• Interaction and multiscale mechanics
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• 제5권1호
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• pp.27-40
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• 2012

The two-dimensional incompressible flow of a linear viscoelastic fluid we considered in this research has rapidly oscillating initial conditions which contain both the large scale and small scale information. In order to grasp this double-scale phenomenon of the complex flow, a multiscale analysis method is developed based on the mathematical homogenization theory. For the incompressible flow of a linear viscoelastic Maxwell fluid, a well-posed multiscale system, including averaged equations and cell problems, is derived by employing the appropriate multiple scale asymptotic expansions to approximate the velocity, pressure and stress fields. And then, this multiscale system is solved numerically using the pseudospectral algorithm based on a time-splitting semi-implicit influence matrix method. The comparisons between the multiscale solutions and the direct numerical simulations demonstrate that the multiscale model not only captures large scale features accurately, but also reflects kinetic interactions between the large and small scale of the incompressible flow of a linear viscoelastic fluid.

• Interaction and multiscale mechanics
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• 제2권4호
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• pp.353-374
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• 2009

A new seamless multiscale simulation was developed for coupling the continuum model with its molecular dynamics. Kriging-based Finite Element Method (K-FEM) is employed to model the continuum base of the entire domain, while the molecular dynamics (MD) is confined in a localized domain of interest. In the coupling zone, where the MD domain overlaps the continuum model, the overall Hamiltonian is postulated by contributions from the continuum and the molecular overlays, based on a quartic spline scaling parameter. The displacement compatibility in this coupling zone is then enforced by the Lagrange multiplier technique. A multiple-time-step velocity Verlet algorithm is adopted for its time integration. The validation of the present method is reported through numerical tests of one dimensional atomic lattice. The results reveal that at the continuum/MD interface, the commonly reported spurious waves in the literature are effectively eliminated in this study. In addition, the smoothness of the transition from MD to the continuum can be significantly improved by either increasing the size of the coupling zone or expanding the nodal domain of influence associated with K-FEM.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.

• Nuclear Engineering and Technology
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• 제36권3호
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• pp.229-236
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• 2004

Radiation hardening is a multiscale phenomenon involving various processes over a wide range of time and length. We present a multiscale model for estimating the amount of radiation hardening in pressure vessel steel in the environment of a light water reactor. The model comprises two main parts: molecular dynamics (MD) simulation and a point defect cluster (PDC) model. The MD simulation was used to investigate the primary damage caused by displacement cascades. The PDC model mathematically formulates interactions between point defects and their clusters, which explains the evolution of microstructures. We then used a dislocation barrier model to calculate the hardening due to the PDCs. The key input for this multiscale model is a neutron spectrum at the inner surface of reactor pressure vessel steel of the Younggwang Nuclear Power Plant No.5. A combined calculation from the MD simulation and the PDC model provides a convenient tool for estimating the amount of radiation hardening.

• Korean Chemical Engineering Research
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• 제45권6호
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• pp.582-590
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• 2007

Water gas shift reaction(WGSR)이 일어나는 파이럿 규모 고온반응기에서의 거동 및 성능을 예측하기 위하여 수학적 모델을 수립하고 모사를 수행하였다. 반응기의 형상, 유체 및 열 이동에 대해 상세한 모델링이 가능한 전산유체역학 기법과 공정시스템 공학에서 사용되는 공정모사 기법을 함께 사용한 multiscale 모델링 및 모사를 수행하였으며, 그 결과를 일반 공정모사와 비교하였다. Multiscale 모사를 통해 CO의 전환율은 최고 0.85, 발열반응으로 인해 충전층의 온도는 약 720 K까지 오름을 알 수 있었다. 또한 동적모사를 통해 시간에 따른 반응기내에서의 온도분포, 전환율 분포 등의 주요한 변수 및 성능들의 시간에 따른 변화를 예측할 수 있었다. Multiscale 모사 기법은 파이럿 규모의 반응기뿐 아니라 상업규모의 공정에 대해 실제 상황을 상세히 반영하여 정확한 예측이 가능하므로, 상업공정 설계에 주요한 기술로 사용될 수 있다.

