On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media

Benveniste, Y.; Dvorak, George J.; Chen, T.

doi:10.1016/0022-5096(91)90012-d

Cited by 187 publications

(98 citation statements)

References 24 publications

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“…The assumption of uniform mean stress was described as reasonable for bi-phase composite and composites with ideal uniform random orientation of inclusions [4,6,24]. The results shown in previous section are in good agreement with this conclusion.…”

Section: 3) Mori-tanaka Formulation and Pgmt For Non-uniform Distrisupporting

confidence: 78%

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Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Jain

Lomov

Abdin

et al. 2013

Composites Science and Technology

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For modelling damage in short fibre composites, both the predictions of the effective properties and the stresses in the individual inclusions and in the matrix are necessary. Mean field theorems are usually used to calculate the effective properties of composite materials, most common among them is Mori-Tanaka formulation. Owing to occasional mathematical and physical admissibility problems with the Mori-Tanaka formulation; a pseudo-grain discretized Mori-Tanaka formulation (PGMT) was proposed in literature. This paper looks at the predictive capabilities for stresses in individual inclusions and matrix as well as the average stresses in inclusion phase for full Mori-Tanaka formulation and PGMT for 2D-orientation of inclusions.The average stresses inside inclusions and the matrix are compared to solutions of full-scale FE models for a wide range of configurations. It was seen that the Mori-Tanaka formulation gave excellent predictions of average stresses in individual inclusions, even when the basic assumptions of Mori-Tanaka were reported to be too simplistic, while the predictions of PGMT were off significantly in all the cases. However, the predictions of the matrix stresses by the two methods were found to be very similar to each other. The average value of stress averaged over the entire inclusion phase was also very close to each other. Mori-Tanaka must be used as the first choice homogenization scheme.

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Section: 3) Mori-tanaka Formulation and Pgmt For Non-uniform Distrisupporting

confidence: 78%

“…Mori-Tanaka and self-consistent schemes were shown by Benveniste et al, [4] to yield a symmetric effective stiffness tensor, only if the composite had reinforcements of similar shape and alignment. Weng [5] noticed that the Mori-Tanaka approach in multi-phase composites could violate the Hashin -Shtrikman bounds.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Jain

Lomov

Abdin

et al. 2013

Composites Science and Technology

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“…As is well known (Benveniste et al, 1991;Qu and Cherkaoui, 2007;Lester et al, 2011;Dvorak, 2013;Hossain et al, 2015) the effective stiffness tensor of a composite material with M different types of inhomogeneities can be expressed in terms of the stiffness tensors of the constituent materials, their corresponding volume fraction and the global strain concentration tensor through the equation…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…The L FM in the above expression is provided in a global coordinate system, while c r denotes the total volume fraction of the r-th inhomogeneity. Among others, Norris (1989);Ferrari (1991); Benveniste et al (1991); Christensen et al (1992); Schjødt-Thomsen and Pyrz (2001); Dvorak (2013), discuss the restrictions on constituent shape alignment in the application of equation (31). As discussed in these references, for general ellipsoidal fiber shape the obtained macroscopic tensor L SMC may not be symmetric and proper regularization is required for symmetrize it.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Hierarchical micromechanical modeling of the viscoelastic behavior coupled to damage in SMC and SMC-hybrid composites

Anagnostou

Chatzigeorgiou

Chemisky

et al. 2018

Composites Part B: Engineering

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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 aim of this paper is to study, through a multiscale analysis, the viscoelastic behavior of glass reinforced sheet molding compound (SMC) composites and SMC-hybrid composites mixing two types of bundle reinforcement: glass and carbon fibers. SMC exhibit more than two distinct characteristic length scales, so that a sequence of scale transitions is required to obtain the overall behavior of the composite. An analytical procedure is used consisting of properly selected well-established micromechanical methods like the Mori-Tanaka (MTM) and the composite cylinders (CCM) accounting for each scale transition. After selecting a representative volume element (RVE) for each scale, the material response of any given length scale is described on the basis of the homogenized behavior of the next finer one. This hierarchical approach is appropriately extended to the viscoelastic domain to account for the time dependent overall response of the SMC composite material. The anisotropic damage has been introduced through a micromechanical model considering matrix penny-shape microcrack density inside bundles. The capabilities of the hierarchical modeling are illustrated with various parametric studies and simulation of experimental data for glass-based SMC composites.

