1. Continuum Simulation Monday, 9/30/2002

2. Class Progress Visualization: abstract concept (stress,2D, 3D), mechanical field Stochastic simulations: random walk, Brownian movement Monte Carlo method (MC) Ensemble Molecular Dynamics (MD) Trajectory Multiscale simulation Adaptive Mesh Refinement/Coarsening; Renormalization Continuum simulation Finite Element Method (FEM); Material Point Method (MPM)

3. Continuum vs. Atomistic ContinuumAtomistic MatterIndefinitely divisible Atom aggregate InteractionStress; strainInteratomic force ModelConstitutive model Potential model

4. Continuum Problems Equilibrium equations: Material constitutive equations (linear): Boundary conditions

5. Discretization in Finite Element Method (FEM) The basic concept is that a body or structure may be divided into smaller elements.

6. Discretization in Material Point Method (MPM) Solid line is an outline of the body analyzed. Black dots are the material points. Dashed lines show a regular, background grid for calculation.

7. Lagrangian & Eulerian Description Lagrangian: quantities like position, velocity, stress, are given for a particular moving particle at varying times. Eulerian: the velocities are given at fixed points in space as time varies. Imagine a case where both the measuring device and the frame of reference are fixed.

8. Approximation to Region MPMFEM

9. FEM Simulation of Crack Tip Process

10. MPM Simulation of Crack Tip Process

11. Adaptive Mesh Refinement/Coarsening

12. MPM Simulation of Fragmentation