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Models for Plastic Deformation Based on NonModels for Plastic Deformation Based on Non--LinearLinearResponse for FEM Implementation Response for FEM Implementation

Zachry Department of Civil Engineering Texas A&M University, College Station, TX

Eyad MasadEyad Masad

Acknowledge Funding byAsphalt Research Consortium

International Workshop on Asphalt Binders and MasticsMadison, Wisconsin. September 16-17

Outline

Motivation

Viscoelastic-Viscoplastic-Viscodamage Models

Identification of model parameters and model validation

Implementation procedure

Application of the model for rutting performance simulation

Conclusions and future works

MotivationMotivationPrediction of pavement performance

Material Characteristics

Aggregate shape

Anisotropy

Adhesive and Cohesive bond strengths

Healing

Binder rheology

Pavement Structure

Thickness

Sub grade type

Loading Conditions

Type of loading

Tire pavement interaction

FEM Modeling

Environmental Factors

Temperature

Humidity differential

Rainfall

Calibration (minimize shift factor dependency)

Prediction of material distress

Mechanical Response of Asphalt MixesMechanical Response of Asphalt MixesThermo-Chemo-Hygro-Mechanical Constitutive ModelViscoelastic-Viscoplastic-Viscodamage

VE VPPercent of Strain

Temperature Increase and/or decrease in strain rate

Viscoelastic

Strain

Time

Viscoplastic

Strain

Time

Mechanical Response of Asphalt MixesMechanical Response of Asphalt MixesThermo-Chemo-Hygro-Mechanical Constitutive ModelViscoelastic-Viscoplastic-Viscodamage

Rate- and Time-dependent softening

Displacement control tests

0

2500

5000

7500

10000

0 2 4 6 8 10 12 14

Strain

Stress

0

1

2

3

4

5

0 200 400 600 800 1000 1200

Axi

al st

rain

(%)

Time (Sec)

Repeated creep-recovery test

Outline

Viscoelastic-Viscoplastic-Viscodamage Models

Viscoelastic PropertiesViscoelastic PropertiesThermo-Chemo-Hygro-Mechanical Constitutive ModelNonlinear Viscoelastic Model (Schapery, 1969)

0 0 1 20

ve t dg D g D g dd

Nonlinear contribution in the elastic response, due to the level of stress

Nonlinear contribution in the transient response

Nonlinear contribution in the viscoelastic response due to the level of stress

1

1 expN

n nn

D D t

Prony series coefficients Retardation time

0

t

T

dta

Temperature shift factor

Viscoplastic PropertiesViscoplastic Properties

ve vpij ij ij Perzyna Model

1vp vpij e ef F I Yield surface(Extended Drucker-Prager)

Viscoelastic

Yield surface

Viscoplastic0f

f 0 1 21 exp vpe Hardening function

Nvp vpijij

gT f

Flow Rule:

1g I Plastic potential function:

0 00

ff

f f

Overstress function

Viscoplastic Model (Perzyna, 1971)

Extended DruckerExtended Drucker--Prager Yield SurfacePrager Yield Surface

1f I

1g I

Accounts for:Dilation and confinement pressureThe effect of shear stressWork hardening of the material

Yield surface

Potential function

vp

1I

Viscoplastic PropertiesViscoplastic Properties

Influence of stress path on the yielding point

Effect of parameter d on the yield surface

2 33/22

1 11 12J J

d d J

Strength Degradation due to DamageStrength Degradation due to Damage

DamagedConfiguration

1

A AA

T

T

A

Effective UndamagedConfiguration

Remove BothVoids and Cracks

A

T

T

0 1

0 Nominal (measured) stress

Effective stress

Damage density

No damage

1 Failure

0 1 Damage

Viscodamage ModelViscodamage Model

20 0

1 exp exp 1q

vd TotY TkY T

Damage force 2 3 13/22

1 11 12J JY I

d d J

Damage is sensitive to hydrostatic pressure

Damage is sensitive toLoading Mode

Damage response is different in compression or extension

I1 : First stress invariant

J2 and J3 : The second and the third deviatoric stress invariants

Viscodamage model (Darabi, Abu Al-Rub, Masad, Little; 2010)

Determination of Model ParametersDetermination of Model Parameters

Separate viscoelastic (recoverable) and viscoplastic (irrecoverable) strains.

Creep-Recovery test @ reference temperature

Determination of viscoelastic parameters @ reference temperature

Recovery part of the Creep-Recovery test @ reference temperature

Determination of viscoplastic parameters @ reference temperature

Creep part of the Creep-Recovery test @ reference temperature

Determination of viscodamage parameters @ reference temperature

Two creep tests that show tertiary behavior @ reference temperature

Determination temperature-dependent model parametersCreep-recovery and creep tests @ other temperatures

Determination of d parametersCreep test in tension@ reference temperature


Separate viscoelastic (recoverable) and viscoplastic (irrecoverable) strains.

