Material Point Method (MPM) 2D

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Material Point Method (MPM)2D
Monday, 10/14/2002
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Equations of Motion
2D problem
1D problem
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Equations of Motion (Variational form)
? arbitrary spatial function
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Variational Equation
2D problem
Divergence theorem
1D problem
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Divergence Theorem
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Particle Discretization
2D problem Free boundary
1D problem Free boundary
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Grid Equation
2D problem Free boundary
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Arbitrary function y
2D problem Free boundary
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Arbitrary function in Matrix
? arbitrary value
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Shape Functions (1D)
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2D Shape Function
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2D Interpolation
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Shape Function (2D)
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Bilinear Shape Function
Global shape function constructed from bilinear
shape function.
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Properties of Shape Function
Partition of unity
Positive
Kronecker delta
Interpolation
Smooth everywhere, except at nodes where they are
continuous.
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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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Linear Elastic Constitutive Model
Plane stress