Multi-scale computational homogenization: Trends and challenges

Geers, M.G.D.; Kouznetsova, V Varvara; Brekelmans, W.A.M.

doi:10.1016/j.cam.2009.08.077

Cited by 798 publications

(506 citation statements)

References 37 publications

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“…Detailed reviews on computational homogenization can be found in Refs. [197] and [198]. One of the widely used approaches in modeling heterogeneous materials is the unit-cell method which leads to a global macroscopic constitutive model for a heterogeneous material based on detailed modeling of the microstructure [199][200][201][202][203].…”

Section: Computational Homogenizationmentioning

confidence: 99%

“…On the other hand, it must remain sufficiently small to be considered as a volume element of continuum mechanics [223]. The first-order computational homogenization scheme critically relies on the principle of separation of scales, which requires that "the microscopic length scale is assumed to be much smaller than the characteristic length over which the macroscopic loading varies in space" [197]. This assumption is particularly valid when macrogradients remain small and material failure does not occur.…”

Section: 22mentioning

confidence: 99%

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Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

178

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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Section: Computational Homogenizationmentioning

confidence: 99%

Section: 22mentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

178

138

View full text Add to dashboard Cite

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“…This means that different structural models are used at different scales, which makes classical computational homogenisation, e.g. Geers et al (2010), not directly applicable as shown in detail by Edmans et al (2013), where an extension of that theory has been formulated. Referring to the original paper for the details of the derivation, a geometrically non-linear formulation is assumed at the large scale: in particular, it is assumed that displacements and rotations are large, while macro strains are small enough so that a geometrically linear formulation can be adopted at the small scale.…”

Section: Fully Nested Multiscale Analysis Of Risersmentioning

confidence: 99%

“…An alternative approach which does not have this limitation is a fully-nested multi-scale procedure (Geers et al, 2010), currently in widespread use for the modelling of composite materials. With this method, at each integration point (i.e.…”

Section: Introductionmentioning

confidence: 99%

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An accurate and computationally efficient small-scale nonlinear FEA of flexible risers

2016

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a b s t r a c tThis paper presents a highly efficient small-scale, detailed finite-element modelling method for flexible risers which can be effectively implemented in a fully-nested (FE 2 ) multiscale analysis based on computational homogenisation. By exploiting cyclic symmetry and applying periodic boundary conditions, only a small fraction of a flexible pipe is used for a detailed nonlinear finite-element analysis at the small scale. In this model, using three-dimensional elements, all layer components are individually modelled and a surface-to-surface frictional contact model is used to simulate their interaction. The approach is applied on a 5-layered pipe made of inner, outer and intermediate polymer layers and two intermediate armour layers, each made of 40 steel tendons. The capability of the method in capturing the detailed nonlinear effects and the great advantage in terms of significant CPU time saving are demonstrated by comparing the results obtained on elements of pipe of different lengths, equal to one pitch length L p as

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Elastostatics of Lattice Materials

Pasini¹,

Arabnejad²

2017

Dynamics of Lattice Materials

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Multi-scale computational homogenization: Trends and challenges

Cited by 798 publications

References 37 publications

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

An accurate and computationally efficient small-scale nonlinear FEA of flexible risers

Elastostatics of Lattice Materials

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