simulation in materials summary
DESCRIPTION
Simulation in Materials Summary. Friday, 12/6/2002. MATLAB programming. Visualization: Stress matrix visualization Stress field visualization Color expression Simulation methods: Atomistic simulation Brownian movement Molecular dynamics (MD) Monte Carlo method (MC) - PowerPoint PPT PresentationTRANSCRIPT
MATLAB programming
Visualization:Stress matrix visualizationStress field visualizationColor expression
Simulation methods:Atomistic simulation
Brownian movementMolecular dynamics (MD)Monte Carlo method (MC)
Continuum SimulationMaterial Point Method (MPM)Finite Element Method (FEM)
Visualization
Stress field visualizationhole under stretchingcrack tip
Stress matrix visualizationhedgehog for 2D stress matrixbean-bag for 3D stress matrix
Color expressiondisplacement distribution in FEM
Bean-Bag Method
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σ11 σ12 σ13
σ21 σ 22 σ 23
σ31 σ 32 σ 33
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥ =
1 2 3
2 2 −1
3 −1 1
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
Visualization of FEM Results
Displacementfield
Pixel:The smallest image-forming unit of a video display.
Extension of Random WalkThis model is a two-dimensional extension of a random walk. Displayed is the territory covered by 500 random walkers. As the number of walkers increases the resulting interface becomes more smooth.
Monte Carlo Method1. Current configuration: C(n)
2. Generate a trial configuration by selecting an atom at random and move it.
3. Calculate the change in energy for the trial configuration, U.
Essence of MD
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ax(i ) =
Fx(i ) +fx
(i )
m(i)
ay(i ) =
Fy(i ) +fy
(i )
m(i)
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fx(i ) = fx
(i, j )
j≠i
∑
fy(i ) = fy
(i, j )
j≠i
∑
Internal forces External forces
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Fx(i)
Fy(i)
MPM
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a x(n) =
1M (n) F x
(n) + f x(n)
( )
a y(n) =
1M (n) F y
(n) + f y(n)
( )
⎧
⎨ ⎪
⎩ ⎪
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v x(n) =
1M (n) m( p)vx
( p)N(n,p)
p
∑
v y(n) =
1M (n) m( p)vy
( p)N(n,p)
p
∑
⎧
⎨ ⎪
⎩ ⎪