• Composites Research
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• 제33권4호
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• pp.198-204
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• 2020

본 연구에서는 탄소나노튜브 다발을 포함하는 나노복합재료의 열-기계적 특성을 정량적으로 예측하기 위하여 분자동역학 전산모사와 유한요소 기반 균질화 기법을 적용하였다. 응집된 탄소나노튜브의 수가 증가함에 따라 동일한 탄소나노튜브의 체적분율에도 불구하고, 면내 영률 및 면내 전단계수는 감소하였고, 면내 열팽창계수는 증가함을 확인할 수 있었다. 계면의 두께를 조사하기 위하여 밀도의 반경 방향 분포(Radial density distribution)을 조사하였으며, 계면의 두께는 탄소나노튜브의 수와는 거의 무관함을 확인할 수 있었다. 기지와 계면은 등방성 재료로 가정하였으며, 예측한 계면의 열-기계적 특성에 따르면, 응집된 탄소나노튜브의 수가 증가함에 따라 계면의 영률 및 전단계수는 감소하였으며, 열팽창계수는 반대로 증가하였다. 이를 토대로, 탄소나노튜브 다발을 포함하는 PLA 나노복합재료의 열-기계적 특성 예측을 위한 멀티스케일 균질화 모델을 개발하였다.

• Geomechanics and Engineering
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• 제16권3호
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• pp.257-271
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• 2018

In this paper, the effect of the homogenization models on buckling and free vibration is presented for simply supported functionally graded plates (FGM) resting on elastic foundation. The majority of investigations developed in the last decade, explored the Voigt homogenization model to predict the effective proprieties of functionally graded materials at the macroscopic-scale for FGM mechanical behavior. For this reason, various models have been used to derive the effective proprieties of FGMs and simulate thereby their effects on the buckling and free vibration of FGM plates based on comparative studies that may differ in terms of several parameters. The refined plate theory, as used in this paper, is based on dividing the transverse displacement into both bending and shear components. This leads to a reduction in the number of unknowns and governing equations. Furthermore the present formulation utilizes a sinusoidal variation of displacement field across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the buckling and free vibration analysis are obtained for simply supported plates. The obtained results are compared with those predicted by other plate theories. This study shows the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Comprehensive visualization of results is provided. The analysis is relevant to aerospace, nuclear, civil and other structures.

• Structural Engineering and Mechanics
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• 제85권1호
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• pp.105-118
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• 2023

The present work is an attempt to develop a simple and accurate finite element formulation for the assessment of thermal shock/thermally induced vibrations in pretwisted and tapered functionally graded material thin (FGM) blades obtained from Voigt and local representative volume elements (LRVE) homogenization models, based on neutral surface approach. The neutral surface of the FGM blade does not coincide with its mid-surface. A finite element model (FEM) is developed using first-order shear deformation theory (FSDT) and the FGM turbine blade is modelled according to the shallow shell theory. The top and the bottom layers of the FGM blade are made of pure ceramic and pure metal, respectively and temperature-dependent material properties are functionally graded in the thickness direction, the position of the neutral surface also depends on the temperature. The material properties are estimated according to two different homogenization models viz., Voigt or LRVE. The top layer of the FGM blade is subjected to high temperature and the bottom surface is either thermally insulated or kept at room temperature. The solution of the nonlinear profile of the temperature in the thickness direction is obtained from the Fourier law of heat conduction in the unsteady state. The results obtained from the present FEM are compared with the benchmark examples. Next, the effect of angle of twist, intensity of thermal shock, variable chord and span and volume fraction index on the transient response due to thermal shock obtained from the two homogenization models viz., Voigt and LRVE scheme is investigated. It is shown that there can be a significant difference in the transient response calculated by the two homogenization models for a particular set of material and geometric parameters.

• 한국소음진동공학회논문집
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• 제26권7호
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• pp.851-856
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• 2016

In this paper, the free vibration characteristics of longitudinally corrugated cylindrical shells is investigated by the theoretical analysis. The equivalent homogenization model is adapted to investigate the overall mechanical behavior of these corrugated shells. The corrugated element can be represented as an orthotropic material. Both the effective extensional and flexural stiffness of this equivalent orthotropic material are considered in the analysis. To demonstrate the validity of the proposed theoretical approach, the theoretical results are compared with those from 3D finite element analysis using ANSYS commercial code. Some numerical results are presented to check the effect of the geometric properties.

