On the Effective Elastic Properties of Macroscopically Isotropic Media Containing Randomly Dispersed Spherical Particles

Cojocaru, D.; Karlsson, Anette M.

doi:10.1115/1.4000229

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…Large deviations between the MT predictions and the FEM results occur primarily for the effective Poisson's ratio, which is generally underestimated by the MT for higher porosity levels. These findings are of practical relevance for the homogenisation of porous thin films and perforated layers, as well as for the evaluation of the in-plane properties of cellular solids under plane stress conditions, and might, with limitations, even be used to estimate the effective properties of RVEs with random distributions of spherical pores, as discussed by Cojocaru and Karlsson (2010) and Fiedler et al (2010). The effective elastic properties of such materials can be conveniently predicted using both the SCM and the MT if their level of porosity lies within the stated intervals.…”

Section: Discussionmentioning

confidence: 90%

Homogenisation of porous thin films and perforated layers: Comparison of analytical and numerical approaches

Richter

2015

Mechanics of Materials

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Keywords:Finite element method Self-consistent method Mori-Tanaka approach Micromechanics Porous thin films Constitutive behaviour a b s t r a c tThe mechanical properties of porous thin films and perforated layers are affected by pore content, shape and arrangement. The experimental determination of the in-plane mechanical properties of such materials is challenging, yet reliable data are essential for materials development and component design. Analytical and numerical approaches therefore provide valuable, supplementary tools for evaluating the effect of porosity on the mechanical properties of such materials.The applicability of both the classical self-consistent method and the Mori-Tanaka approach to the estimation of the effective elastic properties of porous thin films and perforated layers is investigated in this paper. For generic model microstructures with various arrangements of pores, variable pore content and varying matrix Poisson's ratio, the effective elastic properties predicted by the classical self-consistent method and by the Mori-Tanaka approach are quantitatively compared with results obtained by numerical experiments. Based upon this comparison, the range of validity of both the classical self-consistent method and the Mori-Tanaka approach with regard to the different arrangements of pores investigated is defined, and the deviation to be expected if critical values of pore content or inter-pore distance are exceeded and interactions between adjacent pores are occurring is assessed.

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Section: Discussionmentioning

confidence: 90%

Homogenisation of porous thin films and perforated layers: Comparison of analytical and numerical approaches

Richter

2015

Mechanics of Materials

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“…The Finite Element Method (FEM) has been the most commonly used technique for computing the local fields in heterogeneous materials (Llorca et al, 2000;Bohm et al, 2002;Segurado and Llorca, 2002;Kari et al, 2007;Barello and Lévesque, 2008;Klusemann and Svendsen, 2010;Cojocaru and Karlsson, 2010;ElMourid et al, 2012;Pahlavanpour et al, 2013;Moussaddy et al, 2013). The method consists of meshing a unit cell and computing the local fields when it is submitted to an external load.…”

Section: Computation Of Local Fields In Heterogeneous Materialsmentioning

confidence: 99%

Homogenization models for predicting local field statistics in ellipsoidal particles reinforced composites: Comparisons and validations

Ghossein¹,

Lévesque²

2015

International Journal of Solids and Structures

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Local fields statistics First and second order moments Load independent metric a b s t r a c t This paper validates the performance of analytical homogenization models at predicting the local field statistics in randomly distributed and oriented ellipsoidal particles reinforced composites. The numerical validation was based on a newly introduced load independent metric, which allowed to formulate general conclusions. A large validation campaign was conducted and the Representative Volume Element (RVE) was rigorously determined for each combination of phases mechanical properties, particles volume fraction and aspect ratio. The load independent properties computed numerically were compared to those predicted by a range of analytical models. The study revealed that the original Benveniste's interpretation of the Mori-Tanaka scheme led to the most accurate first order moments and intra-matrix second order moments, provided that the mechanical properties contrast between the particles and the matrix are low. For higher contrasts, Lielens' model delivers the most accurate estimates. The self-consistent scheme is the most suited model to predict the intra-particle second order moments when the particles aspect ratio is low. For particles with high aspect ratio, Lielens' model could be an alternative to the self-consistent scheme. Furthermore, an interpolation model has been developed and it has been shown to predict accurately the mean and covariance tensors of the intraphase stress fields.

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“…Kari et al (2007) used RVEs for computing the properties of fiber-reinforced composites. Cojocaru and Karlsson (2010) reduced the RVE to an equivalent representative area to predict the effective elastic properties of a material composed of spherical particles dispersed in a matrix. The concept of RVE was given a statistical definition by Kanit et al (2003), who conducted a statistical study and showed that the effective properties can be computed within a prescribed accuracy by increasing the number of statistical realizations, provided that the bias in mechanical properties is overcome.…”

Section: Numerical Homogenizationmentioning

confidence: 99%

On the relevance of using homogeneous biphasic models to characterize the mechanical behavior of the growth plate

Collin

Villemure

Lévesque

2015

Mech Time-Depend Mater

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The purpose of this work was to theoretically evaluate the relevance of using homogeneous biphasic models to represent the mechanical behavior of the growth plate. To that end, representative volume elements (RVEs) of reserve and proliferative zones, where the extracellular matrix was modeled as poroelastic and the chondrocytes were assumed to be isotropic and linearly elastic, were meshed by finite elements. The matrix obeyed either the biphasic poroelastic (BPE) or the transversely isotropic biphasic poroelastic (TIBPE) models. The RVEs were submitted to unconfined compression (UC), confined compression (CC) and to a hybrid loading featuring a prescribed pore pressure. The overall responses of the RVEs to UC and CC were fit by either the BPE or the TIBPE models. The study revealed that the BPE model was unable to predict the responses under UC and CC simultaneously for both modeled zones. The TIBPE model fit with good accuracy the RVEs effective responses under UC and CC, but failed to predict the response of the hybrid loading. These results show that a mixture of poroelastic phases does not lead to an overall behavior that can be fit with the same formulation. Moreover, this study exemplified the fact the even if the TIBPE model fits experimental data under UC and CC due to its increased number of parameters, it can fail to predict other loading cases. This motivates further micromechanical studies where the local behavior of the constituent phases would carefully be evaluated.

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On the Effective Elastic Properties of Macroscopically Isotropic Media Containing Randomly Dispersed Spherical Particles

Cited by 6 publications

References 23 publications

Homogenisation of porous thin films and perforated layers: Comparison of analytical and numerical approaches

Homogenisation of porous thin films and perforated layers: Comparison of analytical and numerical approaches

Homogenization models for predicting local field statistics in ellipsoidal particles reinforced composites: Comparisons and validations

On the relevance of using homogeneous biphasic models to characterize the mechanical behavior of the growth plate

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