A class of general algorithms for multi-scale analyses of heterogeneous media

By Kenjiro Terada, Noboru Kikuchi. 2001

485 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/09240dceab221b91267c734abbf3cff7c4918f47

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Concurrent topology optimization of multiscale structures with multiple porous materials under random field loading uncertainty (2017, unknown): “…: DMA xð Þ ¼ P xð Þð ÞαDH : ð2Þ The macro scale and micro scale correlate with each other through the mathematical homogenization theory (Bensoussan et al. 1978; Terada and Kikuchi 2001) which will produce DH in the following equation, DH ¼ 1 Yj j ∫YD MI yð Þ−DMI yð Þ:∇yΨ yð Þdy; ð3Þ where |Y| is…”
Micro‐macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis (2018, unknown): “min f (U, s; ?̂?) = ∫∂B0 T̂M · UdΓ, (21)”
Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme (2002, background): “The basic ideas of this approach have been presented in papers by Suquet [9], Guedes and Kikuchi [10], Terada and Kikuchi [11], and Ghosh et al. [12; 13] and further developed and improved in more recent works by Smit et al. [14], Miehe et al. [15], Michel et al. [16], Feyel and Chaboche [17], Terad”
An efficient multi-scale method for non-linear analysis of composite structures (2015, methodology): “Over time, thanks to the work to several authors, the method was extended to large deformations with arbitrary non-linear material behavior at the microsctructural scale [19, 20, 21, 22, 23, 24].”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, methodology): “The use of RVE-based theories in situations of practical interest relies almost exclusively on techniques of computational homogenization, based on finite element methods [30,57,64,77,78,79,80,81,82, 93,115,121].”