Multiscale Methods for Composites: A Review

Kanouté, Pascale; Boso, Daniela P.; Chaboche, Jean–Louis; Schrefler, Bernhard A.

doi:10.1007/s11831-008-9028-8

Cited by 455 publications

(256 citation statements)

References 156 publications

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“…These are the rates of the plastic strain vector defined in Eq. (33) and assume the following form at the component level…”

Section: 3mentioning

confidence: 99%

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A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Triantafyllou

Chatzi

2014

Comput Mech

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A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments.

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“…These are the rates of the plastic strain vector defined in Eq. (33) and assume the following form at the component level…”

Section: 3mentioning

confidence: 99%

“…On the other hand, multiscale methods use the fine scale information to formulate a numerically equivalent problem that can be solved in a coarser scale, usually through the finite element method [2,55]. An extensive review on the subject can be found in [33].…”

mentioning

confidence: 99%

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Triantafyllou

Chatzi

2014

Comput Mech

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“…Reviews of the different multiscale approaches can be found in Refs. [42][43][44]. The main objective of the homogenization method is to estimate the effective macroscopic properties of a heterogeneous material from the response of its underlying microstructure, thereby allowing to substitute the heterogeneous material with an equivalent homogeneous one.…”

Section: Introductionmentioning

confidence: 99%

“…So, the problem is reformed into the analysis of a single inclusion embedded in an infinite matrix [42]. Eshelby's conjecture on validity of his proposed method for only ellipsoidal inclusions has been addressed in Refs.…”

Section: Introductionmentioning

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

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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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“…The latter are either (semi-) analytical or numerical and predict the macro or meso-scopic response of heterogeneous materials from their micro-structure and constituents properties at reduced computational cost while maintaining an acceptable degree of accuracy. Kanouté et al (2009) ;Geers et al (2010) presented an overview of the different homogenization methods. Among those methods, the mean-field homogenization (MFH) approach is an efficient semi-analytical framework for the modeling of multi-phase composites.…”

Section: Introductionmentioning

confidence: 99%

A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites

Noels

Adam³

et al. 2013

International Journal of Plasticity

101

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This paper presents an incremental secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to define the Linear-Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods.

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Multiscale Methods for Composites: A Review

Cited by 455 publications

References 156 publications

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

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

A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites

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