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Simulation in Materials Summary Friday, 12/6/2002

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MATLAB programming Visualization: Stress matrix visualization Stress field visualization Color expression Simulation methods: Atomistic simulation Brownian movement Molecular dynamics (MD) Monte Carlo method (MC) Continuum Simulation Material Point Method (MPM) Finite Element Method (FEM)

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Visualization Stress field visualization hole under stretching crack tip Stress matrix visualization hedgehog for 2D stress matrix bean-bag for 3D stress matrix Color expression displacement distribution in FEM

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Stress Distribution Visualization Crack tip stress distribution Stress distribution around a hole

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Hedgehog Method

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Bean-Bag Method

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Visualization of FEM Results Displacement field Pixel: The smallest image- forming unit of a video display.

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Atomistic Simulation Brownian movement Molecular dynamics (MD) Monte Carlo method (MC)

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Extension of Random Walk This 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.

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Extension of particles from one room to two rooms

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Monte Carlo Method 1. 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.

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Essence of MD Internal forces External forces

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Continuum Simulation Material Point Method (MPM) Finite Element Method (FEM)

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MPM

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FEM

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