# hypoplasticity and its application in grannular mechanics

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HYPOPLASTICITY AND ITS APPLICATION

CONSTITUTIVE MODELLING OF FRICTIONAL MATERIALS

BY Prof. Samirsinh P Parmar,

Prof. Santhoshkumar GMail: [email protected]

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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

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

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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 itselfGeneral form in tensorial equation:

- Stress rate – Actual Stress – Deformation rate

Ref: D.Kolymbas (1985)4

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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 relationii. pressure sensitivityiii. shear and volumetric couplingiv. dilatant volume change• Can be extended to include many parameters

Ref: D.Kolymbas (2000)

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Constitutive Equations

• Kolymbas (1985). First version of constitutive law

• Gudehus, (1996) -Modified equation with void ratio,

Linear Relation

Non linear Relation

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- Factors corresponding to stiffness and friction angle respectively.

• Stress ratio tensor, •

Constitutive Equationscontd..

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Where,

and are dimensionless constantsLode angle,

Constitutive Equationscontd..

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Applications of Hypoplasticity

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Undrained Triaxial Compression Test

pq form:

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Development of constitutive equations

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Development of constitutive equations contd..

Where,

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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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Results

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Results

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Observations• 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.

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Influence of parameters

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Direct Simple Shear test

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Constitutive Equations

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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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Comparison of modelsWhen C2 set to zero

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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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Bauer’s hypoplastic model simulation results and odometer results

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Results for cyclic triaxial test

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Direct shear test model vs experimental results

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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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Research in Hypoplasticity1991 An outline of hypoplasticity D. Kolymbas,

1996model simulating the soil behaviour around a pile during its vibratory driving, and estimating the

resulting pile penetration speed Bauer and Gudehus

2000Evaluation of different strategies for the integration of hypoplastic constitutive equations:

Application to the CLoE model

Claudio Tamagnini1,*,s, Gioacchino Viggiani2, ReneH

Chambon3 and Jacques Desrues32003 Extended Hypoplastic Models for soils Andrzej Niemunis2004 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 Mašín2008 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 analysisD.K. Reyesa, A.Rodriguez-Marekb,

, A.Lizcano

2014 Modified Bounding Surface Hypoplasticity Model for sands under cyclic loading Gang Wang, M. and Yongning Xie

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References:

• “An outline of Hypoplasticity” Archive of Applied Mechanics 61 (1991) 143—151.• Numerical Simulation of Shear Band Formation with a Hypoplastic Constitutive Model- J. Tejchman &

W. Wub• Hypoplasticity for soils with low friction angles- Herle , D. Kolymbas (2004)• “Hypoplasticity theory for granular materials—I: Two-dimensional plane strain exact solutions”, Grant

M. Cox, James M. Hill, (2005)• “ Hypoplasticity Investigated”, Kambiz Elmi Anaraki, 2008.• “on basic features of constitutive models for geomaterials” Ivo Herle, 2008• “A hypoplastic model for site response analysis” D.K. Reyesa, Rodriguez-Marekb, Lizcanoa (2009)• “Development and applications of hypoplastic constitutive models”, A dissertation of David Masin,

2009.

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Questions please?

Thank You