• Interaction and multiscale mechanics
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• 제2권2호
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.410-415
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• 2004

Molecular dynamics simulations of nanoimprint lithography in which a stamp with patterns is pressed onto amorphous poly-(methylmethacrylate) (PMMA) surface are performed to study the deformation of polymer. Force fields including bond, angle, torsion, inversion, van der Waals and electrostatic potential are used to describe the intermolecular and intramolecular force of PMMA molecules and stamp. Periodic boundary condition is used in horizontal direction and $Nos\acute{e}$-Hoover thermostat is used to control the system temperature. As the simulation results, the adhesion forces between stamp and polymer are calculated and the mechanism of deformation are investigated. The effects of the adhesion force and friction force on the polymer deformation are also studied to analyze the pattern transfer in nanoimprint lithography. The mechanism of polymer deformation is investigated by means of inspecting the indentation process, molecular configurational properties, and molecular configurational energies.

• 대한기계학회논문집A
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• 제29권6호
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• pp.852-859
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• 2005

Molecular dynamics simulations of nanoimprint lithography in which a stamp with patterns is pressed onto amorphous poly-(methylmethacrylate) (PMMA) surface are performed to study the deformation of polymer. Force fields including bond, angle, torsion, inversion, van der Waals and electrostatic potential are used to describe the intermolecular and intramolecular force of PMMA molecules and stamp. Periodic boundary condition is used in horizontal direction and Nose-Hoover thermostat is used to control the system temperature. As the simulation results, the adhesion forces between stamp and polymer are calculated and the mechanism of deformation are investigated. The effects of the adhesion and friction forces on the polymer deformation are also studied to analyze the pattern transfer in nanoimprint lithography. The mechanism of polymer deformation is investigated by means of inspecting the indentation process, molecular configurational properties, and molecular configurational energies.

• 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.

• Structural Engineering and Mechanics
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• 제43권2호
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.337-342
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• 2007

In this study, molecular dynamics simulation of nano imprint lithography in which patterned stamp is pressed onto amorphous polyethylene(PE) surface are performed to study the behaviour of polymer. Force fields including bond, angle, torsion, and Lennard Jones potential are used to describe the inter-molecular and intra-molecular force of PE molecules and stamp, substrate. Periodic boundary condition is used in horizontal direction and canonical NVT ensemble is used to control the system temperature. As the simulation results, the behaviour of polymer is investigated during the imprinting process. The mechanism of polymer deformation is studied by means of inspecting the surface shape, volume, density, atom distribution. Deformation of the polymer resist was found for various of the stamp geometry and the alignment state of the polymer molecules.

• Coupled systems mechanics
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• 제1권2호
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Tribology and Lubricants
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• 제22권5호
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• pp.243-251
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• 2006

Molecular dynamics simulations of nanoimprint lithography NIL) are performed in order to investigate effects of process parameters, such as stamp shape, imprinting temperature and adhesive energy, on nanoimprint lithography process and pattern transfer. The simulation model consists of an amorphous $SiO_{2}$ stamp with line pattern, an amorphous poly-(methylmethacrylate) (PMMA) film and an Si substrate under periodic boundary condition in horizontal direction to represent a real NIL process imprinting long line patterns. The pattern transfer behavior and its related phenomena are investigated by analyzing polymer deformation characteristics, stress distribution and imprinting force. In addition, their dependency on the process parameters are also discussed by varying stamp pattern shapes, adhesive energy between stamp and polymer film, and imprinting temperature. Simulation results indicate that triangular pattern has advantages of low imprinting force, small elastic recovery after separation, and low pattern failure. Adhesive energy between surface is found to be critical to successful pattern transfer without pattern failure. Finally, high imprinting temperature above glass transition temperature reduces the imprinting force.