A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

Vu, Quoc Huy; Brenner, Rénald; Castelnau, Olivier; Moulinec, Hervé; Suquet, Pierre

doi:10.1088/0965-0393/20/2/024003

Cited by 26 publications

(21 citation statements)

References 32 publications

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“…Finally, it can be also noted that the agreement between the FFT and the collocation results, at both moderate and high contrast, confirms the accuracy of the collocation method, as is documented in the literature (see, for instance, Brenner et al, 2002;Rekik and Brenner, 2011;Vu et al, 2012).…”

Section: Granular Two-phase Compositessupporting

confidence: 82%

“…However, the present results apply to more general situations as will be illustrated below (see also Vu et al, 2012, Appendix A).…”

Section: Restrictions On Prony Seriesmentioning

confidence: 63%

“…The viscoelastic response of the checkerboard polycrystal exhibits a continuous effective relaxation spectrum (Masson et al, 2012) and has been investigated under various loading conditions including creep, relaxation and deformation at constant strain-rate in previous studies (Vu et al, 2012;Suquet, 2012;Masson et al, 2012). Here, the harmonic steady-state response of the polycrystal subjected to a sinusoidal macroscopic strain loading with amplitude ε * and frequency ω: ε(t) = ε * e ıωt is considered.…”

Section: Checkerboard Polycrystalsmentioning

confidence: 99%

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Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Brenner

Suquet

2013

International Journal of Solids and Structures

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This paper is devoted to the effective behavior of linear viscoelastic heterogeneous materials with a particular emphasis on their transient response. First, two new asymptotic relations for the overall creep function are derived at short and large times. They are related to the retardation spectrum of the composite and involve second-order moments per phase of the stress field for the purely elastic and purely viscous problems. In the context of harmonic loadings, these relations provide exact frequential asymptotic conditions on the overall storage and loss moduli. Second, by making use of these asymptotic results, an approximate model is proposed. It consists in approximating the retardation spectrum of the composite by a single discrete Dirac mass. Its accuracy is assessed by comparison with exact analytical results, fullfield simulations and collocation results for several classes of composites and polycrystals.

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Section: Granular Two-phase Compositessupporting

confidence: 82%

“…However, the present results apply to more general situations as will be illustrated below (see also Vu et al, 2012, Appendix A).…”

Section: Restrictions On Prony Seriesmentioning

confidence: 63%

Section: Checkerboard Polycrystalsmentioning

confidence: 99%

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Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Brenner

Suquet

2013

International Journal of Solids and Structures

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“…Ricaud and Masson (2009) showed that for specific microstructures (two-phase composites whose overall elastic properties are given by one of the Hashin-Shtrikman bounds) the relaxation spectrum of the composites remains discrete. This implies (Ricaud and Masson, 2009;Vu et al, 2012) that the overall constitutive relations of such composites can be alternatively written with a finite number of internal variables. Conversely for composites with a continuous relaxation spectrum, an infinite number of internal variables is required and the advantage of an analytical model for subsequent use in a macroscopic numerical computation is lost.…”

Section: Introductionmentioning

confidence: 99%

“…Conversely for composites with a continuous relaxation spectrum, an infinite number of internal variables is required and the advantage of an analytical model for subsequent use in a macroscopic numerical computation is lost. This has motivated the introduction of approximate models with a finite number of internal variables (or equivalently with a finite number of relaxation times) mostly based on the approximation of the continuous relaxation spectrum by Prony series (Rekik and Brenner, 2011;Vu et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Extension of the Nonuniform Transformation Field Analysis to linear viscoelastic composites in the presence of aging and swelling

Largenton

Michel

Suquet

2014

Mechanics of Materials

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This study presents a micromechanical modeling by the Nonuniform Transformation Field Analysis (NTFA) of the viscoelastic properties of heterogeneous materials with aging and swelling constituents. The NTFA proposed by Suquet (2003, 2004) is a compromise between analytical models and full-field simulations. Analytical models, which are available only for specific microstructures, provide effective constitutive relations which can be used in macroscopic structural computations, but often fail to deliver sufficiently detailed information at small scale. At the other extreme, full-field simulations provide detailed local fields, in addition to the composite effective response, but come at a high cost when used in nested Finite Element Methods. The NTFA method is a technique of model reduction which achieves a compromise between both approaches. It is based on the observation that the transformation strains (viscous strains, eigenstrains) often exhibit specific patterns called NTFA modes. It delivers both effective constitutive relations and localization rules which allow for the reconstruction of local fields upon post-processing of macroscopic quantities.A prototype of the materials of interest here is MOX (mixed oxides), a nuclear fuel which is a three-phase particulate composite material with two inclusion phases dispersed in a contiguous matrix. Under irradiation, its individual constituents, which can be considered as linear viscoelastic, are subject to creep, to aging (time dependent material properties) and to swelling (inhomogeneous eigenstrains). Its overall behavior is therefore the result of the combination of complex and coupled phenomena. The NTFA is applied here in a three-dimensional setting and extended to account for inhomogeneous eigenstrains in the individual phases.In the present context of linear viscoelasticity the modes can be identified following two procedures, either in each individual constituent, as initially proposed in Suquet (2003, 2004), or globally on the volume element, resulting into two slightly different models.For non aging materials, the predictions of both models are in excellent agreement with full-field simulations for various loading conditions, monotonic as well as non proportional loading, creep and relaxation. The model with global modes turns out to be as predictive as the original one with less internal variables. For aging materials, satisfactory results for the * Corresponding author. Tel: +33 442257382 ; fax: +33 442254747Preprint submitted to Mechanics of Materials.March 10, 2014overall as well as for the local response of the composites are obtained by both models at the expense of enriching the set of modes. The prediction of the global model for the local fields is less accurate but remains acceptable. Use of the global NTFA model is therefore recommended for linear viscoelastic composites.

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Effective behavior of viscoelastic composites: comparison of Laplace–Carson and time-domain mean-field approach

et al. 2022

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A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

Abstract: Abstract.The correspondence principle is customarily used with the Laplace-Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress

Cited by 26 publications

References 32 publications

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Extension of the Nonuniform Transformation Field Analysis to linear viscoelastic composites in the presence of aging and swelling

Effective behavior of viscoelastic composites: comparison of Laplace–Carson and time-domain mean-field approach

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