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A Hybrid Material Point Method for Frictional Contact with Diverse Materials
Xuchen Han, Theodore Gast, Qi Guo, Stephanie Wang, Chenfanfu Jiang and Joseph Teran
A Hybrid Material Point Method for Frictional Contact with Diverse - - PowerPoint PPT Presentation
A Hybrid Material Point Method for Frictional Contact with Diverse - - PowerPoint PPT Presentation
A Hybrid Material Point Method for Frictional Contact with Diverse Materials Xuchen Han , Theodore Gast, Qi Guo, Stephanie Wang, Chenfanfu Jiang and Joseph Teran MPM is hybrid Lagrangian/Eulerian Particles: constitutive modeling - the
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MPM is hybrid Lagrangian/Eulerian
- Particles: constitutive modeling - the physics
- Transfer: quadrature rule, collision detect,
topology change
- Grid handles: the Galerkin DOFs, BC,
discretization
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Stomakhin et al. 2013 Ram et al. 2015 Klar et al. 2016 Stomakhin et al. 2015 Yue et al. 2015 Daviet et al. 2016 Gast et al. 2015 Gao et al. 2018 Wolper et al. 2019 Pradhana et al. 2018
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Elastic potential Element wise energy density Deformation gradient Grid node force Grid node position Particle position
MPM for meshed objects
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Jiang et al. 2017 Jiang et al. 2017 Guo et al. 2018 Guo et al. 2018
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Drawbacks of MPM
Numerical Friction
Δ"Grid = 0.1Δ"Mesh Δ"Grid = Δ"Mesh Δ"Grid = 0.01Δ"Mesh
Grid Dependency
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MPM Collision Prevention
- Type I: Collision modes penalized via potential energy
- Type II: Smooth interpolation
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Type I Collision Resolution
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Traction in a continuum
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Traction in a continuum
+
- Cauchy stress
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Friction and plasticity
Normal force Frictional force Coulomb friction Traction
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Friction and plasticity
Yield surface
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MPM Our method
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MPM Our method
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MPM Collision Prevention
- Type I: Collision modes penalized via potential energy
- Move the DOFs to the Lagrangian Mesh
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MPM Collision Prevention
- Type I: Collision modes penalized via potential energy
- Type II: Smooth interpolation
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Type II Collision Resolution
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MPM Collision Prevention
- Type I: Collision modes penalized via potential energy
- Type II: Smooth interpolation
Modify
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Hybrid MPM
/0 = /1
⋆ − /1
45 /0 ⋅ /1 < 0: Δ/1 = 91:1 ;1 + ;4= ∥ /? ∥, −A 91 ;1 /? ∥ /? ∥ Δ/B = /B
CDE − /B ∗ = ∑ 1
H
˜ B1Δ/1
H
˜ B1 =
HB1;1 ∑0HB0;0 /? = /0 − /0 ⋅ :1:1
/1
/0
/1
⋆
:1
DOF Quadrature
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Hybrid MPM
- 1) Lagrangian Update
- 2) Transfer to grid
- 3) Transfer to collision particles
- 4) Apply impulses
- 5) Update positions
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Type II Collision Resolution
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Modify Type II Collision
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Δ"Grid = 0.1Δ"Mesh Δ"Grid = Δ"Mesh Δ"Grid = 0.01Δ"Mesh
Modify Type II Collision
Our Method MPM
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Coupling with granular Material
MPM (186s/frame) Our Method (66s/frame)
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220s/frame 73s/frame
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Strands
Curve Surface
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Strands
Jiang et al. (2017) Our Method
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Strands: Method (Continuous)
- Decompose motion into J = JK ∘ JM
- O = OKOM and OK = OK,POK,Q
- Strand energy: Ψ = ΨM(OK,P) + ΨUPV(OM)
- ΨUPV(OM) consists of stretching, twisting, and bending potentials, see [Bergou et al. 2010]
- ΨM(OK,P) is the St.Venant-Kirchhoff Hencky energy, chosen for the ease of plasticity return
mapping
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Strands: Method (Discrete)
- Strand energy: Ψ = ΨM(OK,P) + ΨUPV(OM)
- ΨUPV(OM) Lagrangian
- ΨM(OK,P) MPM
- Clean up with geometric collision algorithm
/B
∗ = /B C + ΔW XB UPV
;B
Type to enter a caption. Similar to Bridson et al. [2002]
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Strands Comparison
McAdams et al. (2009) Our Method
More than 500 thousand missed collisions 120 missed collisions 156 seconds/frame 55 seconds/frame
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Results
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Results
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Results
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Results
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Results
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