• 소성∙가공
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• 제21권6호
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• pp.366-371
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• 2012

Atomistic simulations have become useful tools for exploring new insights in materials science, but the length and time scale that can be handled with atomistic simulations are seriously limiting their practical applications. In order to make meaningful quantitative predictions, atomistic simulations are necessarily combined with higher-scale modeling. The present research is thus concerned with the development of a multi-scale model and its application to the prediction of the mechanical properties of body-centered cubic(BCC) iron with an emphasis on the coupling of atomistic molecular dynamics with meso-scale discrete dislocation dynamics modeling. In order to achieve predictive multi-scale simulations, it is necessary to properly incorporate atomistic details into the meso-scale approach. This challenge is handled with the proposed hierarchical information passing strategy from atomistic to meso-scale by obtaining material properties and dislocation mobility. Finally, this fundamental and physics-based meso-scale approach is employed for quantitative predictions of the mechanical response of single crystal iron.

• Interaction and multiscale mechanics
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• 제3권2호
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• pp.111-121
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• 2010

Dynamic analysis of nano/micro bio-sensors based on a multiscale atomistic/continuum theory is introduced. We use a generalized atomistic finite element method (GAFEM) to analyze a bio-sensor which has $3{\times}N_a{\times}N_p$ degrees of freedom, where $N_p$ is the number of representative unit cells and $N_a$ is the number of atoms per unit cell. The stiffness matrix is derived from interatomic potential between pairs of atoms. This work contains two studies: (1) the resonance analysis of nano bio-sensors with different amount of target analyte and (2) the dependence of resonance frequency on finite element mesh. We also examine the Courant-Friedrichs-Lewy (CFL) condition based on the highest resonance frequency. The CFL condition is the criterion for the time step used in the dynamic analysis by GAFEM. Our studies can be utilized to predict the performance of micro/nano bio-sensors from atomistic perspective.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.395-402
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• 2006

In analyzing the nano-scale phenomena or behaviors of nano devices or materials, it is often desirable to deal with more atoms than can be treated only with a full atomistic simulation. However, even now, it is advisable to apply the atomistic simulation to the narrow region where the deformation field changes rapidly but to apply the conventional continuum model to the region far from that region. This equivalent continuum model can be formulated by applying the Cauchy-Born rule to the exact atomistic potential as in the quasicontinuum method. To couple the atomistic model with the equivalent continuum model, continuum displacements are conformed to the molecular displacements at the discrete positions of the atoms within the bridging domain. To satisfy the coupling constraints, we apply the Lagrange multiplier method. The continuum model in the bridging model should be applied on the region where the deformation field changes gradually. Then we can make the nodal spacing in the continuum model be much larger than the atomic spacing. In the first step, we generate the atomic-resolution mesh with the nodal spacing equal to the atomic spacing, and then we eliminate the nodal degrees of freedom adaptively using the node deactivation techniques. We eliminate more DOFs as the regions are more far from the atomistic region. Computing time and computational resources can be greatly reduced by the present node deactivation technique in multi scale analysis.

• 반도체디스플레이기술학회지
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• 제3권3호
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• pp.27-29
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• 2004

The responses of hypothetical silicon nanotubes under torsion have been investigated using an atomistic simulation based on the Tersoff potential. A torque, proportional to the deformation within Hooke's law, resulted in the ribbon-like flattened shapes and eventually led to a breaking of hypothetical silicon nanotubes. Each shape change of hypothetical silicon nanotubes corresponded to an abrupt energy change and a singularity in the strain energy curve as a function of the external tangential force, torque, or twisted angle. The dynamics of silicon nanotubes under torsion can be modelled in the continuum elasticity theory.

• Interaction and multiscale mechanics
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• 제4권2호
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• pp.107-122
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• 2011

Mechanical behavior in nano-sized structures differs from those in macro sized structures due to surface effect. As the ratio of surface to volume increases, surface effect is not negligible and causes size-dependent mechanical behavior. In order to identify this size effect, atomistic simulations are required; however, it has many limitations because too much computational resource and time are needed. To overcome the restrictions of the atomistic simulations and graft the well-established continuum theories, the continuum model considering surface effect, which is based on the bridging technique between atomistic and continuum simulations, is introduced. Because it reflects the size effect, it is possible to carry out a variety of analysis which is intractable in the atomistic simulations. As a part of the application examples, the homogenization method is applied to micro/nano thin films with porosity and the homogenized elastic coefficients of the nano scale thickness porous films are computed in this paper.

