Material Point Method Solution Procedure

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Material Point MethodSolution Procedure
Map from particles to grid Interpolate from grid
to particles Constitutive model Boundary
conditions
Wednesday, 10/9/2002
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Mass matrix
Compact mass matrix Only matrix elements close
to diagonal are not zero.
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Lumped Mass Matrix
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Solution

1. Particle discretization, grid
2. Initialize particle information
3. Map particle information to grid
4. Solve the motion equations on grid
5. Interpolate from grid to particles
6. Update the information on particles

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Particle information
position
velocity
stress
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Mapping particle ?grid
External force
Internal force
Mass matrix
Momentum
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Solve Equations on the Grid
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Update particle position
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Update particle velocity
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Update particle stress
Linear elastic constitutive model
E is Youngs modulus.
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Particle strain rate
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Stress-strain curve
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Boundary Conditions
If v(1)lt0 contact
Momentum change
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Next few classes
2D MPM How to write MPM code in MATLAB Techniques
in programming, data structure