• 대한조선학회논문집
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• 제33권3호
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• pp.94-102
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• 1996

유한변형문제에서 변형구배텐서를 탄소성 성분으로 분해하기 위한 가산분해와 곱분해방법에 대해서 설명하고, 이 두 방법에서 파생되는 역학량들의 의미와 그 차이점을 보였다. 변형구배에 대한 기존의 곱분해와 가산분해로 얻어지는 변형속도구배는 가산적으로 표현되지 않으며, 소성변형속도구배는 탄성변형의 영향을 받고 있다. 본 연구에서는 공축소성 가정을 도입하고, 수정된 곱분해를 통하여 소성변형속도구배가 탄성변형에 영향을 받지 않는 가산적인 변형속도 구배를 얻었다.

• 한국컴퓨터그래픽스학회논문지
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• 제28권4호
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• pp.13-22
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• 2022

본 논문에서는 최소 입자 단위의 역동적인 회전 움직임을 나타낼 수 있는 MPM(Material Point Method) 기반 단일 프레임워크를 소개한다. 우리가 표현하고자 하는 입자는 다양한 형상(Shape)을 가질 수 있음과 동시에, 선형(Linear momentum), 회전(Angular momentum) 운동을 함께 묘사할 수 있다. 그 결과 기존 구형 입자의 선형 움직임만을 나타내던 입자 기반 시뮬레이션과는 달리, 시각적으로 단일 입자의 역동적인 모습을 표현할 수 있다. 제안하는 프레임워크는 회전 운동을 큰 변형(Large Deformation)으로부터 분해 및 추출 할 수 있다는 점에서 MPM을 활용하였다. 본 기법은 MPM 적분 과정 중 계산되는 변형 구배 텐서(Deformation Gradient Tensor)를 극 분해(Polar Decomposition)하는 과정을 통해 회전 텐서(Rotation Tensor)를 추출하고, 각 입자의 선형 운동과 함께 이를 적용하여 결과적으로 입자 자체의 회전, 선형 운동을 동시에 표현 하는 것이 가능하다. 본 연구에서는 제안하는 기법의 검증을 위해 바람에 흩날리며 회전하는 입자의 모습 및 움직이는 물체와 정지한 입자간의 상호작용 시뮬레이션을 기존 MPM을 이용한 시뮬레이션과의 비교를 통해 진행하였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.736-739
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• 1995

The meshless adaptive method based on multiple scale analysis is developed to simulate large deformation problems. In the procedure, new particles are simply added to the orginal particle distribution because meshless methods do not require mesh structures in the formulations. The high scale component of the approximated solution detects the localized region where a refinement is needed. The high scale component of the second invariant od Green-Lagrangian strain tensor is suggested as the new high gradient detector for adaptive procedures. The feasibility of the proposed theory is demonstrated by a numerical experiment for the large deformation of hyperelastic materials.

• Structural Engineering and Mechanics
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• 제76권1호
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• pp.17-26
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• 2020

The objective of this paper is to study the deformation in transversely isotropic thermoelastic solid using new modified couple stress theory subjected to ramp-type thermal source and without energy dissipation. This theory contains three material length scale parameters which can determine the size effects. The couple stress constitutive relationships are introduced for transversely isotropic thermoelastic solid, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of length scale parameters are depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the scale effects of microstructures.

• 한국전산유체공학회지
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• 제6권4호
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• pp.15-25
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• 2001

Numerical prediction of the diffusion controlled transition in a turbine gas pass is important because it can change the local heat transfer rate over a turbine blade as much as three times. In this study, the gas flow over turbine blade is simplified to the flat plate boundary layer, and an adaptive grid scheme redistributing grid points within the computation domain is proposed with a great emphasis on the construction of the grid control function. The function is sensitized to the second invariant of the mean strain tensor, its spatial gradient, and the interaction of pressure gradient and flow deformation. The transition process is assumed to be described with a κ-ε turbulence model. An elliptic solver is employed to integrate governing equations. Numerical results show that the proposed adaptive grid scheme is very effective in obtaining grid independent numerical solution with a very low grid number. It is expected that present scheme is helpful in predicting actual flow within a turbine to improve computation efficiency.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 춘계학술대회논문집
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• pp.156-159
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• 2003

Surface normal vector and surface velocity are very important parameters to simulate rolling processes precisely. In this study, Local displacement functions are constructed for each node on the contact surface and parameters are found by the least square fitting of displacement on the neighbor nodes. Deformation gradient tensor is calculated from the displacement function and surface normal vector and velocity also can be derived. Flat rolling simulation model is presented on the basis of the suggested contact scheme. Series of rolling process simulation are carried out and the results are compared with the experiments.

• Smart Structures and Systems
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• 제30권3호
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• pp.221-237
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• 2022

This paper is concerned with nonlinear modeling and efficient numerical simulation of electrostrictive materials and structures. Two types of such materials are considered: relaxor ferroelectric ceramics and electrostrictive polymers. For ceramics, a geometrically linear formulation is developed, whereas polymers are studied in a geometrically nonlinear regime. In the paper, we focus on constitutive modeling first. For the reversible constitutive response under consideration, we introduce the augmented Helmholtz free energy, which is composed of a purely elastic part, a dielectric part and an augmentation term. For the elastic part, we involve an additive decomposition of the strain tensor into an elastic strain and an electrostrictive eigenstrain, which depends on the polarization of the material. In the geometrically nonlinear case, a corresponding multiplicative decomposition of the deformation gradient tensor replaces the additive strain decomposition used in the geometrically linear formulation. For the dielectric part, we first introduce the internal energy, to which a Legendre transformation is applied to compute the free energy. The augmentation term accounts for the contribution from vacuum to the energy. In our formulation, the augmented free energy depends not only on the strain and the electric field, but also on the polarization and an internal polarization; the latter two are internal variables. With the constitutive framework established, a Finite Element implementation is briefly discussed. We use high-order elements for the discretization of the independent variables, which include also the internal variables and, in case the material is assumed incompressible, the hydrostatic pressure, which is introduced as a Lagrange multiplier. The elements are implemented in the open source code Netgen/NGSolve. Finally, example problems are solved for both, relaxor ferroelectric ceramics and electrostrictive polymers. We focus on thin plate-type structures to show the efficiency of the numerical scheme and its applicability to thin electrostrictive structures.

• Composites Research
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• 제22권4호
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• pp.20-26
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• 2009

본 연구에서는 직조섬유복합재료를 이용한 계란판 모양의 시편에 대한 드래이핑 공정과 압축 해석을 비직교성 재료 모델을 이용하여 수행하였다. 비 직교 재료 구성 모델은 Xue 등이 2003년에 발표한 것을 상용 프로그램인 LS-DYNA에서 제공하는 사용자 부프로그램 (user subroutine)을 이용하여 본 연구에 적용하였다. 비 직교 재료 구성 모델에서 빙향성은 변형 기울기 텐서를 이용하여 계산하였고, 각 단계마다 재료 물성 행렬을 갱신하였다. 비 직교 물성 모델은 바이어스 인장 실험 결과와 비교 검증을 한 후에 계란 판 성형에 적용하였다. 계란 판 해석을 위해 본 연구에서는 열 성형 공정 (드래이핑)과 압축 해석을 수행하였다. 압축 해석을 위한 유한요소 모델은 드래이핑 해석으로부터 얻은 유한요소결과를 이용하여 구축하였다.