Multi-scale computational homogenization: Trends and challenges

By Mgd Marc Geers, V. Kouznetsova, W. Brekelmans. Journal of Computational and Applied Mathematics, 2010

1,075 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8a1e89698a08415c07e82aa56fafbddad37f8427

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Citations in the corpus

An efficient multi-scale method for non-linear analysis of composite structures (2015, background): “Most of the work on FE(2) multi-scale procedures are done on analyzing the numerical performance of RVE [33, 34] or on connecting different scales [35].”
Homogenization-based multiscale crack modelling: from micro diffusive damage to macro cracks (2011, methodology): “Although the method is computationally expensive, it has been proved to be a valuable and flexible (due to the lack of an assumption on the macroscopic constitutive model) tool for analyzing a wide range of heterogeneous materials with complex microstructures with highly nonlinear behavior see, amon”
Multiscale modeling meets machine learning: What can we learn? (2019, background): “…boundary conditions in terms of the first derivatives of the macroscale fields, first order coupling, or higher derivatives, higher order coupling [33, 49, 107]; (ii) micromechanics approaches [70, 89]; (iii) reduced order and simplified models for upscaling [108, 120]; (iv) scale-bridging or…”
Novel boundary conditions for strain localization analyses in microstructural volume elements (2012, background): “The outcome provides the constitutive input for macroscale analyses, whereas simultaneous insight is obtained into the fine-scale phenomena, see for example references [4–25], a recent review paper [26], and references therein.”
The heterogeneous multiscale method* (2012, neutral): “In the chemistry and biology literature, this is often called the stochastic simulation algorithm (SSA), or Gillespie algorithm, named after an algorithm that realizes this process exactly (see Gillespie (1976)).”
Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation (2012, neutral): “[10], as a nonexhaustive list).”
Computational homogenization in magneto-mechanics (2013, methodology): “Reviews of different multi-scales approaches are available in the literature (Kanouté et al., 2009; Pindera et al., 2009; Charalambakis, 2010; Geers et al., 2010).”
Bridging multiple structural scales with a generalized finite element method (2015, background): “The aforementioned list of mutiscale methods is far from exhaustive; a recent review of the state-of-the-art in multiscale computational homogenization techniques is available in [35].”
High-performance model reduction techniques in computational multiscale homogenization (2014, methodology): “In the homogenization approach adopted in this work — commonly known as ﬁrst-order homogenization [32,40] — the strain ﬁeld (cid:2) ð x Þ at any point x 2 X is assumed to be decomposed into macroscopic and ﬂuctu-ating contributions; under the hypothesis of inﬁnitesimal deformations, this…”
Development of an ABAQUS plugin tool for periodic RVE homogenisation (2018, methodology): “Therefore, using the periodic RVE homogenisation approach is essential, as it can analyse general geometries [19].”
Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties (2016, background): “Computational homogenization, also referred to as FE2, is a nested finite element method that, in recent years, has proven to be very effective [4].”
Adaptive reduced basis finite element heterogeneous multiscale method (2013, background): “capturing the effective behavior of a problem without scale resolution on the whole computational domain has therefore received major attention during the past few years [1, 2, 3, 4, 5].”