1. Simulation in Materials Summary Friday, 12/6/2002

2. 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)

3. 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

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

5. Hedgehog Method

6. Bean-Bag Method

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

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

9. 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.

10. Extension of particles from one room to two rooms

11. 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.

12. Essence of MD Internal forces External forces

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

14. MPM

15. FEM