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“…Unfortunately, the application of traditional scale transition models such as Mori-Tanaka or Eshelby-Kröner self-consistent models to the case of multi-phase materials containing heterogeneities of different shapes does not simultaneously satisfy all these five fundamental criteria. It often occurs that the first three criteria are not fulfilled [5,9].…”

Section: Normalized Self-consistent Modelingmentioning

confidence: 99%

Accounting for a Distribution of Morphologies and Orientations on Stresses Analysis by X-Ray and Neutron Diffraction: Normalized Self-Consistent Modeling

Hounkpati

Fréour

Gloaguen

et al. 2014

AMR

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Abstract. The historical Eshelby-Kröner self-consistent model is only valid in the case when grains can be assumed similar to ellipsoids aligned preferentially along a same direction into the polycrystal. In this work, distributions of crystallites morphologies and geometrical orientations were accounted for, owing to the so-called normalized self-consistent model, in order to satisfy Hill's averages principles. Different nonlinear εϕψ-vs.-sin 2 ψ distributions were predicted in elasticity, even in the absence of crystallographic texture, in the case when several morphologies and geometrical orientations coexist within the same polycrystal. IntroductionPolycrystals with a morphological texture have macroscopic anisotropic properties in the absence of crystallographic texture. Many studies have been conducted to characterize the mechanical properties of such materials. The classical Eshelby-Kröner self-consistent model enables to take into account non-spherical grains when certain conditions are fulfilled [1][2][3]. According to these restrictions, only an ideal morphological texture can be taken into account through (identical) ellipsoidal inclusions whose principal axes are aligned along specific directions in the specimen. Such a microstructure is not generally observed in a real specimen; several morphologies or several grains with different morphological orientations could coexist within the same crystalline material. It is the case, for example, of titanium alloy Ti-17 polycrystal which consists of needle-shaped α crystallites mixed to slightly equiaxed prior β-grains [4]. Another example could be chosen among composite materials, made of epoxy resin and carbon-epoxy reinforcing strips, exhibiting an inplane distribution on the morphologies [5], the microstructure of which was successfully modeled through disc-shaped inclusions.It was recently numerically shown [5] that in such a situation, the Eshelby-Kröner self-consistent model does not simultaneously fulfil anymore both the so-called "Hill's average relations over the mechanical states", historically established in [6]. Therefore, this theoretical approach fails to represent a morphological texture featuring various grain shapes or a relative disorientation of the morphologies coexisting. The main interest of the present contribution is to show the possible influence of this morphological texture in the context of stress analysis by diffraction, in elasticity, using a normalized elastic self-consistent model. Then, we will be interested in the εϕψ-vs.-sin 2 ψ diagrams. If transversely isotropic grains are randomly oriented, the effective property of the polycrystal will be approximately isotropic, with values depending on the volume fraction and aspect ratio of the inclusions [7]. A random morphologic texture can then be neglected without consequence, within the context of modelling the multi-scale behaviour of heterogeneous materials consisting of quasi-isotropic elementary inclusions. This was demonstrated, at least numerically in [4]. Therefore, spec...

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On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media

Cited by 187 publications

References 24 publications

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Hierarchical micromechanical modeling of the viscoelastic behavior coupled to damage in SMC and SMC-hybrid composites

Accounting for a Distribution of Morphologies and Orientations on Stresses Analysis by X-Ray and Neutron Diffraction: Normalized Self-Consistent Modeling

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