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MODELING OF CONCRETE MATERIALS AND STRUCTURES
Kaspar Willam, University of Colorado at BoulderWith contributions by Dr. Inkyu Rhee, Dr. Jaesung Lee and Keun Lee, UC-Boulder
Class Meeting #7: Discrete Interface Formulations
Zero-Thickness Interface Models:Cohesive Damage and Elasto-Plastic Traction-Separation Models
Inherent Length Scale:Fracture Energy Basis GI
f and GIIf of Softening
Example Problems:- Thermal Softening of Axial Strength due Mismatch- High Temperature Bond: Pull-Out Experiment vs FE Model
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
MULTI-SCALE ASPECTS OF CONCRETE MATERIALS
Four Scales of Observation, Continuum vs Particle Models-Size Effects?
(Real Structure)Meter Level
Millimeter Level(Concrete)
Micrometer Level(Cement Paste)
Nanometer Level(Calcium Silicate Hydr
X1000
X1000
X1000
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
HIGH TEMPERATURE EFFECTS IN CONCRETE MATERIALS
Concrete Spalling: Temperature gradient vs pore pressure effects.
Transient Effects: Load-induced thermal strains-LITS.
Andersen and Thelandersen [1984]: Thermal sweep experiments.
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000
Temperature, C
/ f'c
TEST 1 C / min
TEST 5 C / min
−σ
11
-10
-5
0
5
10
0 200 400 600 800 1000
Temperature, C
Str
ain
[%
]
σ a
= -0.675 f'c σ a
= -0.45 f'c
σ a
= -0.225 f'c
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
THERMAL MISMATCH OF CONCRETE MATERIALS
Heterogeneity of Mesostructure:
Aggregate vs Cement Paste and Bond of ITZ
x
y
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
ZERO-THICKNESS INTERFACE FORMULATION
Weak ITZ-Cohesive Traction-Separation Relations:Softening Damage and Plasticity Models
Fracture Energy Basis:Coupling of Mode I and Mode II Softening Damage/Plasticity Models(softening of tensile bond vs tangential shear strength).
x
y[|un
|]1
n
s
[|u s|]1
ξ[|u n|]2
[|u s|]2
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
BIMATERIAL INTERFACE CONDITIONS
Perfect Bond:
[|uN |] = uaN − uc
N = 0 and [|tN |] = taN − tc
N = 0
Weak Discontinuities: all strain components exhibit jumps across interfaceexcept for εa
TT = εcTT restraint.
Note: Jump of tangential normal stress, σaTT 6= σc
TT .
Imperfect Contact:
[|uN |] = uaN − uc
N 6= 0 whereas [|tN |] = taN − tc
N = 0
Strong Discontinuities: all displacement components exhibit jumps acrossinterface.
Note: FE Displacement method enforces traction continuity in ‘weak’ senseonly, hence [|tN |] 6= 0.
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
ZERO-THICKNESS INTERFACE FORMULATION
Deformed FE Mesh after Thermal Sweep:
Diagonal separation of RVE due to slip.
x
y
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
ZERO-THICKNESS INTERFACE FORMULATION
Axial Thermal Stress due to Temperature Sweep:
Experimental observations vs computational results.
0 200 400 600 800Temperature [
oC]
0
0.2
0.4
0.6
0.8
1
- σ11
/ f’
c
TEST 1oC/min
TEST 5oC/min
T
ε 11 = 0
0 200 400 600 800Temperature [C]
-40
-30
-20
-10
0
Stre
ss_Y
Y[M
pa]
at O
uter
Edg
e of
Con
fine
d Su
rfac
es
ContinuumDiscrete, b=0.1Discrete, b=0.5Discrete, b=1.0
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
HIGH TEMPERATURE BOND
Pull-Out Test Setup: Residual Experiments after Cooling.
Test Variables:
- Coated-Uncoated Rebars- Slow-Rapid Heating Rates- Target Temperatures: 20oC, 200oC, 400oC, 600oC- Natural-Water Cooling
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
HIGH TEMPERATURE BOND
Pull-Out Test Program: Residual Experiments after Cooling.
