The role of constitutive models in ... - Alert Geomaterials
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12/5/2017 1 The role of constitutive models in large deformation MPM simulations Elliot James Fern University of California, Berkeley [email protected] Tuesday, 05 December 2017 © NY Times 2014
Transcript of The role of constitutive models in ... - Alert Geomaterials
12/5/2017
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The role of constitutive models in large deformation MPM simulations
Elliot James FernUniversity of California, Berkeley
Tuesday, 05 December 2017
© NY Times 2014
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Observe Understand Model Simulate
ENGINEERING FLOW CHART
Granular Column Collapse
∗
∗
(Fern and Soga 2016)
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Granular Column CollapseN
ormalised H
eight [-]
MECHANICS OF SAND
Dry pluviated Chiba sand (Fern 2016)
not CS
not CS
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0
MOHR-COULOMB (Terzaghi 1943)
Option 2: Large Deformation
Option 1: Small Deformation
⋅ tan
Does the small strain behaviour playa role in the large deformation simulations?
0causes unrealistic results
⋅ tan
→
→
→
→
0 →
MOHR-COULOMB STRAIN SOFTENING (Terzaghi 1943, Abbo and Sloan 1995)
Large Deformation
Small Deformation
Does the absence of energy dissipation in the ‘elastic hardening’ phase play a role?
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1
1 1
⋅ … ⋅ ,
Nor-Sand (Jefferies 1993)
Hardening rule
Yield Surface
Stress-Dilatancy rule
Nor-Sand (Jefferies 1993)
, 1
Maximum Yield Surface
Ψ
⋅ Ψ
Causes instabilities at large deformation.
→ ,
→ ,
→ ,
Ψ 0 →
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Material Point Method www.anura3d.com
(Fern and Soga, 2016a)
Granular Column Collapse
(Fern and Soga, 2016a)
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Granular Column Collapse
Mohr-Coulomb (critical state parameters)
One could curve-fit by numerical damping but, excessive damping is cheating!
Granular Column Collapse
Mohr-Coulomb Strain Softening – loose sand
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Granular Column Collapse
Mohr-Coulomb Strain Softening – dense sand
Granular Column Collapse
Nor-Sand – loose sand
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Granular Column Collapse
Nor-Sand – dense sand
Granular Column Collapse
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Energy Considerations
Small columns
⋅ ⋅
cot 1
Large columns
Failure angle (Bolton, 1986)
⋅ ⋅ ⋅ ⋅
tan 1
0.8
⋅
ln
Granular Column Collapse
(Fern and Soga, 2016a) (Fern and Soga, 2017)
(Fern et al., 2016b)
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Conclusion
• The constitutive model has a two-fold influence.- It defines the failure surface (hence the mobilised energy)
- Therefore, the small strain behaviour cannot be neglected from ‘large deformation simulations’- and it controls the energy dissipation (hence the run-out distance)
- Which becomes increasingly important with large deformation
• The initial density influences the constitutive model - indirectly through an enhancement of the model parameters (i.e. Mohr–Coulomb)- or directly through its inclusion as model variable (i.e. Nor-Sand.and)
• The requirements and implementations of constitutive models for large deformation MPM simulations can differ from small deformation FE simulations.
• The choice of the constitutive model plays a major role in the predictions of the failure (i.e. type of failure, run-out distance) and its choice is not trivial.
Acknowledgement
www.anura3d.com
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END
