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Continuum Simulation Monday, 9/30/2002.

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Presentation on theme: "Continuum Simulation Monday, 9/30/2002."— Presentation transcript:

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
Matter Indefinitely divisible Atom aggregate Interaction Stress; strain Interatomic force Model Constitutive 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
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 of Crack Tip Process

10 MPM Simulation of Crack Tip Process

11 Adaptive Mesh Refinement/Coarsening

12 MPM Simulation of Fragmentation


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