57
Johan Gaume and Chenfanfu Jiang A Material Point Method for snow and avalanche mechanics GRAPHYS, Grenoble, 26-27 October 2019
WSL Institute for Snow and Avalanche Research SLF
Johan Gaume and Chenfanfu Jiang
A Material Point Method
for snow and avalanche mechanics
GRAPHYS, Grenoble, 26-27 October 2019
Acknowledgments
Dr. Ted Gast
Prof. Joseph Teran
Prof. Chenfanfu Jiang
Dr. Alec van Herwijnen
Stephanie Wang
Dr. Xingyue Li
Lars Blatny
Bertil Trottet
Princess Elsa of
Arendelle
ContextProcesses of dry-snow slab avalanche release
Flow
Adapted from Schweizer et al., (2016)
ContextProcesses of dry-snow slab avalanche release
Flow
DEM
FBM
FEM FEM
FV
Adapted from Schweizer et al., (2016)
DEM
FEM
DEM
CAM
?
ContextProcesses of dry-snow slab avalanche release
Flow
Adapted from Schweizer et al., (2016)
NO UNIFIED APPROACH
DEM
FBM
FEM
FV
DEM
FEM
DEM
CAM
?
FEM
Context: Another challengeVolumetric collapse of the weak layer
Field experiments:
The Propagation Saw Test (PST)
van Herwijnen, Gaume, Bair, Reuter, Birkeland, Schweizer (2016).
Journal of Glaciology
Context: Another challengeVolumetric collapse of the weak layer
2D DEM modeling: onset and
dynamics of crack propagation
Field experiments:
The Propagation Saw Test (PST)
Gaume et al. (2015) – Gaume et al. (2017). The Cryosphere
van Herwijnen, Gaume, Bair, Reuter, Birkeland, Schweizer (2016).
Journal of Glaciology
Context: Another challengeVolumetric collapse of the weak layer
2D DEM modeling: onset and
dynamics of crack propagation
Field experiments:
The Propagation Saw Test (PST)
Gaume et al. (2015) – Gaume et al. (2017). The Cryosphere
van Herwijnen, Gaume, Bair, Reuter, Birkeland, Schweizer (2016).
Journal of Glaciology
NO RELEVANT CONSTITUTIVE
MODEL INCLUDING “COLLAPSE”
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
How does it work?We need 3 ingredients:
How does it work?We need 3 ingredients:
1. A hybrid
numerical method
How does it work?We need 3 ingredients:
2. A snow
model
1. A hybrid
numerical method
How does it work?We need 3 ingredients:
2. A snow
model
3. A weak layer
model
1. A hybrid
numerical method
© ASARC
A hybrid numerical methodThe Material Point Method (hybrid Eulerian-Lagrangian)
Momentum balance equation
Adapted from Stomakhin et al. (2013), SIGGRAPH and
Gaume et al. (2018). Nature Communications, 9(1), 3047
A hybrid numerical methodThe Material Point Method (hybrid Eulerian-Lagrangian)
Momentum balance equation
Adapted from Stomakhin et al. (2013), SIGGRAPH and
Gaume et al. (2018). Nature Communications, 9(1), 3047
A snow mechanical modelWhat do we want?
1. A mixed-mode yield surface (tension, shear, compression)
2. Hardening in compression (promoting compaction)
3. Softening in tension (promoting fracture)
► Fracture
(softening)
► Compaction
(hardening)
A snow mechanical model1. A mixed-mode yield surface: our model
q
elastic
non admissible
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
𝝉 = 𝐶: 𝝐
p
Yield surface:
Stress invariants:
Associative flow rule:
Simo and Meschke 1993
elastic right Cauchy-Green
strain tensorLie derivative plastic right Cauchy-Green
strain tensor
A snow mechanical model1. A mixed-mode yield surface: our model
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
p0
• p0: compressive strength
q
p
A snow mechanical model1. A mixed-mode yield surface: our model
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
-bp0 p0
• p0: compressive strength
• bp0: tensile strength (COHESION)
q
p
A snow mechanical model1. A mixed-mode yield surface: our model
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
-bp0 p0
M
• p0: compressive strength
• bp0: tensile strength (COHESION)
• M: slope of the Critical State Line (FRICTION)
q
p
A snow mechanical model2. Hardening in compression
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
q
p
Hardening rule:
A snow mechanical model2. Hardening in compression
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING IN
COMPRESSION
q
p
Hardening rule:
A snow mechanical model2. Hardening in compression
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING IN
COMPRESSION
q
p
Hardening rule:
A snow mechanical model2. Hardening in compression
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING IN
COMPRESSION
q
p
Hardening rule:
A snow mechanical model2. Hardening in compression
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
stress
strain
HARDENING IN
COMPRESSION
q
p
A snow mechanical model3. Softening in tension
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
SOFTENING
q
p
Hardening rule:
A snow mechanical model3. Softening in tension
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
SOFTENING
q
p
Hardening rule:
A snow mechanical model3. Softening in tension
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
SOFTENING
q
p
Hardening rule:
A snow mechanical model3. Softening in tension
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
SOFTENING
stress
strain
q
p
A good snow mechanical model2. Snow simulations
Ref: Gaume, Gast, Teran, van Herwijnen, Jiang. Dynamic anticrack propagation in snow
using large strain continuum elastoplasticity. Under review
A weak layer mechanical modelWhat do we want?
