• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.3 s.258
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• pp.388-394
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• 2007

Many engineering problems require the calculation of effective material properties of a structure which is composed of repeated micro-structures. The homogenization method has been used to calculate the effective (homogenized) properties of composites and several homogenization procedures for different physical fields have been introduced. This research describes the modified homogenization technique for magnetostatic problems. Assuming that the material is periodically repeated, its effective permeability can be prescribed by calculating the homogenized magnetic reluctivity using the finite element analysis of the micro unit cell. Validity of the suggested method is confirmed by comparing the results by the energy based method as well as the widely known homogenization method.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.684-689
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• 2008

In this study, homogenization method combined with the effective interface model for the characterization of properties of the nanoparticulate composites is developed. In order to characterize particle size effect of nanocomposites, effective interface model has been developed. The application range of analytical micromechanics approach is limited because a simple analytical approach is valid only for simple and uniform geometry of fiber particles. Therefore this study focuses on the analysis of mechanical properties of the effect interface through the continuum homogenization method instead of using analytical micromechanics approach. Using the homogenization method, elastic stiffness properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. The suggested homogenization method is expected to be applied to optimization problems for nanocomposite design.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.134-136
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• 2005

Homogenization method is adopted to predict the permeability tenor for glass fiber plain woven fabrics. Calculating the permeability tensor numerically is an encouraging task because the permeability tensor is a key parameter in resin transfer molding (RTM). Based on multi-scale approach of the homogenization method, the permeability for the micro-unit cell within fiber tow is computed and compared with that obtained from flow analysis for the same micro-unit cell. It is found that they are in good agreement. In order to calculate the permeability tensor of macro-unit cell for the plain woven fabrics, the Stokes and Brinkman equations which describe inter-tow and intra-tow flow respectively are employed as governing equations. The effective permeabilities homogenized by considering intra-tow flow are compared with those obtained experimentally. Control volume finite element method (CVFEM) is used as a numerical method. It is shown that the asymptotic expansion homogenization method is an attractive method to predict the effective permeability for heterogeneous media.

• Structural Engineering and Mechanics
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• v.38 no.4
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• pp.503-516
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• 2011

Uncertainty in concrete properties, including concrete modulus of elasticity and modulus of rupture, are predicted by developing a microstructural homogenization model. The homogenization model is developed by analyzing a concrete representative volume element (RVE) using the finite element (FE) method. The concrete RVE considers concrete as a three phase composite material including: cement paste, aggregate and interfacial transition zone (ITZ). The homogenization model allows for considering two sources of variability in concrete, randomly dispersed aggregates in the concrete matrix and uncertain mechanical properties of composite phases of concrete. Using the proposed homogenization technique, the uncertainty in concrete modulus of elasticity and modulus of rupture (described by numerical cumulative probability density function) are determined. Deflection uncertainty of reinforced concrete (RC) beams, propagated from uncertainties in concrete properties, is quantified using Monte Carlo (MC) simulation. Cracked plane frame analysis is used to account for tension stiffening in concrete. Concrete homogenization enables a unique opportunity to bridge the gap between concrete materials and structural modeling, which is necessary for realistic serviceability prediction.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.19-26
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• 2023

Because of the development of computational resources, an entire structure in which many components are combined can be analyzed. To do so, the calculation time and number of data points are increased. In many practical industry structures, there are many parts with repeated patterns. To analyze the repetitive structures effectively, a homogenization method is usually employed. In a homogenization module, including commercial programs, it is generally assumed that a unit cell is repeated in all directions. However, the practical industry structures usually have complicated, repeated patterns or structures. Complicated patterns are difficult to address using the conventional homogenization method. Therefore, in this study, a multilevel homogenization method was devised to consider complex regularities. The proposed homogenization method divides the structure into several areas and performs multiple homogenizations, resulting in a more accurate analysis than that provided by the previous method.

• Nuclear Engineering and Technology
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• v.44 no.1
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• pp.43-52
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• 2012

To compute a permeability coefficient along a rough fracture that takes into account the fracture geometry, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate the permeability coefficient on the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in the microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the facture geometry. The Cpermeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of the fractures, such as the roughness and the aperture variation. The homogenization analysis may allow us to produce more accurate results than are possible with the preexisting equations for calculating permeability.

• Nuclear Engineering and Technology
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• v.55 no.4
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• pp.1365-1381
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• 2023

In this paper, a procedure for evaluating the structural integrity of the PCSG (Printed Circuit Steam Generator) unit block is presented with a simplified FE (finite element) analysis technique by applying the homogenization method. The homogenization method converts an inhomogeneous elastic body into a homogeneous elastic body with same mechanical behaviour. This method is effective when the inhomogeneous elastic body has repetitive microstructures, and thus the method was applied to the sheet assembly among the PCSG unit block components. From the method, the homogenized equivalent elastic constants of the sheet assembly were derived. The validity of the determined material properties was verified by comparing the mechanical behaviour with the reference model. Thermo-mechanical analysis was then performed to evaluate the structural integrity of the PCSG unit block, and it was found that the contact region between the steam header and the sheet assembly is a critical point where large bending stress occurs due to the temperature difference.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.1041-1069
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• 2009

We study the periodic homogenization of the non-stationary Stokes equations. The fundamental homogenization theorem and corrector theorem are proved under a very general assumption on the viscosity coefficients and data. The proofs are based on a weak formulation suitable for an application of classical Tartar's method of oscillating test functions. Such a weak formulation is derived by adapting an argument in Teman's book [Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984].

• Composites Research
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• v.15 no.5
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• pp.44-52
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• 2002

To study numerically the mechanical behaviors of advanced composite materials considering the microscopic phenomena as well as the macroscopic properties and behaviors, a multi-scale modeling and analysis by the mathematical homogenization method with the help of the finite element method(FEM) are reviewed. The hierarchical modeling strategy and the formulation are briefly described first to give some idea of the multi-scale framework. The latter half of this article focuses on the verification of the multi-scale analysis by the homogenization method in its applications to real advanced materials. The first example is the verification of the predicted macroscopic(homogenized) properties based on the microstructure of porous ceramics. In spite of the complexity of the random microstructure, the error between the predicted and the measured values was only 1%. Next, two applications to the process simulation of fiber reinforced polymer matrix composites are presented. The permeability characteristics are evaluated for sheared weave fabrics for resin transfer molding(RTM) simulation, and the thermoforming of FRTP sheet is analyzed considering the large deformation of the knit structure during the deep-draw forming was verified by comparison with the experimental results.

• Composites Research
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• v.36 no.5
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• pp.329-334
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• 2023

The classical multiscale finite element (FE² ) method involves iterative calculations of micro-boundary value problems for representative volume elements at every integration point in macro scale, making it a computationally time and data storage space. To overcome this, we developed the data-driven multiscale analysis method based on the mean-field homogenization (MFH). Data-driven computational mechanics (DDCM) analysis is a model-free approach that directly utilizes strain-stress datasets. For performing multiscale analysis, we efficiently construct a strain-stress database for the microstructure of composite materials using mean-field homogenization and conduct data-driven computational mechanics simulations based on this database. In this paper, we apply the developed multiscale analysis framework to an example, confirming the results of data-driven computational mechanics simulations considering the microstructure of a hyperelastic composite material. Therefore, the application of data-driven computational mechanics approach in multiscale analysis can be applied to various materials and structures, opening up new possibilities for multiscale analysis research and applications.