Creep-Recovery test @ reference temperature

Stress

Time

Time

Strain

at

at

at t

0 0 1 2 vpa a at g D g g D t t

1 2 vpat g g D t D t t t

vp vpat t During the recovery:

0 0 1 2 a

a

ag D g g D t

t

D t D t t

t

Pure viscoelastic response.Can be used for identifying VE parameters


Time

Strain

at

Determination of viscoplastic parameters @ reference temperature

Creep part of the Creep-Recovery test @ reference temperature

Total strain (experimental measurements) Viscoelastic response.

Model predictions using the Identified VE model parameters.

Viscoplastic response. Obtained by subtracting the VE response from the experimental measurements

Pure viscoplastic response.Can be used for identifying VP parameters

Determination of Model ParametersDetermination of Model ParametersDetermination of viscodamage parameters @ reference temperature

A creep tests that show tertiary behavior @ reference temperature and stress level

Time

Strain

Total strain (experimental measurements)@ reference temperature and stress level

Model response using identified VE-VP model parameters

Deviation from the experimental data at tertiary stage due to damage

21 expvd Totk @ reference temperature T=T00

exp 1 1TT

@ reference stress Y=Y0

Identify these damage parametersUsing the creep test at reference temperature

and stress level

Determination of Model ParametersDetermination of Model ParametersDetermination of viscodamage parameters @ reference temperature

Another creep tests that show tertiary behavior @ reference temperature and other stress level

20

1 expq

vd TotY kY

@ reference temperature T=T0

0exp 1 1T

T

Identify the stress dependency parameter q

Time

Strain

Total strain (experimental measurements)@ reference temperature and stress level

Model response using identified VE-VP-VD model parameters

Deviation from the time of failure due to stress dependency parameter q

Known

Stress Levels within the Pavements

Gibson et al., 2010

Model Validation Tests

Test Temperature(oC)Stress Level

(kPa)Loading time

(Sec)Strain Rate

(1/Sec)

Compression

Creep-Recovery

10 2000, 2500 300, 350, 400

20 1000, 1500 30, 40, 130, 210

40 500, 750 35, 130, 180

Creep

10 2000, 2500

20 1000, 1500

40 500, 750

Constant strain rate test

10 0.005, 0.005, 0.00005

20 0.005, 0.005, 0.00005

40 0.005, 0.005

TensionCreep

10 500, 1000, 1500

20 500, 700

35 100, 150

Constant strain rate test 20 0.0167, 0.00167

Outline

Model Validation

Model Validation (Creep-Recovery Test)

102000kPa

oT C

102500kPa

oT C

Creep-recovery testCompression

@ T=10oC

1- Model can predict creep-recovery data at different temperatures and stress levels. (Compression)



@ T=20oC


201000kPa

oT C

201500kPa

oT C



@ T=40oC


40500kPa

oT C

40750kPa

oT C

Model Validation (Creep Test)

Creep testCompression

2-Model predictions agrees well with creep data at different temperatures and stress levels. Tertiary creep behavior is also captured.

10oT C 20oT C

Model Validation (Creep Test)

Creep testCompression

2-Model predictions agrees well with creep data at different temperatures and stress levels. Tertiary creep behavior is also captured.

40oT C

Model Validation (Constant Strain Rate Test)

Constant strain rate testCompression

Loading rate: 0.005/Sec

3-Model predicts temperature and rate-dependent behavior of asphalt mixes. Post peak behavior is captured well.

T=10

T=40

T=20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12

Dam

age d

ensi

ty

Strain (%)

T=10T=20T=40

Model Validation (Constant Strain Rate Test)



3-Model predicts temperature and rate-dependent behavior of asphalt mixes. Post peak behavior is captured well.

T=10

T=20

T=40

T=10

T=20

T=40

0

500

1000

1500

2000

2500

3000

0 2 4 6 8 10 12 14St

ress

(kPa

)Strain (%)

T=10

T=20



Model Validation in Tension (Creep Test)4-Model predicts experimental data in tension. Tertiary stage and time of failure are captured well.

Creep testTension

Temperature: 10oC

0.0

0.5

1.0

1.5

2.0

2.5

0 300 600 900 1200 1500

Axi

al st

rain

(%)

Time (Sec)

Experimental dataModel prediction

1500 kPa

1000 kPa 500 kPa

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500

Axi

al st

rain

(%)

Time (Sec)


700 kPa 500 kPa

300 kPa

Creep testTension

Temperature: 20oC

Model Validation in Tension (Creep Test)4-Model predicts experimental data in tension. Tertiary stage and time of failure are captured well.

Creep testTension

Temperature: 35oC

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200

Axi

al st

rain

(%)

Time (Sec)


150 kPa

100 kPa

Model Validation in Tension (Creep Test)4-Model predicts experimental data in tension.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12D

amag

e den

sity

Strain (%)

Strain rate=0.0167/Sec

Strain rate=0.00167/Sec

0

1000

2000

3000

4000

5000

0 2 4 6 8 10 12

Stre

ss (k

Pa)

Strain (%)

0.0167 / Sec

0.00167 / Sec

Constant strain rate testTension

Temperature: 20oC

Outline

Implementation procedure

Abaqus interfaceAbaqus interface

Running and viewing the simulation resultsRunning and viewing the simulation results

Creating geometry, mesh, and applying loadingCreating geometry, mesh, and applying loading

Pavement Section

MeshBoundary Conditions

Loaded region

Simulating Rutting

UMATA Fortran code includes the Continuum Damage Model

UMATA Fortran code includes the Continuum Damage Model

FortranFortran compiler is used to compile UMAT (i.e. translates programming commands into action).

