Introduction to Hypo plasticity, Modelling Approach, What is Hypo-plasticity, ?Why Hypo-plasticity?, Constitutive Equations, Applications of Hypo-plasticity, Influence parameters, Research Trends in Hypo-plasticity, Constitutive methods- GTE, IIT Kanpur- Geo tech, Term Paper

1. CE-637 : CONSTITUTIVE MODELLING
OF FRICTIONAL MATERIALS
Term work- Dr Arghya Das
BY
Group 9
9a. Samirsinh P. G-14103277
9b. Santhoshkumar G-14203265
QIP Research Scholar, IITK,
GEOTECHNICAL ENGINEERING, (2014 Batch)

2. INTRODUCTION
• Constitutive models – numerical calculations of boundary value
problems
• Very simple to extremely complex
• Prerequisite knowledge about yield surfaces and complicated
hardening rules
• Basic Soil features – nonlinearity, irreversibility, failure criterion,
stress-volumetric coupling, deformation history, anisotropy, time-
dependence etc.
• Models - simulate at least some primary features
• Tested with experimental results obtained from more than one
apparatus
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

3. Modelling approach
Elasticity
Elastoplasticity
Perfect Plasticity
Hardening
Plasticity
Isotropic
Hardening
Kinematic and
Mixed
Hardening
Bounding
Surface Plasticity
Hypo elasticity Hypoplasticity
Endochronic
Theory
Ref: “ON BASIC FEATURES OF CONSTITUTIVE MODELS FOR GEOMATERIALS”, by Ivo Herle, Journal of Theoretical and Applied Mechanics, Sofia, 2008, vol. 38,
No’s 1-2, pp. 61-80 3
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

4. What is Hypoplasticity ?
• An alternate to Elastoplastic theory
• A plastic model without using yield surface
• Captures the non linearity in the stress-strain relation from the very
beginning itself
General form in tensorial equation:
𝑇 = ℎ 𝑇, 𝐷, …
𝑇 - Stress rate
𝑇 – Actual Stress
𝐷– Deformation rate
Ref: D.Kolymbas (1985)
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

5. Why Hypoplasticity ?
• Simplicity.
• Single constitutive equation (for loading and unloading).
• No decomposition in to elastic and plastic deformation.
• Takes into account :
i. nonlinear stress-strain relation
ii. pressure sensitivity
iii. shear and volumetric coupling
iv. dilatant volume change
• Can be extended to include many parameters
Ref: D.Kolymbas (2000) 5
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

6. Constitutive Equations
• Kolymbas (1985). First version of constitutive law
𝑇 = 𝐹 𝑇, 𝐷
• Gudehus, (1996) -Modified equation with void ratio,
𝑇 = 𝐹 𝑇, 𝑒, 𝐷
𝑇 = 𝐴 𝑇, 𝑒, 𝐷 + 𝐵 𝑒, 𝑇 𝐷
6
Linear
Relation
Non linear
Relation
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

7. 𝐴 𝑇, 𝑒, 𝐷 = 𝑓𝑒 𝑒 . 𝐿(𝑇, 𝐷)
𝐵 𝑒, 𝑇 𝐷 = 𝑓𝑒 𝑒 . 𝑓𝑑 𝑒 . 𝑁(𝑇)
𝑓𝑒 𝑒 &𝑓𝑑 𝑒 - Factors corresponding to stiffness and friction angle
respectively.
• Stress ratio tensor, 𝑇 =
T
tr T
• 𝑇∗ = 𝑇 −
Deviatoric part of 𝑇
3
7
Constitutive Equationscontd..
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

8. 𝐿 𝑇, 𝐷 = 𝑎1
2
. 𝐷 + 𝑇. 𝑡𝑟(𝑇, 𝐷)
𝑁 𝑇 = 𝑎1. (𝑇 + 𝑇∗)
Where,
𝑎1 =
1
𝐶1+𝐶2 𝑇 .(1+cos 3𝜃 )
𝐶1 and 𝐶2 are dimensionless constants
Lode angle, cos 3𝜃 = − 6.
𝑡𝑟(𝑇∗
3)
𝑡𝑟(𝑇∗
2)
1/2
8
Constitutive Equationscontd..
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

10. Undrained Triaxial Compression Test
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pq form:
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

11. Development of constitutive equations
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

12. Development of constitutive equations contd..
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Where,
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

