8/12/2019 csd-ppt[1]
1/72
Constitutive Modelling for
Engineering Materials inComputational Procedures
By
Chandrakant S. Desai
8/12/2019 csd-ppt[1]
2/72
8/12/2019 csd-ppt[1]
3/72
Solids, Interfaces and Joints
8/12/2019 csd-ppt[1]
4/72
8/12/2019 csd-ppt[1]
5/72
8/12/2019 csd-ppt[1]
6/72
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.
8/12/2019 csd-ppt[1]
7/72
8/12/2019 csd-ppt[1]
8/72
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.
8/12/2019 csd-ppt[1]
9/72
8/12/2019 csd-ppt[1]
10/72
8/12/2019 csd-ppt[1]
11/72
8/12/2019 csd-ppt[1]
12/72
DSC : BASICS
8/12/2019 csd-ppt[1]
13/72
8/12/2019 csd-ppt[1]
14/72
8/12/2019 csd-ppt[1]
15/72
(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
8/12/2019 csd-ppt[1]
16/72
8/12/2019 csd-ppt[1]
17/72
8/12/2019 csd-ppt[1]
18/72
Relative Intact (RI) Response
8/12/2019 csd-ppt[1]
19/72
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
8/12/2019 csd-ppt[1]
20/72
(b) Octahedral plane; ( for convexity)
(a)
3
R
Ultimate
Envelope
PhaseChange
Line
(Critical
State)
Figure 8. Plots of Yield Surface, F, in
Stress Spaces
8/12/2019 csd-ppt[1]
21/72
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.
8/12/2019 csd-ppt[1]
22/72
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
8/12/2019 csd-ppt[1]
23/72
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.
8/12/2019 csd-ppt[1]
24/72
Fully Adjusted State
Zero Strength :0
~ =
Critical State : ,12 .JmJcD =
= a
c
ccpJee 3ln
10
Partially Saturated Soil: Saturated State
~~~
C=
8/12/2019 csd-ppt[1]
25/72
DISTURBANCE
8/12/2019 csd-ppt[1]
26/72
(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
8/12/2019 csd-ppt[1]
27/72
8/12/2019 csd-ppt[1]
28/72
8/12/2019 csd-ppt[1]
29/72
8/12/2019 csd-ppt[1]
30/72
8/12/2019 csd-ppt[1]
31/72
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
8/12/2019 csd-ppt[1]
32/72
8/12/2019 csd-ppt[1]
33/72
Multicomponent DSC Models for Creep
8/12/2019 csd-ppt[1]
34/72
8/12/2019 csd-ppt[1]
35/72
8/12/2019 csd-ppt[1]
36/72
DSC for Interfaces and Joints
8/12/2019 csd-ppt[1]
37/72
8/12/2019 csd-ppt[1]
38/72
DSC FOR INTERFACES/
JOINTS
Two Dimensional
8/12/2019 csd-ppt[1]
39/72
DSC Parameters and Testing
8/12/2019 csd-ppt[1]
40/72
8/12/2019 csd-ppt[1]
41/72
8/12/2019 csd-ppt[1]
42/72
8/12/2019 csd-ppt[1]
43/72
8/12/2019 csd-ppt[1]
44/72
COMP U TER Implementation
8/12/2019 csd-ppt[1]
45/72
8/12/2019 csd-ppt[1]
46/72
APPLICATIONS
8/12/2019 csd-ppt[1]
47/72
8/12/2019 csd-ppt[1]
48/72
APPLICATION 1: DYNAMIC, LIQUEFACTION-SHAKE TABLE TEST
8/12/2019 csd-ppt[1]
49/72
8/12/2019 csd-ppt[1]
50/72
8/12/2019 csd-ppt[1]
51/72
8/12/2019 csd-ppt[1]
52/72
8/12/2019 csd-ppt[1]
53/72
8/12/2019 csd-ppt[1]
54/72
8/12/2019 csd-ppt[1]
55/72
8/12/2019 csd-ppt[1]
56/72
APPLICATION 2: DYNAMIC-LIQUEFACTION-CENTRIFUGE PILE
TEST
8/12/2019 csd-ppt[1]
57/72
pore pressure
displacement
bending moment
acceleration
9.3
m
11.4
m
Dr 80%
Dr 55%
8/12/2019 csd-ppt[1]
58/72
(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
8/12/2019 csd-ppt[1]
59/72
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
8/12/2019 csd-ppt[1]
60/72
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.
8/12/2019 csd-ppt[1]
61/72
APPICATION 3:
REINFORCED EARTH
8/12/2019 csd-ppt[1]
62/72
Laboratory Triaxial
Tests on Back Fill
8/12/2019 csd-ppt[1]
63/72
Interface Tests Using CYMDOF: Cyclic
Multi Degree of Freedom Shear Device
Saturated and Dry
8/12/2019 csd-ppt[1]
64/72
8/12/2019 csd-ppt[1]
65/72
Mesh near geogrid in fine mesh
8/12/2019 csd-ppt[1]
66/72
8/12/2019 csd-ppt[1]
67/72
8/12/2019 csd-ppt[1]
68/72
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
8/12/2019 csd-ppt[1]
69/72
31
mm35
mm
31
mm35
mmX
Y
Figure 2: Pin layout for 313-pin PBGA
(Zwick)
8/12/2019 csd-ppt[1]
70/72
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
8/12/2019 csd-ppt[1]
71/72
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.
8/12/2019 csd-ppt[1]
72/72
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