FortranFortran compiler is used to compile UMAT (i.e. translates programming commands into action).

Procedure to Run the Performance Prediction Continuum Damage ModelProcedure to Run the Performance Prediction Continuum Damage ModProcedure to Run the Performance Prediction Continuum Damage Modelel

Abaqus calls UMAT to run the Continuum Damage Model and UMAT gives Abaqus the material response

Abaqus calls UMAT to run the Continuum Damage Model and UMAT gives Abaqus the material response

Implementation Procedure

Outline

Application of the model for rutting performance simulation

2D FE Model 3D FE Model

Application for Simulation of Wheel Tracking Test

Application: Different Loading CasesMode Loading approach

Loading Area Schematic representation of loading modes

1 (2D) Pulse loading (plane strain)

One wheel

2 (2D) Equivalent loading (plane strain)

One wheel

3 (2D) Pulse loading

(axisymmetric) One wheel

4 (2D) Equivalent loading

(axisymmetric) One wheel

5 (3D) Pulse loading One wheel

6 (3D) Equivalent loading One wheel

7 (3D) Pulse loading Whole

wheel path

8 (3D) Equivalent loading Whole

wheel path

9 (3D) Pulse loading Circular

loading area

10 (3D) Equivalent loading Circular loading area

11 (3D) Moving loading One wheel Moving Direction

Application: Different Loading Modes and Constitutive Models

0

0.02

0.04

0.06

0.08

0.1

0.12

0 200 400 600 800 1000

Rut

ting (

mm

)

Cycles (N)

Loading Mode 1 Loading Mode 2




Viscoelastic-Viscoplastic Constitutive Model

0

0.02

0.04

0.06

0.08

0.1

0.12

0 200 400 600 800 1000

Rut

ting (

mm

)

Cycles (N)





0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 200 400 600 800 1000

Rut

ting (

mm

)

Cycles (N)





Viscoelastic-Viscoplastic-Viscodamage Model

Elastic-Viscoplastic Constitutive Model

2D Rutting simulation results:Different constitutive models.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 200 400 600 800 1000

Rut

ting (

mm

)

Cycles (N)




Loading Mode 11

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 200 400 600 800 1000

Rut

ting (

mm

)

Cycles (N)

Loading Mode 5Loading Mode 6Loading Mode 7Loading Mode 8Loading Mode 9Loading Mode 10Loading Mode 11

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 200 400 600 800 1000

Rut

ting (

mm

)

Cycles (N)

Loading Mode 5Loading Mode 6Loading Mode 7Loading Mode 8Loading Mode 9Loading Mode 10Loading Mode 11


Viscoelastic-Viscoplastic Constitutive Model

Viscoelastic-Viscoplastic-Viscodamage Model

Elastic-Viscoplastic Constitutive Model

3D Rutting simulation results:Different constitutive models.


Simplified loading assumptions can be used when using elasto-viscoplasticmodel.

Simplified loading assumptions should be used carefully when viscoelasticresponse is significant.

Using simplified loading assumptions causes significant error when the damage level is significant.

2D Results 3D Results

Simulation Results

Viscoplastic strain

2D Results 3D Results

Simulation Results

Damage evolution

0

2

4

6

8

10

12

14

0 20000 40000 60000 80000 100000 120000

Rut

ting (

mm

)

Cycles (N)

Experimental Measurements2D results3D results

Compare with Experimental Data

ALF Data-Variable StressApplied stress (T=55oC)

Dev

iato

ric st

ress

(kPa

)

Time (Sec)

Model Validation: ALF Data (Strain Response)

1st Cycle 2nd Cycle

3rd Cycle 4th Cycle

Model Validation: ALF Data (Strain Response)

5th Cycle 6th Cycle

7th Cycle 8th Cycle

Model Validation: ALF Data (Strain Response)Model predictions at large loading cycles

At large loading cycles model predictions using VE-VP deviates from experimental measurements

This deviation is due to damage and should be compensated using the damage model.

1.50E03

2.00E03

2.50E03

3.00E03

3.50E03

4.00E03

4.50E03

3004 3006 3008 3010 3012 3014 3016

Time(Sec)

TotalStrain

exp

cal.

Deviatoric stress: 712kPa

Model Validation: ALF Data (Strain Response)Constant Stress-Variable Time Loading

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 10 20 30 40 50 60

Cycle

VP s

trai

n

model

exp

Cycle

Vis

copl

astic

Stra

in

Conclusions and Future Works

Conclusions:

Proposed viscoelastic-viscoplastic-viscodamage model predicts rate-, time-, and temperature-dependent behavior of asphalt mixes in both tension and compression.

Model can be used to predict performance simulations.

Challenges and future works: Including healing to the model.

Including environmental effects such as aging and moisture induced damage to the model.

Validating the model over an extensive experimental measurements.

Performing performance simulations in pavements.

Questions?Questions?

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