1. Material Point Method Solution Procedure Wednesday, 10/9/2002 Map from particles to grid Interpolate from grid to particles Constitutive model Boundary conditions

2. Mass matrix Compact mass matrix: Only matrix elements close to diagonal are not zero.

3. Lumped Mass Matrix

4. 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

5. Particle information stress: position: velocity:

6. Mapping: particle  grid External force Internal force Mass matrix Momentum

7. Solve Equations on the Grid

8. Update particle position

9. Update particle velocity

10. Update particle stress E is Young’s modulus. Linear elastic constitutive model

11. Particle strain rate

12. Stress-strain curve

13. Boundary Conditions If v (1) <0: contact Momentum change:

14. Next few classes 2D MPM How to write MPM code in MATLAB Techniques in programming, data structure