Theoretical Analyses of Surface Interaction Stresses Considering Two-Dimensional Periodic Material Distributions

2017 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Ryoya Miyake ◽  
Satoru Maegawa ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Shear Stresses ◽  
Material Distribution ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Complex Fourier Series ◽  
Spatially Periodic ◽  
Basic Characteristics ◽  
Theoretical Analyses

The interaction stresses (pressure and shear stress) for (001) surface between a half-space consisting of a uniform material and a half-space with a spatially periodic material distribution have been derived based on the Lennard-Jones potential. The periodically distributed material property function is expanded as a complex Fourier series. The interaction pressures consist of non-fluctuation terms and fluctuation terms, while the shear stresses have only fluctuation terms. The interaction stresses for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The basic characteristics of the interaction stresses are clarified.

Theoretical Study of Surface Interaction Stresses Considering One-Dimensional Material Distributions in the In-Plane Direction Based on the Lennard-Jones Potential

2016 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Teppei Tanaka ◽  
Ryoya Miyake ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Material Distribution ◽  
Elementary Functions ◽  
Jones Potential ◽  
One Dimensional ◽  
Single Interface ◽  
Periodic Distribution ◽  
Lennard Jones ◽  
Plane Direction ◽  
Basic Characteristics

The interaction stresses acting between a half-space consisting of a uniform material and a half-space with a one-dimensional material distribution in the in-plane direction have been derived. Two patterns of the material distribution are considered: a periodic distribution of materials (Pattern 1) and a distribution of two materials with a single interface (Pattern 2). The interaction stresses for Pattern 1 were derived using a Fourier series, while the interaction stresses for Pattern 2 were derived as elementary functions. The basic characteristics of these interaction stresses were clarified.

scholarly journals Dislocation Mobility in Two-Dimensional Lennard-Jones Material

1999 ◽  
Vol 578 ◽  
Author(s):  
Nicholas P. Bailey ◽  
James P. Sethna ◽  
Christopher R. Myers
Keyword(s):  
Energy Barrier ◽  
Thermal Activation ◽  
Functional Form ◽  
Finite Energy ◽  
Atomistic Simulations ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Accurate Knowledge ◽  
Dimensional Crystal

AbstractIn seeking to understand at a microscopic level the response of dislocations to stress we have undertaken to study as completely as possible the simplest case: a single dislocation in a two dimensional crystal. The intention is that results from this study will be used as input parameters in larger length scale simulations involving many defects. We present atomistic simulations of defect motion in a two-dimensional material consisting of atoms interacting through a modified Lennard-Jones potential. We focus on the regime where the shear stress is smaller than its critical value, where there is a finite energy barrier for the dislocation to hop one lattice spacing. In this regime motion of the dislocation will occur as single hops through thermal activation over the barrier. Accurate knowledge of the barrier height is crucial for obtaining the rates of such processes. We have calculated the energy barrier as a function of two components of the stress tensor in a small system, and have obtained good fits to a functional form with only a few adjustable parameters.

scholarly journals Two-step melting of the Weeks-Chandler-Anderson system in two dimensions

Soft Matter ◽  
2021 ◽  
Author(s):  
Shubhendu Shekhar Khali ◽  
Dipanjan Chakraborty ◽  
Debasish Chaudhuri
Keyword(s):  
Numerical Simulation ◽  
Two Dimensions ◽  
Dimensional System ◽  
Lennard Jones Potential ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
System Of Particles ◽  
Two Dimensional System ◽  
Repulsive Part

We present a detailed numerical simulation study of a two-dimensional system of particles interacting via the Weeks-Chandler-Anderson potential, the repulsive part of the Lennard-Jones potential. With the reduction of density,...

MASS DISTRIBUTION OF A TWO-DIMENSIONAL FRAGMENTATION PROCESS

2005 ◽  
Vol 16 (02) ◽  
pp. 253-258 ◽  
Author(s):  
L. E. ARARIPE ◽  
A. DIEHL ◽  
J. S. ANDRADE ◽  
R. N. COSTA FILHO
Keyword(s):  
Mass Distribution ◽  
Radial Component ◽  
Fragmentation Process ◽  
Lennard Jones Potential ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Mass Size ◽  
Dynamics Simulations ◽  
Number Of Particles

We perform extensive molecular dynamics simulations to study the mass size distribution of a two-dimensional fragmentation process. Our model consists of a large number of particles interacting through the Lennard–Jones potential. The fragmentation is induced by suddenly imposing a radial component on the particles' velocities, in order to mimic an explosion phenomenon. We then investigate the effect of the input energy on the resulting mass distribution of fragments.

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