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

Berbenni, Stéphane; Capolungo, Laurent

doi:10.1016/j.crme.2014.12.003

Cited by 23 publications

(17 citation statements)

References 26 publications

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“…Furthermore, the present SC-TF-AFF approach provides results which are closer to the FFT response than the ones given by the original SC-TF-SEC method. Also, for such microstructures with a relatively low volume fraction of fibres, these results (figures 1 and 2) confirm that the Mori-Tanaka's estimate, derived by Berbenni and Capolungo (2014), or the Hashin's CCA, developed by Lahellec and Suquet (2007b), give more accurate results than the self-consistent scheme, especially regarding the asymptotic state at large physical times. However, for m = 0.2, figure 2 shows that the overall response calculated from the SC-TF-AFF approach during the transition from the elastic regime to the viscoplastic regime, i.e.…”

Section: Fibre-reinforced Compositessupporting

confidence: 78%

“…In the present work, the contribution of thermal expansion is also considered so that the proposed model may be used to investigate the response of disordered materials subjected to thermo-mechanical loading paths. Using the Mori-Tanaka approximation, a first order affine extension to the model of Paquin et al (1999) has already been proposed for two-phase materials by Berbenni and Capolungo (2014). It was shown that predictions are very close to the ones obtained with the incremental variational approach developed by Lahellec and Suquet (2007b) for two-phase fibrereinforced composites.…”

mentioning

confidence: 94%

“…The interest for studying such composite materials is twofold. First, a Mori-Tanaka approximation based on translated field techniques and coupled with a first order affine formulation (labeled as MT-TF-AFF) has been recently developed by Berbenni and Capolungo (2014). It is therefore interesting to compare the self-consistent and Mori-Tanaka schemes for two-phase composite materials with an elastoviscoplastic behavior.…”

Section: Fibre-reinforced Compositesmentioning

confidence: 99%

“…The calculated overall stress-strain responses obtained from the present SC-TF-AFF approach are first compared to the results given by the FFT method (Lahellec and Suquet, 2007b), the SEC (EIV+HS) approach (Lahellec and Suquet, 2007b) and the MT-TF-AFF approach (Berbenni and Capolungo, 2014) in figures 1 and 2 for two different strain-rate sensitivities m = 1 and m = 0.2, as initially done in Lahellec and Suquet (2007b). Figure 1 reports the results of the SC-TF-AFF approach for m = 1 (linear case).…”

Section: Fibre-reinforced Compositesmentioning

confidence: 99%

“…As an illustration, some applications are presented in the second section. The case of two-phase fibre-reinforced composites is first examined in order to compare the results from the proposed self-consistent approach with those given by others (Berbenni and Capolungo, 2014;Lahellec and Suquet, 2007b;Paquin et al, 1999). Then, the model is used to describe the behavior of polycrystalline materials when they are subjected to various thermomechanical loading conditions.…”

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confidence: 99%

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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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Section: Fibre-reinforced Compositessupporting

confidence: 78%

mentioning

confidence: 94%

Section: Fibre-reinforced Compositesmentioning

confidence: 99%

Section: Fibre-reinforced Compositesmentioning

confidence: 99%

mentioning

confidence: 99%

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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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Analytical Micromechanical Methods for Elasto‐Viscoplastic Composites and Polycrystals

BERBENNI,

FOREST

2024

Digital Materials

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An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

Choo

Semnani

White

2020

Num Anal Meth Geomechanics

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Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic—specifically, transversely isotropic—and closely linked to the layered composite structure at the microscale. In this work, we develop a two‐scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semianalytical homogenization of a bilayer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic modified Cam‐Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time‐dependent borehole closure in a shale formation with different bedding plane directions.

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

Cited by 23 publications

References 26 publications

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

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

Analytical Micromechanical Methods for Elasto‐Viscoplastic Composites and Polycrystals

An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

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