Continuum finite element modeling

frizzflowerUrban and Civil

Nov 29, 2013 (3 years and 10 months ago)

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Continuum finite element modeling
of concrete structural components


-

Nilanjan Mitra

Crack modeling for concrete

Discrete crack model

Advanced remeshing

(Ingraffea & Saouma,

Cervenka)

Adaptive boundary/fem

(Carter, Spievak)

Advanced fem



Meshfree fem


(Belytschko)



X fem


(Sukumar, Moes, Dolbow)



Lattice methods

(van Mier, Bolander)

Smeared crack model

Enriched continua

Empirical global

(Vecchio & Collins, Hsu)

Phenomenological

(Rots, de Borst, Willam,

Crisfield, Blaauwendraad)



Fixed crack



Coaxial rotating



Multi
-
directional fixed

Damage Plasticity

(de Borst, Simo, Lubliner,

Desai, Fenves, Govindjee)

Microplane models

(Bazant, Prat, Ozbolt, Caner)

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:

0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0
100
200
300
400
500
600
700
800
Displacement (in)
Load (lbs)


Exp. Data: FR-33-R1
Exp. Data: FR-33-R2
Exp. Data: FR-33-R3
Exp. Data: FR-33-R4
Simulated Data
counterweight
counterweight
l
d
d
notch
d
throat
applied load
~
0
.
25
in
.
Detail A
potentiometer
Front Elevation View
d
b
L
Deflected shape

Cracks

Martin, J., Stanton, J.,
Mitra, N.
, and Lowes, L. N.(2007),
ACI Materials Journal,

104, 575
-
584

Parametric study for fracture energy test

Variation with f
t

Variation with E
c

0
0.002
0.004
0.006
0.008
0
100
200
300
400
500
600
700
800
Displacement (in.)
Load (lbs.)


Experimental
Prototype simulated
10% increase
10% decrease
0
0.002
0.004
0.006
0.008
0
100
200
300
400
500
600
700
800
Displacement (in.)
Load (lbs.)


Experimental
Prototype simulated
10% increase
10% decrease
Parametric study for fracture energy test

0
0.002
0.004
0.006
0.008
0
100
200
300
400
500
600
700
800
Displacement (in.)
Load (lbs.)


Experimental
Prototype simulated
10% increase
10% decrease
Variation with G
f

0
0.005
0.01
0.015
0.02
0.025
0.03
0
100
200
300
400
500
600
700
800
Displacement (in.)
Load (lbs.)


Experimental
Prototype simulated (with

0.001)
TSSFC model with

0.001
TSSFC model with

0.05
TSCRC model
Variation with shear retention,

Different crack models

Parametric study for fracture energy test

0
0.004
0.008
0.012
0.014
0
200
400
600
800
1000
Displacement (in.)
Load (lbs.)


Experimental
Prototype - 8 noded 2*2 integration
Prototype - 8 noded 3*3 integration
Prototype - 4 noded 2*2 integration
Different element types

0
0.004
0.008
0.012
0.016
0
100
200
300
400
500
600
700
800
Displacement (in.)
Load (lbs.)


Experimental
Prototype simulated (with

60)
Prototype simulated (with

90)
Variation with threshold angle




Q4 (2*2) Q8 (2*2) Q8 (3*3)




-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0
2
4
6
8
10
12
14
x 10
4
Bresler and Scordelis beam test: Specimen A1
displacement (in)
load (lbs)
with bond, shear retention = 1.0
with bond, shear retention = 0.1
without bond, shear retention = 1.0
without bond, shear retention = 0.1
experimental
Benchmark analysis using DIANA

Beam flexure tests:


-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0
0.5
1
1.5
2
2.5
3
3.5
4
x 10
4
Burns and Seiss Q4 beam test
displacement (in)
load (lb)
shear retention = 1.0
shear retention = 0.1
experimental
Without bond
-
slip


Perfect bond

With bond
-
slip

Without bond
-
slip


Perfect bond

Benchmark analysis using DIANA

Flexural bending mechanism bond test

Anchorage mechanism bond test

Bond tests:

Compressive Stress distribution within the joint

Joint region

Top reinforcement

bar steel stress



Four noded quad elements for concrete



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

Model Highlights

Joint Analysis

Crack development

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

Beam and column as
line element

Connection region

Monotonic increasing
lateral load

Constant axial load

Simulated Joint with loading
and boundary condition.

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.