2015/05/06

A New XFEM Modeling Technique For The

Pinching Effect in RC Columns Subjected To

Lateral Cyclic Loads

Jiangtao Yu,

Associate Professor, Research Institute of Structural Engineering and Disaster Reduction, College of Civil

Engineering, Tongji University, Shanghai, China. Corresponding author. E-mail: yujiangtao@tongji.edu.cn

Wanli Xu

M.S., Candidate, Research Institute of Structural Engineering and Disaster Reduction, College of Civil

Engineering, Tongji University, Shanghai, China. Email: 1_vanie@tongji.edu.cn

第四届全国抗震加固改造技术学术研讨会The seismic performance of RC members

3

Cracking propagation by XFEMCracking propagation by XFEM

Principles and Methods in Simulation

Principles ：1. Concrete is a typical quasi-brittle, discontinuous material, not an elastic-plastic, continuous material;

2. The crack opening and closing of concrete is mechanical based behavior, instead of material property;

3. Artificial simplifications, such as plane section assumption and the coupling between steel bar and

concrete, should be avoided as far as possible.

Methods:

1. Discontinuous algorithm for discontinuous materials. Extended Finite Element Method is adopted to

simulate the initiation and propagation of crack;

2. Traction–separation law, together with fracture energy dissipation rate, is used to judge the concrete

behavior in post-cracking period;

3. Contact algorithm is used to simulate the crack closure;

4. Multi-cracking in concrete structure is exhibited by considering the interaction between concrete and

bar.

Inputs for ABAQUS and XFEM

Constitutive of the material

1. Concrete behavior before cracking: modulus and maximum circumferential tensile strength

(maximum tensile circumferential stress intensity factor criterion);

2. Concrete behavior after cracking: BK mixed mode, fracture energy dissipation rate;

3. Compressive behavior of concrete: elastic-plastic model based on isotropic hardening law;

4. Crack closure: Use phantom nodes (XFEM) to compute surface contact;

5. Tensile and compressive behavior of steel: classic bilinear elastic-plastic model, identical for

compression and tension. Bauschinger effect is taken into consideration by kinematic hardening

law. Buckling of bar is considered in certain circumstances.

6.Bond-slip relationship: CEB-FIP bond-slip model

Member select in ABAQUS:

Concrete: CPS4R; Steel bar: Truss Member T2D2; Bond-slip relationship: CONNECTOR 。

Validation in macroscopic level

http://www.collapseprevention.net/list.asp?adID=1

Validation in macroscopic level

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1000 2000 3000 4000

Loa

ding

late

ral d

ispl

acem

ent (

m)

Load step

TestModelLoading diagram of

displacement history

1st crack (R side)

2nd crack (R side)

3rd crack (R side)

4th crack (R side)

1st crack (L side)

2nd crack (L side)

3rd crack (L side)

4th crack (L side)

cracking element

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0

10000

20000

30000

40000

50000

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Lat

eral

load

(N)

Displacement (m)

Numerical

Tested EZ-A

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-40000

-30000

-20000

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0

10000

20000

30000

40000

50000

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Late

ral l

oad (

N) Displacement (m)

Numerical

Tested EZ-B

-60000

-40000

-20000

0

20000

40000

60000

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Lat

eral

load

(N)

Displacement (m)

Numerical

Tested IZ-A

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-40000

-20000

0

20000

40000

60000

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Lat

eral

load

(N)

Displacement (m)

Numerical

Tested IZ-B

Crack initiating Comparison of hysteretic loops

Validation in macroscopic level

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40000

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Lat

eral

load

(N)

Displacement(m)

Tested EZ-A

numerical

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0

10000

20000

30000

40000

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Lat

eral

load

(N)

Displacement(m)

Tested EZ-B

numerical

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0

10000

20000

30000

40000

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Late

ral L

oad

(N)

Displacement (m)

Tested EZ-ANumerical

Ideal Hysteretic loop

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40000

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Late

ral lo

ad (N

)

Displacement (m)

Tested IZ-ANumerical

Ideal Hysteretic loop

Comparison of skeleton curves

Single loop of load-displacement

Validation in macroscopic level

Further discussion

Three Mechanisms, Five Keywords

The formation mechanism of the pseudo-constitutive relationship of concrete;

The formation mechanism of multi-crack in reinforced concrete;

The formation mechanism of pinching effect in reinforced concrete;

Keywords: Mesoscopic; discontinuous; fluctuation; mismatch; counteraction;

-3.E+7

-2.E+7

-1.E+7

0.E+0

1.E+7

-0.2 -0.1 0.0 0.1 0.2 0.3

Stre

ss (P

a)

Strain (ε)

Computed(XFEM model)

Artificially defined(most FEM modle)

