• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.47-50
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• 2009

본 논문에서는 불균질 재료의 균열진전을 해석하기 위한 방법으로 변절점 유한요소를 이용한 멀티스케일 기법을 제시하였다. 효율적인 해석을 위하여 서로 다른 스케일의 요소망을 적용하여 전체 모델의 자유도를 감소시킨다. 균열선단과 비교적 멀리 떨어져 있는 영역은 균질화 기법을 도입하여 불균질 재료에 대한 등가물성을 갖는 성긴 요소망으로 대체하고, 균열선단 주변의 요소망은 재료의 기하학적 특성과 불균질성을 반영하도록 조밀하게 구성한다. 한편 균열선단에 존재하는 응력 특이성을 표현하기 위하여 균열선단을 포함한 요소를 더욱 조밀한 요소망으로 분할하여 구성한다. 여기에서 서로 다른 스케일의 요소망 경계에는 변절점 유한요소를 적용함으로써 경계에서의 절점 연결조건과 적합성을 만족시킬 수 있다. 제시한 멀티스케일 기법을 수치예제에 적용함으로써 정확성과 효율성을 검증하였으며, 특히 불균질 성분이 균열진전에 미치는 영향을 경계조건과 T-응력의 관점에서 분석하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.261-264
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• 2011

유한 요소 기법을 이용한 허니콤 구조물의 해석은 모델링 작업 및 격자 생성의 어려움뿐만 아니라 과도한 해석 시간이 요구되기 때문에 균질화 기법은 계산상의 효율성을 증대시킬 수 있는 매우 유용한 방법이라 할 수 있다. 그러나 나노 크기의 구조물에서는 표면 효과로 인하여 거시적인 구조물에서와는 매우 상이한 기계적 거동 양상을 띠게 되며 균질화 기법을 나노 크기의 허니콤 구조물에 적용하기 위해서는 이러한 표면 효과를 반영해야만 한다. 본 논문에서는 표면 효과를 고려한 유한 요소를 제안하고 이를 이용하여 나노 크기의 3차원 허니콤 구조물을 균질화 기법을 이용하여 등가의 2차원 판으로 대체하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.4
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• pp.315-321
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• 2012

In this study, a sequential multiscale homogenization method to characterize the effective thermal conductivity of nano particulate polymer nanocomposites is proposed through a molecular dynamics(MD) simulations and a finite element-based homogenization method. The thermal conductivity of the nanocomposites embedding different-sized nanoparticles at a fixed volume fraction of 5.8% are obtained from MD simulations. Due to the Kapitza thermal resistance, the thermal conductivity of the nanocomposites decreases as the size of the embedded nanoparticle decreases. In order to describe the nanoparticle size effect using the homogenization method with accuracy, the Kapitza interface in which the temperature discontinuity condition appears and the effective interphase zone formed by highly densified matrix polymer are modeled as independent phases that constitutes the nanocomposites microstructure, thus, the overall nanocomposites domain is modeled as a four-phase structure consists of the nanoparticle, Kapitza interface, effective interphase, and polymer matrix. The thermal conductivity of the effective interphase is inversely predicted from the thermal conductivity of the nanocomposites through the multiscale homogenization method, then, exponentially fitted to a function of the particle radius. Using the multiscale homogenization method, the thermal conductivities of the nanocomposites at various particle radii and volume fractions are obtained, and parametric studies are conducted to examine the effect of the effective interphase on the overall thermal conductivity of the nanocomposites.

• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.1
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• pp.13-20
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• 2008

Graded layers in which two different constituent particles are mixed are inserted into functionally graded material such that the volume fractions of constituent particles vary continuously and functionally over the entire material domain. The material properties of this dual-phase graded region, which is essential for the numerical analysis of the thermo-mechanical behavior of FGM, have been predicted by traditional homogenization methods. But, these methods are limited to predict the global equivalent material properties of FGMs because the detailed geometry information such as the particel shape and the dispersion structure is not considered. In this context, this study intends to investigate the characteristics of these homogenization methods through the finite element analysis utilizing the discrete micromechanics models of the graded layer, for various volume fractions and external loading conditions.

• Aerospace Engineering and Technology
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• v.12 no.2
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• pp.48-56
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• 2013

In this paper, the equivalent elastic properties of fiber reinforced plastic laminar are investigated using various homogenization schemes. Although there are several methods for predicting the equivalent elastic properties such as analytical formula or semi-empirical formula, most of them have some limitations or are not much accurate when handling new composite material consisting of various fiber, matrix and fiber-volume fraction ratio. To resolve the issues, computational homogenization scheme is adopted with a representative volume element (RVE) comprised of a set of finite elements. Finally, the equivalent elastic properties are obtained by applying periodic boundary conditions. The obtained results are compared with those by the existing methods and test results. Also its effect on structural analysis results of the composite satellite panel is investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.105-114
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• 2018

In this paper, the computer simulations are carried out by using the peridynamic theory model with various conditions including quasi-static loads, dynamic loads and crack propagation, branching crack pattern and isotropic materials, orthotropic materials. Three examples, a plate with a hole under quasi-static loading, a plate with a pre-existing crack under dynamic loading and a lamina with a pre-existing crack under quasi-static loading are analyzed by computational simulations. In order to simulate the quasi-static load, an adaptive dynamic relaxation technique is used. In the orthotropic material analysis, a homogenization method is used considering the strain energy density ratio between the classical continuum mechanics and the peridynamic. As a result, crack propagation and branching cracks are observed successfully and the direction and initiation of the crack are also captured within the peridynamic modeling. In case of applying peridynamic used homogenization method to a relatively complicated orthotropic material, it is also verified by comparing with experimental results.

• Computational Structural Engineering
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• v.8 no.3
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• pp.51-57
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• 1995

A simplified stress analysis of perforated plates was carried out using homogenization technique. Homogenization technique, which introduced miroscale expansion in the standard finite element method, reconstructed the plate with regularly placed holes into a set of macroscale and microscale models. The microscale model helped compute homogenized material constants of the unit cell, which were used to compute macroscale displacements in the macroscale model. Also it was possible to compute the stress field of the plate using the microscale model. It was found that reasonable equivalent material constants were computed and that the required degrees of freedom was drastically reduced when homogenization technique was employed in the stress analyses. The microscale modeling in the homogenization technique provided a useful concept of pre- and post-processing in the stress analysis of perforated plates.

• Composites Research
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• v.33 no.4
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• pp.198-204
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• 2020

In this study, we employ the full atomistic molecular dynamics simulation and finite element homogenization method to predict the thermo-mechanical properties of nanocomposites including carbon nanotube bundle. As the number of carbon nanotubes within the single bundle increases, the effective in-plane Young's modulus and in-plane shear modulus decrease, and in-plane thermal expansion coefficient increases, despite the same volume fraction of carbon nanotubes. To investigate the thickness of interphase zone, we employ the radial density distribution. It is investigated that the interphase thickness is almost independent on the number of carbon nanotubes within the single bundle. It is assumed that the matrix and interphase are isotropic materials. According to the predicted thermo-mechanical properties of interphase zone, the Young's modulus and shear modulus of interphase zone clearly decrease, and the thermal expansion coefficient increases. Based on the thermo-mechanical interphase behavior, we developed the multiscale homogenization model to predict the thermo-mechanical properties of PLA nanocomposites that include the carbon nanotube bundle.