• 응용통계연구
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• 제24권6호
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• pp.995-1006
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• 2011

A time series can be decomposed into simple components with a multiscale method. Empirical mode decomposition(EMD) is a recently invented multiscale method in Huang et al. (1998). It is natural to apply a classical prediction method such a vector autoregressive(AR) model to the obtained simple components instead of the original time series; in addition, a prediction procedure combining a classical prediction model to EMD and Hilbert spectrum is proposed in Kim et al. (2008). In this paper, we suggest to adopt principal component analysis(PCA) to the prediction procedure that enables the efficient selection of input variables among obtained components by EMD. We discuss the utility of adopting PCA in the prediction procedure based on EMD and Hilbert spectrum and analyze the daily worm account data by the proposed PCA adopted prediction method.

• Computers and Concrete
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• 제33권3호
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• pp.325-340
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• 2024

The growing demands for sustainable and high-performance construction materials necessitate a deep understanding of their physicochemical properties by that of these heterogeneities. This paper presents a comprehensive review of the state-of-the-art hierarchical multiscale modeling approach aimed at predicting the intricate physicochemical characteristics of construction materials. Emphasizing the heterogeneity inherent in these materials, the review briefly introduces single-scale analyses, including the ab initio method, molecular dynamics, and micromechanics, through a scale-bridging technique. Herein, the limitations of these models are also overviewed by that of effectively scale-bridging methods of length or time scales. The hierarchical multiscale model demonstrates these physicochemical properties considering chemical reactions, material defects from nano to macro scale, microscopic properties, and their influence on macroscopic events. Thereby, hierarchical multiscale modeling can facilitate the efficient design and development of next-generation construction.

• Composites Research
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• 제36권5호
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• pp.329-334
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• 2023

기존의 멀티스케일 유한요소법(Multiscale finite element, FE² )은 거시 스케일의 모든 적분점에서 대표 체적요소(representative volume element, RVE)의 미시 경계치 문제를 반복적으로 계산하기 때문에 긴 해석 시간과 많은 데이터 저장 공간을 필요로 한다. 이를 해결하기 위해 본 연구에서 평균장 균질화 데이터 기반 멀티스케일 해석 기법을 개발하였다. 데이터 기반 전산역학(data-driven computational mechanics, DDCM) 해석은 변형률-응력 데이터 셋을 직접적으로 사용하는 모델-프리(model-free)접근 방식이다. 멀티스케일 해석을 수행하기 위해, 평균장 균질화(mean-field homogenization)를 활용하여 복합재의 미세구조에 대한 변형률-응력 데이터베이스(database)를 효율적으로 구축하고, 이를 기반으로 데이터 기반 전산역학 시뮬레이션을 수행하였다. 본 논문에서는 개발한 멀티 스케일 해석 프레임워크(framework)를 예제에 적용하여, 초탄성(hyperelasticity) 복합재의 미세 구조를 고려한 데이터 기반 전산역학 시뮬레이션 결과를 확인하였다. 따라서, 데이터 기반 전산역학 접근 방식을 활용한 멀티스케일 해석기법은 다양한 재료 및 구조에 적용될 수 있으며, 멀티스케일 해석 연구 및 응용 가능성을 열어줄 것으로 기대된다.

• Nuclear Engineering and Technology
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• 제41권1호
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• pp.11-20
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• 2009

Radiation effects on materials are inherently multiscale phenomena in view of the fact that various processes spanning a broad range of time and length scales are involved. A multiscale modeling approach to embrittlement of pressure vessel steels is presented here. The approach includes an investigation of the mechanisms of defect accumulation, microstructure evolution and the corresponding effects on mechanical properties. An understanding of these phenomena is required to predict the behavior of structural materials under irradiation. We used molecular dynamics (MD) simulations at an atomic scale to study the evolution of high-energy displacement cascade reactions. The MD simulations yield quantitative information on primary damage. Using a database of displacement cascades generated by the MD simulations, we can estimate the accumulation of defects over diffusional length and time scales by applying kinetic Monte Carlo simulations. The evolution of the local microstructure under irradiation is responsible for changes in the physical and mechanical properties of materials. Mechanical property changes in irradiated materials are modeled by dislocation dynamics simulations, which simulate a collective motion of dislocations that interact with the defects. In this paper, we present a multi scale modeling methodology that describes reactor pressure vessel embrittlement in a light water reactor environment.

• Interaction and multiscale mechanics
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• 제1권1호
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• pp.1-31
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• 2008

The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors' own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.