• 한국정밀공학회지
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• 제22권2호
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• pp.79-88
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• 2005

Evaluating the effective properties of materials containing various types of in-homogeneities is an important issue in the analysis of structures composed of those materials. A simple and effective method for the purpose is to impose the periodic displacement boundary conditions on the finite element model of a unit cell. Their theoretical background is explained based on the purely kinematical relations in the regularly spaced in-homogeneity problems, and the strategies to implement them into the analysis and to evaluate the homogenized material constants are introduced. The creep behavior of a thin sheet with square arrayed rectangular voids is characterized, where the orthotropy is induced by the presence of the voids. The homogenization method is validated through the comparison of the analysis of detailed model with that of the simplified one with the effective parameters.

• Computers and Concrete
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• 제15권5호
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• pp.735-758
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• 2015

This work deals with unilateral effect of quasi-brittle materials, such as concrete. For this propose, a two-dimensional meso-scale model is presented. The material is considered as a three-phase material consisting of interface zone, matrix and inclusions - each constituent modeled by an appropriate constitutive model. The Representative Volume Element (RVE) consists of inclusions idealized as circular shapes randomly placed into the specimen. The interface zone is modeled by means of cohesive contact finite elements developed here in order to capture the effects of phase debonding and interface crack closure/opening. As an initial approximation, the inclusion is modeled as linear elastic as well as the matrix. Our main goal here is to show a computational homogenization-based approach as an alternative to complex macroscopic constitutive models for the mechanical behavior of the quasi-brittle materials using a finite element procedure within a purely kinematical multi-scale framework. A set of numerical examples, involving the microcracking processes, is provided. It illustrates the performance of the proposed model. In summary, the proposed homogenization-based model is found to be a suitable tool for the identification of macroscopic mechanical behavior of quasi-brittle materials dealing with unilateral effect.

• 한국태양에너지학회 논문집
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• 제36권3호
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• 한국암반공학회:학술대회논문집
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• 한국암반공학회 2000년도 암반공학문제의 수치해석(Numerical Analysis in Rock Engineering Problems)
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• pp.55-61
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• 2000

암반이나 암석의 역학적 거동을 파악하기 위하여 각종시험 및 수치해석을 수행할 때 대표요소체적(REV)의 크기를 객관적으로 결정할 필요가 있다. 본 연구에서는 영주화강암을 대상으로 암석의 역학적 거동에 영향을 미티는 여러 가지 요소 중 조암광물의 함유율에 주목하여 해석모델의 크기변화에 따른 조암광물의 비율과 탄성제수의 변화를 검토하여 REV를 산정하였다. 조암광물의 분포는 해석모델의 면적이 약 702$ extrm{mm}^2$(900 요소)을 초과하면서부터 일정해 지고 있으며, 탄성계수는 해석모델의 면적이 약 900$ extrm{mm}^2$(1156요소)을 초과하면서부터 일정치를 보여준다.

• 터널과지하공간
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• 제10권3호
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• pp.309-315
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• 2000

암반이나 암석의 역학적 거동을 파악하기 위하여 각종시험 및 수치해석을 수행할 때 대표요소체적 (REV)의 크기를 객관적으로 결정할 필요가 있다. 본 연구에서는 영주화강암을 대상으로 암석의 역학적 거동에 영향을 미치는 여러 가지 요소 중 조암광물의 함유율에 주목하여 해석모델의 크기변화에 따른 조암광물의 비율과 탄성계수의 변화를 검토하여 REV를 산정 하였다. 조암광물의 분포는 해석모델의 면적이 약 702$\textrm{mm}^2$(900 요소)을 초과하면서부터 일정해 지고 있으며, 탄성계수는 해석모델의 면적이 약 900$\textrm{mm}^2$(1156 요소)을 초과하면서부터 일정치를 보여준다.

• 소성∙가공
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• 제33권1호
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• pp.18-35
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• 2024

In the present work, the evolution rules for the internal variables including continuum damage factors are obtained using the thermodynamic framework, which are in turn facilitated to derive the elastic-plastic constitutive relation for the particulate composites. Using the Mori-Tanaka scheme, the homogenization on state and internal variables such as back-stress and damage factors is carried out to procure the rate independent plasticity relations. Moreover, the degradation of mechanical properties of constituents is depicted by the distinctive damages such that the phase and interfacial damages are treated individually accordingly, whereas the kinematic hardening is depicted by combining the Armstrong-Frederick and Phillips' back-stress evolutions. On the other hand, the present constitutive relation for each phase is expressed in terms of the respective damage-free effective quantities, then, followed by transformation into the damage affected overall nominal relations using the aforementioned homogenization concentration factors. An emphasis is placed on the qualitative analyses for strain localization by observing the perturbation growth instead of the conventional bifurcation analyses. It turns out that the proposed constitutive model offers a wide range of strain localization behavior depending on the evolution of various internal variable descriptions.