material behavior efficiently without losing crucial finer scale details [6,13,14,25,27,39].”