13. Analysis
• Parametric analysis in constitutive equations
• Incremental strain with respect to increment in Mean stress, deviatoric
stress, Maximum shear stress and Stress ratio
• Void ratio and initial stress varied.
• Void ratio has a strong influence on the simulation results.
• Influence of parameters in hypoplastic constitutive equations on simulation
results also studied
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

14. Results
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

15. Results
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

16. Observations
16
• Cyclic triaxial undrained test can be modelled using the same
hypoplastic constitutive equation with the modification of
parameters.
• Model can be used to simulate small strain amplitude cyclic tests.
• Cyclic degradation is not captured completely at large strain
amplitude.
Reason: Model considered grain structure history as a significant factor
resulting in difficulty in obtaining first loading curve.
*Model without considering grain structure used for cyclic tests.
*n parameter has to be degraded to simulate the degradation behavior.
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

17. Influence of parameters
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

18. Direct Simple Shear test
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

19. Constitutive Equations
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

20. Direct Simple Shear test
• Analysis, simulation and parametric studies done similar to previous
case
• Model can be used to simulated cyclic behavior for small strain
amplitude only.
• For cyclic tests, shape of the hysteresis loops are better than triaxial
test simulation.
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

21. Comparison of models
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When C2 set to zero
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

22. Calibration of parameters
With experimental observations, the parameters involved in the
constitutive equation can be deduced.
Example:
• C1 -from CSL obtained from triaxial compression tests
• C2 -from CSL obtained from triaxial extension tests
• hs and n – from oedometer tests
• a and b - from isotropic compression tests
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23. 23
Bauer’s hypoplastic model simulation results and oedometer results
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

24. Results for cyclic triaxial test
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

25. Direct shear test model vs experimental results
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

26. Conclusion
• A single equation can be used to simulate the soil behavior
• Stress state is completely defined and any type of deformation can be
found out
• Different types of soil behavior can be simulated (contractive and
dilative or only contractive or monotonic soil liquefaction)
• Influence of each parameter can be well identified
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Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

27. Research in Hypoplasticity
1991 An outline of hypoplasticity D. Kolymbas,
1996
model simulating the soil behaviour around a pile during its vibratory driving, and estimating the
resulting pile penetration speed Bauer and Gudehus
2000
Evaluation of different strategies for the integration of hypoplastic constitutive equations:
Application to the CLoE model
Claudio Tamagnini1,*,s,
Gioacchino Viggiani2, ReneH
Chambon3 and Jacques Desrues3
2003 Extended Hypoplastic Models for soils Andrzej Niemunis
2004 Hypoplasticity for soils with low friction angles I. Herle , D. Kolymbas
2005 A hypoplastic constitutive model for clays David Mašín
2005 Hypoplasticity theory for granular materials—I: Two-dimensional plane strain exact solutions Grant M.Cox ∗, James M.Hill
2005 Hypoplasticity theory for granular materials—II:Three-dimensional axially symmetric exact solutions Grant M.Cox ∗, James M.Hill
2007 A hypoplastic constitutive model for clays with meta-stable structure David Mašín
2008 A hypoplastic model for mechanical response of unsaturated soils David Mašín
2008 Review of two hypoplastic equations for clay considering axisymmetric element deformations T. Weifner *, D. Kolymbas
2009 A hypoplastic model for site response analysis
D.K. Reyesa, A.Rodriguez-Marekb,
, A.Lizcano
2014 Modified Bounding Surface Hypoplasticity Model for sands under cyclic loading Gang Wang, M. and Yongning Xie 27
Hypoplasticity & its Applications, IITK, GTE-PHD, Civil Engg.

28. References:
1. “An outline of Hypoplasticity” Archive of Applied Mechanics 61 (1991) 143—151.
2. Numerical Simulation of Shear Band Formation with a Hypoplastic Constitutive Model- J. Tejchman &
W. Wub
3. Hypoplasticity for soils with low friction angles- Herle , D. Kolymbas (2004)
4. “Hypoplasticity theory for granular materials—I: Two-dimensional plane strain exact solutions”,
Grant M. Cox, James M. Hill, (2005)
5. “ Hypoplasticity Investigated”, Kambiz Elmi Anaraki, 2008.
6. “on basic features of constitutive models for geomaterials” Ivo Herle, 2008
7. “A hypoplastic model for site response analysis” D.K. Reyesa, Rodriguez-Marekb, Lizcanoa (2009)
8. “Development and applications of hypoplastic constitutive models”, A dissertation of David Masin,
2009.
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