Micromechanics of particle-reinforced elasto-viscoplastic composites: Finite element simulations versus affine homogenization

Pierard, Olivier; LLorca, J.; Segurado, J.; Doghri, Issam

doi:10.1016/j.ijplas.2006.09.003

Cited by 113 publications

(75 citation statements)

References 39 publications

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“…The reason for that lies in a relatively small contrast in viscous properties of the phases. As already shown in (Mercier and Molinari, 2009), in the examined case the MoriTanaka (MT) averaging scheme applied jointly with the Molinari model (here Variant II of the sequential method) is in the excellent agreement with FEM results reported in (Pierard et al, 2007) as concerns the average response of the composite, while the selfconsistent scheme slightly overestimates the stress level. In turn, the local stress in the stronger phase is somewhat better predicted by the self-consistent model, especially at the advanced stage of the process.…”

Section: A C C E P T E D Accepted Manuscriptsupporting

confidence: 73%

“…the constitutive law has been taken the same as that used by Pierard et al (2007) and Mercier and Molinari (2009); details can be found in these references. A spherical shape of inhomogeneities has been assumed.…”

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 99%

“…In turn, the local stress in the stronger phase is somewhat better predicted by the self-consistent model, especially at the advanced stage of the process. (Pierard et al, 2007) for a viscously non-linear two-phase composite in uniaxial tension, c i = 0.3: a) stress-strain curve for the composite at axial strain-rateε = 10 −3 1/s (top curves) anḋ ε = 10 −4 1/s (bottom curves), b) stress-strain curve in phases forε = 10 −3 1/s (top curves -inhomogeneity, bottom curves -matrix).…”

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 99%

See 2 more Smart Citations

Sequential linearization method for viscous/elastic heterogeneous materials

Kowalczyk-Gajewska

Petryk

2011

European Journal of Mechanics - A/Solids

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The paper addresses the problem of suitable approximation of the interaction between phases in heterogeneous materials that exhibit both viscous and elastic properties. A novel approach is proposed in which linearized subproblems for an inhomogeneity-matrix system with viscous or elastic interaction rules are solved sequentially within one incremental step. It is demonstrated that in the case of a self-consistent averaging scheme, an additional accommodation subproblem, besides purely viscous and elastic subproblems, is to be solved in order to estimate the material response satisfactorily. By examples of an isotropic two-phase material it is shown that the proposed approach provides acceptable predictions in comparison with the existing models.

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Section: A C C E P T E D Accepted Manuscriptsupporting

confidence: 73%

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 99%

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 99%

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Sequential linearization method for viscous/elastic heterogeneous materials

Kowalczyk-Gajewska

Petryk

2011

European Journal of Mechanics - A/Solids

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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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“…Although multiscale homogenization methods in general, and MFH schemes in particular, often exhibit an acceptable, sometimes even high, level of accuracy to capture the non-linear behavior of composites (Pierard et al, 2007b), some limitations, assumptions or complexity in the formulation remain in the existing methods. For example, as previously said, to remain accurate in the non-linear range, the incremental-tangent method requires the tangent-operator to be made isotropic during the M-T process, as discussed by Doghri and Ouaar (2003); Pierard and Doghri (2006b).…”

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

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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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Micromechanics of particle-reinforced elasto-viscoplastic composites: Finite element simulations versus affine homogenization

Cited by 113 publications

References 39 publications

Sequential linearization method for viscous/elastic heterogeneous materials

Sequential linearization method for viscous/elastic heterogeneous materials

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

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

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