An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites

Pierard, Olivier; Doghri, Issam

doi:10.1016/j.ijplas.2005.04.001

Cited by 97 publications

(52 citation statements)

References 45 publications

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“…The "affine" formulation developed by [8] was developed for non-linear polycrystals in the framework of the self-consistent procedure. Comparisons between an "affine" formulation with the Mori-Tanaka scheme and finite elements calculations were performed in [9].…”

Section: Introductionmentioning

confidence: 99%

A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension

Berbenni

Capolungo

2015

Comptes Rendus. Mécanique

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Section: Introductionmentioning

confidence: 99%

A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension

Berbenni

Capolungo

2015

Comptes Rendus. Mécanique

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“…In the non-linear range where material parameters are time evolving, this induces approximations which are difficult to quantify. Recently, Pierard and Doghri (2006) adopted the affine method together with the Laplace transform to predict the overall behavior of two-phase elastic-viscoplastic composites. Predictions obtained with the Mori-Tanaka scheme were compared to finite element calculations performed on a 2D axisymmetric unit cell.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of elastic–viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes

Mercier

Molinari

2009

International Journal of Plasticity

169

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“…While the theoretical foundations of this approach are robust, the numerical implementation is rather complex mostly because the inversion of LaplaceCarson transforms requires intensive computations. Recently, the results of an enhanced affine formulation for two-phase composites were compared to numerical results obtained by the finite element method in Pierard and Doghri (2006) and Pierard et al (2007).…”

mentioning

confidence: 99%

An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method

Mareau

Berbenni

2015

International Journal of Plasticity

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe modeling of heterogeneous materials with an elasto-viscoplastic behavior is generally complex because of the differential nature of the local constitutive law. Indeed, the resolution of the heterogeneous problem involves space-time couplings which are generally difficult to estimate. In the present paper, a new homogenization model based on an affine linearization of the viscoplastic flow rule is proposed. First, the heterogeneous problem is written in the form of an integral equation. The purely thermoelastic and purely viscoplastic heterogeneous problems are solved independently using the self-consistent approximation. Using translated field techniques, the solutions of the above problems are combined to obtain the final self-consistent formulation. Then, some applications concerning two-phase fibre-reinforced composites and polycrystalline materials are presented. When compared to the reference solutions obtained from a FFT spectral method, a good description of the overall response of heterogeneous materials is obtained with the proposed model even when the viscoplastic flow rule is highly non-linear. Thanks to this approach, which is entirely formulated in the real-time space, the present model can be used for studying the response of heterogeneous materials submitted to complex thermo-mechanical loading paths with a good numerical efficiency.

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An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites

Cited by 97 publications

References 45 publications

A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension

A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension

Homogenization of elastic–viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes

An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method

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