• Journal of Power System Engineering
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• v.10 no.4
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• pp.133-138
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• 2006

Effective thermal conductivity of particulate reinforced composite has been predicted by Eshelby's equivalent inclusion method modified with Mori-Tanaka's mean field theory. The predicted results are compared with the experimental results from the literature. The model composite is polymer matrix filled with ceramic particles such as silica, alumina, and aluminum nitride. The preliminary examination by Eshelby type model shows that the predicted results are in good agreements with the experimental results for the composite with perfect spherical filler. As the shape of filler deviates from the perfect sphere, the predicted error increases. By using the aspect ratio of the filler deduced from the fixed filler volume fraction of 30%, the predicted results coincide well with the experimental results for filler volume fraction of 40% or less. Beyond this fraction, the predicted error increases rapidly. It can be finally concluded from the study that Eshelby type model can be applied to predict the thermal conductivity of the particulate composite with filler volume fraction less than 40%.

• Composites Research
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• v.17 no.6
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• pp.8-13
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• 2004

A new three-dimensional model fur stress-strain relation of a porous shape memory alloy has been proposed, where Eshelby's equivalent inclusion method with Mori-Tanaka's mean field theory is used. The predicted stress-strain relations by the present model are compared and show good agreements with the experimental results for the Ni-Ti shape memory alloy with porosity of 12%. Unlike linear stress-strain relations during phase transformations by other models from the literature, the present model shows nonlinear stress-strain relation in the vicinity of martensite finish region.

• Korean Journal of Materials Research
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• v.11 no.5
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• pp.354-360
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• 2001

By applying Eshelby's theory on the'transformation' and' inhomogeneity'problems of an ellipsoidal inclusion, a microscopic stress-strain is formulated for a composite material consisting of a matrix and a large number of aligned ellipsoidal inclusions. Some of the composites of practical interest, such as unidirectionally fiber- reinforced, Particle dispersion strengthened and layered composites can be treated by changing the axial ratios of the ellipsoidal inclusion. The macroscopic stress-strain relation obtained is applicable to elastic and elasto-plastic deformation of the composite in uniform loading.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2000.05a
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• pp.122-126
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• 2000

In particle or short-fiber reinforced composites cracking of the reinforcements is a significant damage mode because the broken reinformcements lose load carrying capacity . The average stress in the inhomogeneity represents its load carrying capacity and the difference between the average stresses of the intact and broken inhomogeneities indicates the loss of load carrying capacity due to cracking damage. The composite in damage process contains intact and broken reinforcements in a matrix, An incremental constitutive relation of particle or short-fiber reinforced composites including the progressive cracking damage of the reinforcements have been developed based on the Eshelby's equivalent inclusion method and Mori-Tanaka's mean field concept. influence of the cracking damage on the Eshelby's equivalent inclusion method and Mori-Tanaka's mean field concept. Influence of the cracking damage on the stress-strain response of the composites is demonstrated.

• Advances in aircraft and spacecraft science
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• v.9 no.3
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• pp.217-242
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• 2022

This paper proposes a novel time-domain homogenization model combining the viscoelastic constitutive law with Eshelby's inclusion theory-based micromechanics model to predict the mechanical behavior of the particle reinforced composite material. The proposed model is intuitive and straightforward capable of predicting composites' viscoelastic behavior in the time domain. The isotropization technique for non-uniform stress-strain fields and incremental Mori-Tanaka schemes for high volume fraction are adopted in this study. Effects of the imperfectly bonded interphase layer on the viscoelastic behavior on the dynamic mechanical behavior are also investigated. The proposed model is verified by the direct numerical simulation and DMA (dynamic mechanical analysis) experimental results. The proposed model is useful for multiscale analysis of viscoelastic composite materials, and it can also be extended to predict the nonlinear viscoelastic response of composite materials.