1. A mixed-mode yield surface (tension, shear, compression)
2. Softening and collapse under mixed-mode shear-compression loading
3. Frictional behavior after collapse
© ASARC
1. A mixed-mode yield surface: our model
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
-bp0 p0
M
• p0: compressive strength
• bp0: tensile strength (COHESION)
• M: slope of the Critical State Line (FRICTION)
A weak layer mechanical model
q
p
2. Softening
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
SOFTENING IN
COMPRESSION
A weak layer mechanical model
q
p
Hardening rule:
2. Softening
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
A weak layer mechanical model
SOFTENING IN
COMPRESSION
q
p
Hardening rule:
2. Softening
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
A good weak layer mechanical model
SOFTENING IN
COMPRESSION
q
p
Hardening rule:
2. Softening
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
A good weak layer mechanical model
stress
strainSOFTENING IN
COMPRESSION
3. Collapse and frictional behaviour
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING
WITHOUT COHESION
A good weak layer mechanical model
q
p
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING
WITHOUT COHESION
A good weak layer mechanical model3. Collapse and frictional behaviour
q
p
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING
WITHOUT COHESION
A good weak layer mechanical model3. Collapse and frictional behaviour
q
p
Gaume et al., (2018). Dynamic anticrack propagation in snow.
Nature Communications. 9(1), 3047
HARDENING
WITHOUT COHESION
stress
strain
A good weak layer mechanical model3. Collapse and frictional behaviour
q
p
Application to avalanche releasePropagation Saw Test on a 37°slope
Application to avalanche releasePropagation Saw Test on the flat
Application to avalanche releasePropagation Saw Test with crack branching
2D remote avalanche triggering
2D remote avalanche triggering
slab fractures
crack tip in
the weak layer
« shooting cracks »
2D remote avalanche triggering
Crack propagation speed
3D remote avalanche triggering
Crack propagation speed
3D remote avalanche triggering
Crack propagation speed
More recent – preliminary work
MPM simulations of snow microstructure
PhD Thesis of
Lars Blatny
More recent – preliminary work
Crack propagation
PhD Thesis of
Bertil Trottet
More recent – preliminary work
Crack propagation
PhD Thesis of
Bertil Trottet
More recent – preliminary work
Avalanche dynamics
PostDoc
research of
Dr. Xingyue Li
More recent – preliminary work
Avalanche dynamics
M(1+b) = 0.5
M(1+b) = 0.65
M(1+b) = 1.95
M(1+b) = 3
More recent – preliminary work
Avalanche dynamicsM(1+b) = 0.225 M(1+b) = 0.75 M(1+b) = 0.945
More recent – preliminary work
Avalanche dynamics
ConclusionFlow
Avalanche
dynamics
4
Slab releaseCrack propagationFailure initiation
Sliding of the
slab
Dynamic crack
propagation
Onset of crack
propagationCrack
formationDamage
process
microscale (mm – dm) mesoscale (dm – 1 m) macroscale (10 m – 100 m) scale
adapted from Schweizer et al. (2016)
OutlookCurrent work
Snow-tire
interaction by Stephanie Wang
(collab. SLAB x UCLA x UPenn)
Glacier calving
(collab SLAB x UPenn x UZH)
Do you have any questions?
Thanks for your attention!
