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Constitutive Modelling for

Engineering Materials inComputational Procedures

By

Chandrakant S. Desai

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Solids, Interfaces and Joints

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Is Continuum Approach Valid?

May be for some limited materials

In general: Geologic materials contain

discontinuities initially, and/or they

develop during deformations. Then thecontinuum approach may not be valid, e.g.

the definition of stress

= P/A A tends to 0.

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DSC Approach

Sat and Asat: Existence and

Nonexistence

Combines continuum and discontinuum

approaches and takes into accountmicrostructural modifications in a material

element, which may lead to

microcracking, fracture and softening ordegradation. It also accounts for healing or

stiffening.

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DSC : BASICS

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(c) Schematic of Stress-strain

Response

i relative intacta observedc fully adjusted

Dc Df Du

i

c

a

D = 0

Dcd

D = 1

(a) Clusters of RI and FA parts

F

A

R

I

D>0D = 0 (or Do) DDu1

(b) Symbolic Representation of DSC

RI

FA

FA

Ri D = 0

Dc

Df

Du

D = 1

Rc

Schematic Representation of the Disturbed State Concept

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Relative Intact (RI) Response

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HISS as RI response

Where,

22

2

a

DD

p

JJ =

( )2

11

3

ap

RJJ

+=

= 2/32

3.2

27

D

Dr J

JS

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(b) Octahedral plane; ( for convexity)

(a)

3

R

Ultimate

Envelope

PhaseChange

Line

(Critical

State)

Figure 8. Plots of Yield Surface, F, in

Stress Spaces

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The Hierarchical SingleSurface

(HISS) Plasticity Model:Contains most other plasticity

models as special cases:

For Example: Conventional: von Mises,

Mohr Coulomb, Drucker Pragerand Continuous Yielding Models: Critical

Sate, Cap, Matsuoka/Nakai, and Lade et al.

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Critical State Model As a Special ofHISS:

Assume: Soil is normally consolidated and

cohesionless and 3R=0, then HISS specializes to:

which has the form similar to

modified Cam Clay model.

02

1

2

12 =+ JJJ D

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In the critical state model: The critical state

is reached near the end when the materialelement deforms with invariant volume

under shear.

On the other Hand; In the DSC, the

material element may reach the fully

adjusted state (FA) , which can beconsidered to be the critical state, from the

beginning, at distributed locations in the

material . Then, when most of the materialreaches the FA (critical state) , it could fail.

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Fully Adjusted State

Zero Strength :0

~ =

Critical State : ,12 .JmJcD =

= a

c

ccpJee 3ln

10

Partially Saturated Soil: Saturated State

~~~

C=

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DISTURBANCE

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(c) Schematic of Stress-strain

Response

i relative intact

a observedc fully adjusted

Dc Df Du

i

c

a

D = 0

Dcd

D =

1

(a) Clusters of RI and FA parts

F

AR

ID>0D = 0 (or

Do)

DDu1

(b) Symbolic Representation of

DSC

RI

F

A

F

A

Ri D = 0

Dc

Df

Du

D = 1

Rc

Figure 5. Schematic Representation of the Disturbed State Concept

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a

c

d

bSoftenin

g

Residual

Healing

(a) Stress-strain Response

a

c

d

b

D

(b) Disturbance

Figure 7. Representation of Softening and Healing (Stiffening)

Response in DSC

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Multicomponent DSC Models for Creep

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DSC for Interfaces and Joints

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DSC FOR INTERFACES/

JOINTS

Two Dimensional

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DSC Parameters and Testing

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COMP U TER Implementation

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APPLICATIONS

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APPLICATION 1: DYNAMIC, LIQUEFACTION-SHAKE TABLE TEST

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APPLICATION 2: DYNAMIC-LIQUEFACTION-CENTRIFUGE PILE

TEST

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pore pressure

displacement

bending moment

acceleration

9.3

m

11.4

m

Dr 80%

Dr 55%

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(a) Mesh for total domain

1

2

3

4

5

6

7

8

9

12

22.667 m

20.7 m

3.7 m

A D

B C

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Figure 9. Base motion acceleration (Wilson et al. 1997c)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15 20 25

Time (sec)

Acceleration(g)

80

120

kPa

Excess Pore Pressure=Initial'v

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0

40

80

0 9 18 27

Time, sec

PoreP

ressure,

Experimental

0

40

80

120

0 9 18 27

Time, sec

PorePressure,

kPa

With Interface Case

Excess Pore Pressure=Initial

'v

0

40

80

120

0 9 18 27

Time, sec

PorePressure,

kPa

Without Interface Case

Excess Pore Pressure=Initial'v

Comparisons for pore water pressures for Element 139 near pile.

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APPICATION 3:

REINFORCED EARTH

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Laboratory Triaxial

Tests on Back Fill

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Interface Tests Using CYMDOF: Cyclic

Multi Degree of Freedom Shear Device

Saturated and Dry

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Mesh near geogrid in fine mesh

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Wide Range of Applications: Failure and Reliability Analysis of

Computer Chips in Electronic Packaging

Behavior of Glacial Till and Till-Ice

Interface for Prediction of Motion of

Glaciers and Ice Sheets: Global Warming

and Climate Change

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31

mm35

mm

31

mm35

mmX

Y

Figure 2: Pin layout for 313-pin PBGA

(Zwick)

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CONCLUSIONS: DSC: Perhaps ONLY Unified Approach

available for Constitutive Modeling: Solidsand Interfaces/Joints

Contains most previous approaches as

Special cases: Elasticity, Plasticity,Viscoplasticity, Damage, etc and

Critical State or Cap Models commonly

used in Geotechnical Engineering areincluded within DSC

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Conclusions (Continued) Lowest or equal number of parameters

compared to available models ofcomparable capabilities.

Parameters have physical meanings and

can be determined from standardlaboratory tests.

Validated with respect laboratory tests,

impendent tests and Field/laboratorymeasurements.

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Conclusions (continued) ** Applied to a wide range of problems: Static and Dynamic Soil-Structure

interaction, Piles, Retaining walls, Dams,

Tunnels.

Earthquake analysis, and LIQUEFACTION Landslides and Glacier Motions

Electronic Packaging: Computer Chips-

Boeing