Continuum finite element modeling of concrete structural components

- Nilanjan Mitra

Crack modeling for concreteDiscrete 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 FEMCompressive 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 0.0350

100

200

300

400

500

600

700

800

Displacement (in)

Loa

d (l

bs)

Exp. Data: FR-33-R1Exp. Data: FR-33-R2Exp. Data: FR-33-R3Exp. Data: FR-33-R4Simulated Data

counterweight counterweight

l

d

dnotch

dthroat

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 ft

Variation with Ec

0 0.002 0.004 0.006 0.0080

100

200

300

400

500

600

700

800

Displacement (in.)

Loa

d (l

bs.)

ExperimentalPrototype simulated10% increase10% decrease

0 0.002 0.004 0.006 0.0080

100

200

300

400

500

600

700

800

Displacement (in.)

Loa

d (l

bs.)

ExperimentalPrototype simulated10% increase10% decrease

Parametric study for fracture energy test

0 0.002 0.004 0.006 0.0080

100

200

300

400

500

600

700

800

Displacement (in.)

Loa

d (l

bs.)

ExperimentalPrototype simulated10% increase10% decrease

Variation with Gf

0 0.005 0.01 0.015 0.02 0.025 0.030

100

200

300

400

500

600

700

800

Displacement (in.)L

oad

(lbs

.)

ExperimentalPrototype simulated (with 0.001)TSSFC model with 0.001TSSFC model with 0.05TSCRC model

Variation with shear retention,Different crack models

Parametric study for fracture energy test

0 0.004 0.008 0.012 0.0140

200

400

600

800

1000

Displacement (in.)L

oad

(lbs

.)

ExperimentalPrototype - 8 noded 2*2 integrationPrototype - 8 noded 3*3 integrationPrototype - 4 noded 2*2 integration

Different element types

0 0.004 0.008 0.012 0.0160

100

200

300

400

500

600

700

800

Displacement (in.)

Loa

d (l

bs.)

ExperimentalPrototype 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 00

2

4

6

8

10

12

14x 10

4 Bresler and Scordelis beam test: Specimen A1

displacement (in)

load

(lb

s)

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 DIANABeam flexure tests:

-0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 00

0.5

1

1.5

2

2.5

3

3.5

4x 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 testBond 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

Mod

el H

ighl

ight

sJoint 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.