Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme

By V. Kouznetsova, Mgd Marc Geers, W. Brekelmans. 2002

886 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b4feff3ee9e27e4d097a16272a2975887463223b

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In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “Higher-order computational homogenization [98,100] does not assume scale separation; hence, the local kinematic and kinetic quantities of the RVE are homogenized within a finite region of the macroscopic scale by considering their Taylor series expansion with the desired number of higher-order…”
An enhanced multi‐scale approach for masonry wall computations with localization of damage (2007, background): “in which the mesoscopic characteristic length is much smaller than the length scale associated to variations of the macroscopic fields [ 16 ].”
Regularization of first order computational homogenization for multiscale analysis of masonry structures (2015, methodology): “Some approaches regularize the response of the RVE by using a higher order theory at the macro-scale, such that the information about a material characteristic length is naturally taken into account [3, 16, 17, 18, 22, 23, 52].”
Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM (2015, background): “For the detailed description of the procedure, refer, for example, to [27, 28].”
Computational homogenization in magneto-mechanics (2013, background): “Several authors have examined the mechanical response of composites considering finite strains (Hill, 1972; Nemat-Nasser, 1999; Miehe et al., 1999; Kouznetsova et al., 2002; Miehe, 2003; Costanzo et al., 2005; Hirschberger et al., 2008; Temizer and Wriggers, 2008; Ricker et al., 2010; McBride et…”
Multi-scale boundary element modelling of material degradation and fracture (2007, methodology): “Multi-scale homogenization methods provide the advantage of modelling a specific material at different scales simultaneously [6—9].”
Predictive multiscale theory for design of heterogeneous materials (2008, methodology): “The interfacial debonding behavior is modeled via atraction–separation law derived from quantum mechanics calculations [1] and scaled toincludetheeffectofinterfacialdefects[22,23].Thesample is loaded in pure shear strain using fully periodic boundary conditions, the details of which can be found her”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “To account for the homogenized second-order stress tensor Q̂ in the macroscopic scale a SOCH must be used [29, 60, 61].”
Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension (2009, background): “For this type of loading, the deterministic contribution on the shape of the FPZ is significant [30].”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, methodology): “The approach is not restricted linear behaviors, and second-order computational homogenization has been extended to the nonlinear context through the FE(2) method in [35,36,22].”
Computational homogenization for heterogeneous thin sheets (2010, methodology): “[13, 25]) and the second-order computational homogenization [32, 34], the macroscopic deformation gradient tensor is usually enforced to be equal to the RVE volume average of the microstructural deformation gradient tensor.”