Multiscale aggregating discontinuities: A method for circumventing loss of material stability

By Ted Belytschko, S. Loehnert, Jeong‐Hoon Song. 2008

254 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/08ef0a933408cff40c672e1a27de6fea9393440c

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In Mechanics of Materials

Citations in the corpus

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 , ”
Multiscale modeling and characterization of granular matter: From grain kinematics to continuum mechanics (2011, background): “Very recently, a FE2 algorithm was proposed by Belytschko et al. (2008) to aggregate discontinuities across scales in highly distorted areas in solids.”
Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids (2010, methodology): “Recently, computational homogenisation techniques have also been applied to determine constitutive relations for predefined interfaces [8, 9] as well as for cohesive cracks [10].”
The Schwarz alternating method in solid mechanics (2017, methodology): “The second class of methods incorporate micro-structural information from unit cells to compute effective macroscopic properties on the coarse domain [22, 8].”
Regularization of first order computational homogenization for multiscale analysis of masonry structures (2015, unknown): “Others, known as continuousdiscontinuous approaches, up-scale the RVE response to a traction-separation law (upon strain localization) used by a discontinuity inserted into the macro-scale model [6, 8, 30, 31, 32, 33, 37, 39].”
Return mapping for nonsmooth and multiscale elastoplasticity (2009, unknown): “E-mail: j-andrade@northwestern.edu”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, background): “For instance, in [9,8,109] a specific stress homogenization procedure has been proposed which excludes strain localization zones from the”
Homogenization-based multiscale crack modelling: from micro diffusive damage to macro cracks (2011, methodology): “In [18, 1], the authors have developed the MAD (Multiscale Aggregating Discontinuities) method in which a macroscopic crack is determined as equivalent to a bunch of microscale cracks.”
A computational library for multiscale modeling of material failure (2013, methodology): “Please refer to the work of Massart et al. [77,78] for the masonry cracking, Belytschko et al. [21], Belytschko and Song [22] (the MAD method), Allen et al. [124,125], Nguyen et al.[90–92 In the following, we will explain the very basic but general theory of semi-concurrent methods that leads us to…”
Bridging multiple structural scales with a generalized finite element method (2015, methodology): “[8, 9] present the multiscale projection method, another example of a continuous–discontinuous homogenization scheme where the XFEM [10, 11] is used to incorporate discontinuities at the macro-scale.”