• 한국수학사학회지
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• 제19권4호
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• pp.97-106
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• 2006

격자의 기원은 수학에서 비롯된 것이 아니고 논리학에서 시작되었다([22]). 1880 년경 Peirce는 모든 격자는 분배 격자라고 생각하였으나 1890년경 $Schr{\"{o}}der$가 오류를 수정하였고, 1933년 Birkhoff가 lattice라는 단어를 처음 사용하였으나 이는 오늘의 격자와는 그 정의가 다르다. 이 논문에서는 Peirce를 소개하고 atomic 격자, atomistic 격자, J-격자, strong 격자 그리고 분배 격자의 상관관계를 연구한다.

• 한국전기전자재료학회논문지
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• 제16권12S호
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• pp.1157-1164
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• 2003

This paper shows the results of atomistic modeling for the interaction between spherical nano abrasive and substrate in chemical mechanical polishing processes. Atomistic modeling was achieved from 2-dimensional molecular dynamics simulations using the Lennard-Jones 12-6 potentials. The abrasive dynamics was modeled by three cases, such as slipping, rolling, and rotating. Simulation results showed that the different dynamics of the abrasive results the different features of surfaces. This model can be extended to investigate the 3-dimensional chemical mechanical polishing processes.

• Macromolecular Research
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• 제15권7호
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• pp.610-616
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• 2007

We developed a coarse-grained force field and have extended it to polystyrene with longer chain length. A systematic method was introduced and was utilized to explain how the coarse-grained force field for polystyrene could be developed from the atomistic simulation in the paper. We elected to use polystyrene with different chain lengths of 20, 40 and 80 monomers in this study. In three cases, we utilized the same new mapping scheme. The coarse-grained force field does reproduce the bond, angle, and radial distribution of the atomistic model. The coarse-grained model proved successful, as shown by analyses of the static and dynamic properties of different chain lengths.

• Advances in nano research
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• 제3권3호
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• pp.143-168
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• 2015

Initiation of crack and its growth simulation requires accurate model of traction - separation law. Accurate modeling of traction-separation law remains always a great challenge. Atomistic simulations based prediction has great potential in arriving at accurate traction-separation law. The present paper is aimed at establishing a method to address the above problem. A method for traction-separation law prediction via utilizing atomistic simulations data has been proposed. In this direction, firstly, a simpler approach of common neighbor analysis (CNA) for the prediction of crack growth has been proposed and results have been compared with previously used approach of threshold potential energy. Next, a scheme for prediction of crack speed has been demonstrated based on the stable crack growth criteria. Also, an algorithm has been proposed that utilizes a variable relaxation time period for the computation of crack growth, accurate stress behavior, and traction-separation atomistic law. An understanding has been established for the generation of smoother traction-separation law (including the effect of free surface) from a huge amount of raw atomistic data. A new curve fit has also been proposed for predicting traction-separation data generated from the molecular dynamics simulations. The proposed traction-separation law has also been compared with the polynomial and exponential model used earlier for the prediction of traction-separation law for the bulk materials.

• Interaction and multiscale mechanics
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• 제7권1호
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• pp.543-561
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• 2014

We present a full energy and force formulation of the quasicontinuum method with non-local and local transition elements. Non-local transition elements are developed to transmit inhomogeneity from the atomistic to the continuum regions. Local transition elements are developed to resolve the mathematical mismatch between non-local atoms and the local continuum. The rationale behind these transition elements is provided by analyzing the energy and force transitions between atoms and continuum under the Cauchy-Born rule. We show that breakdown of the Cauchy-Born rule occurs for slaved atoms of local elements within the cutoff of non-local atoms. The inadequacy of the Cauchy-Born rule at the transition region naturally leads to the need of atomistic treatment of transition slaved and transition representative atoms. Such an atomistic treatment together with a full or cutoff sampling allows non-local transition elements containing these transition entities to transmit inhomogeneity. Different force formulations for transition representative atoms and pure local representative atoms allow the local transition elements to resolve non-local and local mismatches. The method presented herein is validated by force calculations in an unstressed perfect crystal as well as an unrelaxed grain boundary model. A nanoindentation simulation in 3D is conducted to demonstrate the accuracy and efficiency of the proposed method.