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

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

Lumped Mass Matrix

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

Particle information stress: position: velocity:

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

Solve Equations on the Grid

Update particle position

Update particle velocity

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

Particle strain rate

Stress-strain curve

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

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