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

Mercier, Sébastien; Molinari, A.

doi:10.1016/j.ijplas.2008.08.006

Cited by 169 publications

(104 citation statements)

References 37 publications

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“…Different techniques have been proposed to determine the effective properties of viscoplastic heterogeneous materials (Love and Batra, 2006;Mercier and Molinari, 2009). In this work they are calculated with the modified secant method proposed by Suquet (1995aSuquet ( ,b, 1996, which has been extended for thermal softening effects.…”

Section: Proposed Modifications For the Modelmentioning

confidence: 99%

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

Zaera

Rodríguez-Martínez

Casado³

et al. 2012

International Journal of Plasticity

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a b s t r a c tThis study presents a constitutive model for steels exhibiting SIMT, based on previous sem inal works, and the corresponding methodology to estimate their parameters. The model includes temperature effects in the phase transformation kinetics, and in the softening of each solid phase through the use of a homogenization technique. The model was validated with experimental results of dynamic tensile tests on AISI 304 sheet steel specimens, and their predictions correlate well with the experimental evidence in terms of macroscopic stress strain curves and martensite volume fraction formed at high strain rates. The work shows the value of considering temperature effects in the modeling of metastable austen itic steels submitted to impact conditions. Regarding most of the works reported in the lit erature on SIMT, modeling of the martensitic transformation at high strain rates is the distinctive feature of the present paper.

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Section: Proposed Modifications For the Modelmentioning

confidence: 99%

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

Zaera

Rodríguez-Martínez

Casado³

et al. 2012

International Journal of Plasticity

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“…(73) reduces to that postulated in (Molinari, 2002) for the self-consistent model for elastic-viscoplastic materials, cf. also (Mercier et al, 2005;Mercier and Molinari, 2009). A more consequent (although still simplified) way is to define the overall elastic accommodation strain-rate and the respective overall accommodation stress-rate as followṡ…”

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

confidence: 99%

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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“…This approach was later extended to the case of finite strains by Nemat-Nasser and Obata (1986) and Harren (1991). Mercier and Molinari (2009) used the additive interaction law developed by Molinari (Molinari et al, 1997;Molinari, 2002) to derive a self-consistent model based upon a tangent linearization of the viscoplastic flow rule. The additive interaction law has been later adapted to build a finite strain elasto-viscoplastic self-consistent model for polycrystals (Wang et al, 2010).…”

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

Cited by 169 publications

References 37 publications

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

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

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