A two-scale approach with homogenization for the computation of cracked structures

By Pierre-Alain Guidault, Olivier Allix, L. Champaney, J. Navarro. 2007

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A two‐scale approximation of the Schur complement and its use for non‐intrusive coupling (2011, methodology): “For that reason, we also investigated long-scale approximations, most of which are inspired from multiscale homogenization techniques; that is, to prescribe a small number of interface loads on the whole subdomain, representing their ‘large-scale’ behaviour [12, 13, 17, 19, 20].”
Coarse‐graining of multiscale crack propagation (2010, background): “[17] and Ibrahimbegovic and Markovic [18] are in this class.”
A computational library for multiscale modeling of material failure (2013, methodology): “The works by Guidault et al. [51], Eckardt and Könke [35] and Lloberas-Valls et al. [74] are such examples.”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, methodology): “We refer to the global-local non-intrusive coupling strategy [57–59], the domain decomposition methods [60, 61], and the LATIN method [62–64] for other approaches sharing this splitting concept to handle non-linear localization.”