• Nuclear Engineering and Technology
• /
• v.51 no.5
• /
• pp.1209-1217
• /
• 2019

Due to the limitation of the computers, the conventional homogenization method is based on many assumptions and approximations, and some tough problems such as energy spectrum and boundary condition are faced. To deal with those problems, the Monte Carlo global homogenization is adopted. The Reactor Monte Carlo code RMC is used to study the global homogenization method, and the one-step global homogenization method is proposed. The superimposed mesh geometry is also used to divide the physical models, leading to better geometric flexibility. A set of multigroup homogenization cross sections is online generated for each mesh under the real neutron energy spectrum and boundary condition, the cross sections are adjusted by the superhomogenization method, and no leakage correction is required. During the process of superhomogenization, the author-developed reactor core program NLSP3 is used for global calculation, so the global flux distribution and equivalent homogenization cross sections could be solved simultaneously. Meanwhile, the calculated homogenization cross section could accurately reconstruct the non-homogenization flux distribution and could also be used for fine calculation. This one-step global homogenization method was tested by a PWR assembly and a small reactor model, and the results show the validity.

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

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.5
• /
• pp.1245-1252
• /
• 1994

A solution of heat transfer problems of composite materials has been tried using homogenization technique. Homogenization technique, which was derived by applying asymptotic expansion to the standard finite element method, helped compute the equivalent thermal conductivity matrices of base cells which constituted the composite material with repeated patterns. The homogenization technique made it possible to compute the solution of the heat transfer problem of composite materials with lower degrees of freedom compared to those of other numerical methods. The equivalent thermal conductivities computed by computed by homogenization technique are also applicable to other numerical methods such as finite difference method.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.31 no.3 s.258
• /
• pp.388-394
• /
• 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
• /
• 2008.11a
• /
• pp.684-689
• /
• 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 of Precision Engineering Conference
• /
• 2012.10a
• /
• pp.777-778
• /
• 2012

• Food Science and Biotechnology
• /
• v.17 no.2
• /
• pp.324-329
• /
• 2008

The effect of ultra-high pressure homogenization on the emulsifying properties of whey protein was investigated in a model emulsion made with whey protein isolate and soya oil under various pH. The emulsifying properties, the average diameter of the oil droplets ($d_{vs}$), and the protein load, were measured for each emulsion produced at different homogenization pressures (50 to 200 MPa) and pH values (4.6 to 8.0). According to the results of variance analysis and response surface, the pH had more influence on oil droplet size and protein load than homogenization pressure. The model equations, which were obtained by response surface analysis, show that pH and homogenization pressure had the major effect on oil droplet size and protein load. Higher homogenization pressure decreased the average droplet size and the protein load. Homogenization at high pressure, as opposed to low pressure, causes no overprocessing, but the effect was pH-dependent. The average diameter of the oil droplets increased slightly by decreasing the pH from 8.0 to 6.5 and then increased dramatically toward the isoelectric point of whey protein (i.e., at pH 4.6). Moreover associated droplets were found at acidic pH and their size was increased at high temperature.

• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.1041-1069
• /
• 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
• /
• v.36 no.3
• /
• pp.205-210
• /
• 2023

In this study, we developed a transfer learning framework based on homogenization data for efficient prediction of the effective mechanical properties and thermal conductivity of cellular foam structures. Mean-field homogenization (MFH) based on the Eshelby's tensor allows for efficient prediction of properties in porous structures including ellipsoidal inclusions, but accurately predicting the properties of cellular foam structures is challenging. On the other hand, finite element homogenization (FEH) is more accurate but comes with relatively high computational cost. In this paper, we propose a data-driven transfer learning framework that combines the advantages of mean-field homogenization and finite element homogenization. Specifically, we generate a large amount of mean-field homogenization data to build a pre-trained model, and then fine-tune it using a relatively small amount of finite element homogenization data. Numerical examples were conducted to validate the proposed framework and verify the accuracy of the analysis. The results of this study are expected to be applicable to the analysis of materials with various foam structures.

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