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Continuum Simulation

Continuum Simulation. Monday, 9/30/2002. 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. Continuum simulation

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Continuum Simulation

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  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 Continuum simulation Finite Element Method (FEM); Material Point Method (MPM) Multiscale simulation Adaptive Mesh Refinement/Coarsening; Renormalization

  3. Continuum vs. Atomistic

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

  5. Discretization inFinite 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 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. Lagrangian: quantities like position, velocity, stress, are given for a particular moving particle at varying times.

  8. Approximation to Region MPM FEM

  9. FEM Simulation ofCrack Tip Process

  10. MPM Simulation ofCrack Tip Process

  11. Adaptive Mesh Refinement/Coarsening

  12. MPM Simulation ofFragmentation

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