Formation mechanism of the constitutive relationship of concrete

Formation mechanism of the constitutive relationship of concrete

Concrete element

Rebar element

Connector element

-3.E+7

-2.E+7

-1.E+7

0.E+0

1.E+7

-0.2 -0.1 0.0 0.1 0.2 0.3

Stre

ss (P

a)

Strain (ε)

-3.0E+7

-2.5E+7

-2.0E+7

-1.5E+7

-1.0E+7

-5.0E+6

0.0E+0

5.0E+6

1.0E+7

-2.E-03 -1.E-03 0.E+00 1.E-03 2.E-03 3.E-03 4.E-03

Stre

ss (P

a)

Strain (ε)

1

2

3 4

5

-3.0E+7

-2.5E+7

-2.0E+7

-1.5E+7

-1.0E+7

-5.0E+6

0.0E+0

5.0E+6

-6.E-03 -4.E-03 -2.E-03 0.E+00 2.E-03 4.E-03 6.E-03 8.E-03

Stre

ss (P

a)

Strain (ε)

1

2

4

5

-3.0E+7

-2.5E+7

-2.0E+7

-1.5E+7

-1.0E+7

-5.0E+6

0.0E+0

5.0E+6

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

Stre

ss (P

a)

Strain (ε)

1

2

4

5

（ a ） （ b ）

The formation mechanism of multi-crack in reinforced concrete

X

Y0.35

0.17

Loading point

Long

itudi

nal d

irecti

on, L

P

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

-0.2 -0.1 0 0.1 0.2 0.3 0.4

Disp

lace

men

t (m

)

Longitudinal direction of specimen (m)

LD 0.031

LD 0.016

LD 0.008

1st crack4th crack

LD -0.031 LD -0.016

LD -0.008

strong girder

anchorage region

Deformation fluctuation for concrete and steel

Keyword: fluctuation

-5.0E-04

1.0E-18

5.0E-04

1.0E-03

1.5E-03

2.0E-03

-0.2 -0.1 0 0.1 0.2 0.3 0.4

Dis

plac

emen

t (m

)

Longitudinal direction of specimen (m)

LD= 0.002LD= 0.008LD= 0.016LD= 0.031

-2.0E-04

-1.5E-04

-1.0E-04

-5.0E-05

-1.0E-19

5.0E-05

1.0E-04

-0.2 -0.1 0 0.1 0.2 0.3 0.4

Disp

lace

men

t (m

)

Longitudinal direction of specimen (m)

LD= -0.002LD= -0.008LD= -0.016LD= -0.031

Slips between concrete and steel

One explanation of pinching effect : delayed crack closure.

Following characteristics could be inferred at the circumstance of low axial compressive ratio: 1.Accumulated unrecovered concrete deformation under compression;2.Accumulated unrecovered steel deformation under tension;3.Member tends to elongate

Keyword: mismatch

σCRσCL

MCL

FSRFSR MCR

XY

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Mom

ent (

N*m

)

Displacement (m)

Bending contribution of rebar

Bending contribution of concrete

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30000

40000

50000

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

Mom

ent (

N*m

)

Displacement (m)

Bending contribution of rebar

Bending contribution of concrete

Moment in critical section

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30000

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Mom

ent (

N*m

)

Displacement (m)

MCRMCL

Contribution of tensile concrete

Contribution of compressive concrete

Macroscopic phenomenon

Explanation

Analyze of pinching effect——Concrete

Steel

Bauschinger effect

Steel

Concrete

Concrete

Keyword: counteraction

Bending contribution of rebar and

concrete

Concrete: Quadrant one and three

Steel rebar: all four quadrants

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Mom

ent (

N*m

)

Displacement (m)

Bending contribution of rebar

Bending contribution of concrete

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ater

al lo

ad (N

)

Displacement (m)

Numerical

Tested EZ-A

counteraction

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0.E+0

5.E+4

1.E+5

2.E+5

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Forc

e (N

)

Displacement (m)

FSL

FSR

fy'

fy

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0

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-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Mom

ent

(N*m

)

Displacement (m)

MSL

MSR

MSL+MSR

MSL= -0.5H0×FSLMSR= 0.5H0×FSR

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Def

orm

atio

n (m

)

Displacement (m)

VB-VA+VS1-VS2 (L)VB-VA+VS1-VS2 (R)VB-VA (L)VB-VA (R)VS2-VS1 (R)VS2-VS1 (L) Connector

Concrete

Rebar

Keyword: mismatch; counteract

Compressive zone

Tensile zone

Tensile zone undergoes more slippage in

comparison with that of the compressive zone

Analyze of pinching effect——Rebar

2015/05/06

Thank you for your attention

Reporter: Wanli Xu