• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.5 no.1
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• pp.52-59
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• 2012

The bone material is a composite material consisted of collagen and mineral crystals. Also it shows transversely isotropic symmetry. So far none has shown that the components of the elasticity tensor satisfy the Voigt and Reuss bounds. To determine the effective elastic constant of bone material, the Voigt and Reuss bounds are employed and we show that the components of the elasticity tensor satisfy the Voigt and Reuss bounds. Mathematically this bounds are satisfied on two conditions only out of four conditions.

• Journal of Biomedical Engineering Research
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• v.31 no.3
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• pp.194-198
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• 2010

The effective Young’s modulus of a microfibril surrounded by water may be simply calculated by using the upper (Voigt) and lower (Reuss) bounds, which is one way to estimate the Young’s modulus in composite materials. The Steered Molecular Dynamics (SMD) has been used for estimating the Young’s modulus of a microfibril surrounded by water. In this paper, the result estimated by the upper (Voigt) and lower (Reuss) bounds shows 9.2% to 21.8% discrepancy from the result estimated by SMD, but introducing “efficiency of reinforcement parameter” removes the discrepancy and shows good agreement with the result estimated by SMD. We found the best fit for the Young’s modulus against the size of the gap between microfibrils. Also the steps using these bounds are much simpler than SMD.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.13 no.5
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• pp.432-435
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• 2020

The elasticity tensor for water may be employed to model the fully saturated porous material. Mostly water is assumed to be incompressible with a bulk modulus, however, the upper and lower bounds of off-diagonal components of the elasticity tensor of porous materials filled with water are violated when the bulk modulus is relatively high. In many cases, the generalized Hill inequality describes the general bounds of Voigt and Reuss for eigenvalues, but the bounds for the component of elasticity tensor are more realistic because the principal axis of eigenvalues of two phases, matrix and water, are not coincident. Thus in this paper, for anisotropic material containing pores filled with water, the bounds for the component of elasticity tensor are expressed by the rule of mixture and the upper and lower bounds of fully saturated porous materials are violated for low porosity and high bulk modulus of water.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.1415-1416
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• 2011

• Economic and Environmental Geology
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• v.49 no.3
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• pp.225-242
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• 2016

Rock physics serves as a useful tool for seismic reservoir characterization and monitoring by providing quantitative relationships between rock properties and seismic data. Rock physics models can predict effective moduli for reservoirs with different mineral components and pore fluids from well-log data. The distribution of reservoirs and fluids for the entire seismic volume can also be estimated from rock physics models. The first part of this report discusses the Voigt, Reuss, and Hashin-Shtrikman bounds for effective elastic moduli and the Gassmann fluid substitution. The second part reviews various contact models for moderate- to high-porosity sands. In the third part, constant-cement model, known to work well for the sand that gradually loses porosity with deteriorating sorting, was applied to the well-log data from an oil field in the North Sea. Lastly, the rock physics template constructed from the constant-cement model and the results from the prestack inversion of 2D seismic data were combined to predict the lithology and fluid types for the sand reservoir of this oil field.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.373-392
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• 2001

The main idea behind the paper is to present two alternative methods of homogenization of the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second order perturbation second probabilistic moment method, with its computational implementation known as the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic homogenization method, being extended to probabilistic spaces, is based on the effective modules approach. Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand, to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These computational studies are provided in the range of up to fourth order probabilistic moments of effective conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.

• Steel and Composite Structures
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• v.48 no.2
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• pp.191-206
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• 2023

The present research investigates how micromechanical models affect the behavior of Functionally Graded (FG) plates under different boundary conditions. The study employs diverse micromechanical models to assess the effective material properties of a two-phase particle composite featuring a volume fraction of particles that continuously varies throughout the thickness of the plate. Specifically, the research examines the vibrational response of the plate on a Winkler-Pasternak elastic foundation, considering different boundary conditions. To achieve this, the governing differential equations and boundary conditions are derived using Hamilton's principle, which is based on a four-variable shear deformation refined plate theory. Additionally, the Galerkin method is utilized to compute the plate's natural frequencies. The study explores how the plate's natural frequencies are influenced by various micromechanical models, such as Voigt, Reuss, Hashin-Shtrikman bounds, and Tamura, as well as factors such as boundary conditions, elastic foundation parameters, length-to-thickness ratio, and aspect ratio. The research results can provide valuable insights for future analyses of FG plates with different boundaries, utilizing different micromechanical models.