Continuum Simulation

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Continuum Simulation
Monday, 9/30/2002
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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
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Continuum vs. Atomistic
Continuum Atomistic
Matter Indefinitely divisible Atom aggregate
Interaction Stress strain Interatomic force
Model Constitutive model Potential model
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Continuum Problems
Equilibrium equations
Material constitutive equations (linear)
Boundary conditions
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Discretization inFinite Element Method (FEM)
The basic concept is that a body or structure may
be divided into smaller elements.
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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.
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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.
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Approximation to Region
MPM
FEM
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FEM Simulation ofCrack Tip Process
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MPM Simulation ofCrack Tip Process
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Adaptive Mesh Refinement/Coarsening
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MPM Simulation ofFragmentation