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
HIGH TEMPERATURE BOND
Pull-Out Test Results:
Bond-Slip Relationships for T=20, 200, 400, 600C (rapid heating)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 0.01 0.02 0.03 0.04 0.05 0.06Slip (inch)
Bon
d st
reng
th (k
si)
Uncoated ref.UR15_200NUR15_400NUR15_600N
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
HIGH TEMPERATURE BOND
Pull-Out Test Results:
Bond Strength of slow heating tests up to T = 20o, 200o, 400o, 600oC
1.29
1.11
0.36
0.00
0.99
1.44
0.29
0.60
1.67
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
25 200 400 600 800
Temperature (˚C)
Bon
d st
reng
th (k
si)
UR2 test series (Natural cooling)CR2 test series (Natural cooling)
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
HIGH TEMPERATURE BOND
Pull-Out Test Results:
Bond Strength of rapid heating tests up to T = 20o, 200o, 400o, 600oC
0.94
0.00
0.99
0.35
1.29
1.27
0.160.33
1.44
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
25 200 400 600 800
Temperature (˚C)
Bon
d st
reng
th (k
si)
UR15 test series (Natural cooling)CR15 test series (Natural cooling)
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Finite Element Model of Pull-Out Test Specimen
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
BIMATERIAL INTERFACE CONDITIONS
Perfect Bond:
[|uN |] = ustN − uco
N = 0 and [|tN |] = tstN − tco
N = 0
Weak Discontinuities: all strain components exhibit jumps across interfaceexcept for εst
TT = εcoTT restraint.
Note: Jump of tangential normal stress, σstTT 6= σco
TT .
Imperfect Bond:
[|uN |] = ustN − uco
N 6= 0 whereas [|tN |] = tstN − tco
N = 0
Strong Discontinuities: all displacement components exhibit jumps acrossinterface.
Note: FE Displacement method enforces traction continuity in ‘weak’ senseonly, hence [|tN |] 6= 0.
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
MISMATCH OF THERMAL EXPANSION
3-D Thermoelastic Response:
∆εεεco = EEE−1co : ∆σσσco + αααco∆T and ∆εεεst = EEE−1
st : ∆σσσst + αααst∆T
Interface Bond Kinematics: ∆εstz = ∆εco
z
Interface Bond Traction: ∆σstr = ∆σco
r
Radial Contact Stress:
σr =EcoEst
Estνcon − Ecoνst[αco − αst]∆T + HO
0 100 200 300 400 500Temperature
0.00001
0.0000125
0.000015
0.0000175
0.00002
0.0000225
alpha
0 100 200 300 400 500Temperature
0
50
100
150
200
250
Radial stress@MPaD
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
TRIAXIAL CONCRETE MODEL
Damage-Plasticity Model in ABAQUS: Lee & Fenves [1998]
Damage-Plasticity Model in ABAQUS Standard
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PLANE STRESS FAILURE ENVELOPE
Damage-Plasticity Model: Lee & Fenves [1998]
Triaxial Concrete Model in ABAQUS-Standard
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Evolution of Tensile Damage at Different Outside TemperaturesT = 100, 300, 580oC
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Evolution of Compression Damage at Different Outside TemperaturesT = 100, 300, 580oC
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Circumferential Stress Distribution at Outside TemperaturesT = 100, 300, 580oC
-25
-20
-15
-10
-5
0
5
0 10 20 30 40 50 60
Radius [mm]
Stre
ss [M
Pa]
stress_t at T=108
stress_t at T=300
stress_t at T=580
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Circumferential Stress Contours at Outside Temperature T = 580oC
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Bond Stress-Axial Slip Response (cold vs hot conditions)
0
5
10
15
20
25
0 1 2 3 4 5
Bond stress
τ b in MPa
Displacement in mm
cold
warm
cooled
cold exp. Kurz
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Axial Stress Contours after Heating to T = 580oC
S, S22
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
PULL-OUT PROBLEM
Compression Damage after Heating to T = 580oC
DAMAGEC
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007
CONCLUDING REMARKS
Thermal Mismatch of Steel and Concrete:Full Bond vs Cohesive Interface Formulation - Loss of Confinement.
Mesoscale Analysis of Concrete RVE:Interaction of tensile cracking and shear debonding along weakzero-thickness interface layers-ITZ.
High Temperature Pull-Out:Residual experiments and axisymmetric FE simulation ofsteel-concrete contact separation.
Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007