Continuum finite element modeling
of concrete structural components
- Nilanjan Mitra
Crack modeling for concrete
Discrete crack model
Smeared crack model
Advanced remeshing
Empirical global
(Ingraffea & Saouma,
Cervenka)
(Vecchio & Collins, Hsu)
Phenomenological
Adaptive boundary/fem
(Carter, Spievak)
Advanced fem
• Meshfree fem
(Rots, de Borst, Willam,
Crisfield, Blaauwendraad)
• Fixed crack
• Coaxial rotating
• Multi-directional fixed
(Belytschko)
• X fem
(Sukumar, Moes, Dolbow)
Lattice methods
(van Mier, Bolander)
Damage Plasticity
(de Borst, Simo, Lubliner,
Desai, Fenves, Govindjee)
Microplane models
(Bazant, Prat, Ozbolt, Caner)
Enriched continua
Cosserat continua
(Cosserat, Green, Rivlin,
Mindlin, Vardoulakis,
Muhlhaus, de Borst,
Willam, Sluys, Etse)
Higher order gradient
(Aifantis, Vardoulakis,
de Borst, Pamin, Voyiadjis)
Embedded discontinuity
(Jirasek, Lotfi, Shing,
Spencer, Belytschko, Sluys,
Larsson, Simo, Oliver,
Armero, Olofsson)
• KOS
• SOS
• SKON
Models done with TNO DIANA
Constitutive models for continuum FEM
Compressive model for concrete:
• Yield surface –
Drucker-Prager
• Flow rule
-Associative
• Compression Hardening/Softening function -- calibrated to match Popovics relation
• Plastic strain is zero till 30% of the strength is achieved
• Suitable for biaxial loading -- 16% increase in strength
Tensile model for concrete:
• Linear tension cut-off
• Hordijk model for tension softening
Model for reinforcement steel:
• Associated Von-Mises plasticity with strain hardening
Model for bond in between reinforcement and concrete:
• Elastic radial response
• Transverse response is calibrated to match the Eligehausen model for bond
Benchmark analysis using DIANA
Fracture energy tests at UW:
applied load
counterweight
d
dthroat
~0.25 in.
counterweight
d
dnotch
Detail A
b
potentiometer
800
l
L
Exp. Data: FR-33-R1
Exp. Data: FR-33-R2
Exp. Data: FR-33-R3
Exp. Data: FR-33-R4
Simulated Data
700
Front Elevation View
Load (lbs)
600
Deflected shape
500
400
300
200
100
0
Cracks
0
0.005
0.01
0.025
0.02
0.015
Displacement (in)
0.03
0.035
Martin, J., Stanton, J., Mitra, N., and Lowes, L. N.(2007), ACI Materials Journal, 104, 575-584
Parametric study for fracture energy test
800
Experimental
Prototype simulated
10% increase
10% decrease
700
800
500
700
400
600
300
500
Load (lbs.)
Load (lbs.)
600
200
100
0
0
0.002
0.004
Displacement (in.)
Variation with ft
0.006
Experimental
Prototype simulated
10% increase
10% decrease
400
300
0.008 200
100
0
0
0.002
0.004
Displacement (in.)
0.006
Variation with Ec
0.008
800
Experimental
Prototype simulated
10% increase
10% decrease
700
600
800
500
600
400
500
300
200
400
300
200
100
0
0
Experimental
Prototype simulated (with  0.001)
TSSFC model with  0.001
TSSFC model with  0.05
TSCRC model
700
Load (lbs.)
Load (lbs.)
Parametric study for fracture energy test
0.002
0.004
Displacement (in.)
0.006
Variation with Gf
0.008
100
0
0
0.005
0.01
0.015
0.02
Displacement (in.)
0.025
Variation with shear retention,
Different crack models
0.03
Parametric study for fracture energy test
1000
Experimental
Prototype - 8 noded 2*2 integration
Prototype - 8 noded 3*3 integration
Prototype - 4 noded 2*2 integration
800
Experimental
Prototype simulated (with  60)
Prototype simulated (with  90)
700
Load (lbs.)
600
Load (lbs.)
800
600
400
500
200
400
300
0
0
200
100
0
0
0.004
0.008
Displacement (in.)
0.012
Different element types
0.004
0.008
Displacement (in.)
0.012
Variation with threshold angle
0.016
Q4 (2*2)
Q8 (2*2)
Q8 (3*3)
0.014
Benchmark analysis using DIANA
Beam flexure tests:
Bresler and Scordelis beam test: Specimen A1
4
14
Burns and Seiss Q4 beam test
4
4
x 10
x 10
12
3.5
10
load (lbs)
3
load (lb)
2.5
2
1.5
8
6
with bond, shear retention = 1.0
with bond, shear retention = 0.1
4
shear retention = 1.0
without bond, shear retention = 1.0
shear retention = 0.1
1
without bond, shear retention = 0.1
2
experimental
experimental
0.5
0
-0.8
0
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
displacement (in)
-0.1
-0.05
0
-0.7
-0.6
-0.5
-0.4
-0.3
displacement (in)
-0.2
-0.1
With bond-slip
Without bond-slip  Perfect bond
Without bond-slip  Perfect bond
0
Benchmark analysis using DIANA
Bond tests:
Flexural bending mechanism bond test
Anchorage mechanism bond test
Joint Analysis
Crack development
Joint region
Model Highlights
Compressive Stress distribution within the joint
Top reinforcement
• Four noded quad elements for concrete
bar steel stress
• Drucker Prager associated plasticity for compression
• Phenomenological Multi-directional fixed crack model for tension
• Linear tension cut-off & Hordijk tension softening curve
• Truss element for reinforcement steel in the connection region
• Von-mises plasticity for reinforcement steel
• Interface elements to model bond – Radial response : Elastic
Transverse response: Nonlinear calibrated to Eligehausen uniaxial bond model
• Elastic elements with cracked stiffness to model the beams and columns
Studies carried out with ABAQUS
Model material properties
•
•
•
•
Compression stress-strain curve : Popovics equation[1973].
Tension behavior : Mitra [2008].
Linear response : 30% of maximum compressive strength.
Concrete model: Concrete Damage Plasticity.
Beam-column Joint Model
Monotonic increasing
lateral load
Constant axial load
Connection region
Simulated Joint with loading
and boundary condition.
Beam and column as
line element
Transfer of force/moment to joint : ‘Distributing coupling’ .
Beam-column Joint Model Cont.
Column as
line element
Reinforcements
(24/12ɸ for
column and
16/12ɸ for beam)
Joint
region
Beam as
line
element
Beam-column Joint Model Cont.
• Studies made up to 2% drift.
• Nature of loading :
Behavior of the Beam-Column Joint Under
Lateral Loading Cont.
Bending stress at 2% drift
Shear stress concentration at joint face
Behavior of the Beam-Column Joint Under Lateral Loading
Cont.
More work pending for 3d continuum simulation for joints:
Looking for students to complete the work
Any interested student with some prior expertise in FE modeling,
preferably with concrete modeling can contact me in my email add.