• Composites Research
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• v.18 no.5
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• pp.21-26
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• 2005

The validity of Eshelby-type model with Mori-Tanaka's mean field theory to predict the effective material properties of composites have been investigated in terms of filler size and its arrangement. The 2-dimensional plate composites including constant volume fraction of fillers are used as the model composite for the analytical studies, where the filler size and its arrangement are considered as parameters. The exact effective material properties of the composites are computed by finite element analysis(FEA), which are compared with effective material properties from the Eshelby-type model. Although the fillers are periodically or randomly arranged, the average Young's moduli by Eshelby-type model and FEA are in good agreement, specially for the ratio of specimen size to filler size being smaller than 0.03. However, Poisson's ratio of the composite by the Eshelby-type model is overestimated by $20\%$.

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.321-332
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• 2009

Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young's modulus of the inclusion is negative. Assumption of negative stiffness is a priori in the present analysis. For stress analysis, a closed form solution for the HS model and finite element solutions for the 2D composite are presented. A static loading condition is adopted to estimate the effective modulus of the composites by the ratio of stress to average strain on the loading edges. It is found that the interfacial stresses between the circular inclusion and matrix increase dramatically when the negative stiffness is so tuned that overall stiffness is unbounded. Furthermore, it is found that stress distributions in the inclusion are not uniform, contrary to Eshelby's theorem, which states, for two-phase, infinite composites, the inclusion's stress distribution is uniform when the shape of the inclusion has higher symmetry than an ellipse. The stability of the composites is discussed from the viewpoint of deterioration of perfect interface conditions due to excessive interfacial stresses.

• Composites Research
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• v.17 no.5
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• pp.54-60
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• 2004

A new three-dimensional model for predicting the relationship between the prestrain of the composite and the amount of phase transformation of shape memory alloy inducing shape memory effect has been proposed by using Eshelby's equivalent inclusion method with Mori-Tanaka's mean field theory. The model composite is aluminum matrix reinforced with short TiNi fiber shape memory alloy, where the matrix is work-hardening material of power-law type. The analytical results predicted by the current model show that most of the prestrain is induced by the plastic deformation of the matrix, except the small prestrain region. The strengthening mechanism of the composite by the shape memory effect should be explained by excluding its increase of yield stress due to the work-hardening effect of the matrix.

• Journal of Power System Engineering
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• v.10 no.4
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• pp.99-104
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• 2006

Young's modulus of composite has been predicted by Eshelby's equivalent inclusion method modified with Mori-Tanaka's mean field theory, where short fibers of aspect ratio distribution are assumed to be aligned. Young's modulus of the composite is predicted with the smallest class interval for simulating the actual distribution of fiber aspect ratio, which is compared with that computed using different class intervals. Young's modulus of the composite predicted with mean aspect ratio or the largest class interval is overestimated by the maximum 10%. As the class interval of short fibers for predicting Young's modulus decreases, the predicted results show good agreements with those obtained using the actual distribution of fiber aspect ratio. It can be finally concluded from the study that if and only if the class interval of short fiber normalized by the maximum aspect ratio is smaller than 0.1, the predicted results are consistent with those obtained using the actual distribution of aspect ratio.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.968-978
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• 1999

The effective elastic properties of materials containing spherical inclusions were calculated by the elastic wave scattering theory. In the formulation additional scattering fields by the presence of random multiple scatterers that affects the effective properties were found by the single scattering approximation. In calculating the scattering fields the ensemble average on the displacements and strains inside the scatterer was found from the static approximation at long wavelength limit. The displacements were assumed to be equal to the incident field, while the strains were calculated by Eshelby's equivalent inclusion principle on the single inclusion problem. Four different models were considered and they reflected different degrees of multiple scattering effects based on the approximation introduced in the process of embedding the inclusion in the matrix. The expressions for the effective elastic constants were given in each model, and their relations to the results obtained from other scattering theory and elasticity theory were discussed. The theoretical predictions were compared with experimental results on the epoxy matrix composites containing tungsten particles of different sizes and volume fractions