Bond in Concrete 2012 – General Aspects of Bond J.
W. Cairns, G. Metelli and G. A. Plizzari (eds)2012 Publisher creations, ISBN: 978 - 88 - 907078 - 1 - 0

Japan Concrete Institute TC Activities on Bond Behavior andConstitutive Laws in RC(Part 3: Application of Constitutive Laws for FEA)
T. Kanakubo

University of Tsukuba, Tsukuba, Japan

Y. SatoKyoto University, Kyoto, JapanY. Uchida

Gifu University, Gifu, JapanK. Watanabe

Railway Technical Research Institute, Kokubunji, Japan

H. Shima

Kochi University of Technology, Kochi, Japan
ABSTRACT: Finite Element Analysis (FEA) is the one of the effective simulating methods to represent thebehavior of Reinforced Concrete (RC) members and structures. The Japan Concrete Institute TechnicalCommittee on Bond in Concrete Structures has conducted the following two main research programs in orderto discuss the effective usages of bond models in FEA. The one is the meso-scale analysis using FEA andRigid Body Spring Model (RBSM) by the modeling of bearing between lugs of reinforcements and concrete,
and the other is the actual applications of bond models into FEA of RC members. The objectives of these programs are to understand the bond mechanisms of reinforcements and bond stress - slip relationships, and toabstract the problems of bond-link model in FEA.
1 INTRODUCTION
Brittle fractures of reinforced concrete members include bond fracture and anchorage fracture. The fullunderstanding of bond fractures is, however, very
difficult owing to the interactions of microscopic
stress transmission, the constitutive law of each material, linked fractures at the macroscopic level, etc.
In recent years, the Finite Element Analysis (FEA)
has become a useful tool to determine the behaviorof reinforced concrete members. The FEA is, however, significantly affected by the model of bond behavior, specifically the preconditions in a bondsoftening region considerably affect the accuracy ofthe solution. The Japan Concrete Institute TechnicalCommittee on Bond in Concrete Structures carriedout research activities from 2009 to 2011 aiming tograsp the bond behavior on a microscopic scale, thus
to review the information relating to bond behavior
and to make a proposal for using the information
specifically through determination of the bond constitutive law in FEA aimed at its practical application.
In this paper, the results of the following twomain research programs are reported. The one is themeso-scale analysis using FEA and Rigid Body
Spring Model (RBSM) by the modeling of bearing

between lugs of reinforcements and concrete, andthe other is the actual applications of bond models
into FEA of RC members. The objectives of these
programs are to understand the bond mechanisms ofreinforcements and bond stress - slip relationships,
and to abstract the problems of bond-link model inFEA.
2 MESO-SCALE ANALYSIS OF BOND
BEHAVIOR
Studies began as early as the '80s to determine thebond behavior through direct modeling analysis ofmechanical mating between nodes of a reinforcing
bar and concrete, which is the essence of the bond
between a deformed reinforcing bar and concrete.
(Ingarffea et at. 1984, Kokusho et al. 1981,
Reinhardt et al. 1984, etc.) According to the analysis, the τ-s relation is not regarded as a constitutive
law, and the bond phenomenon is reproduced as aresult of the propagation of fracture of concrete peripheral to the reinforcing bar, such as the internalcracks occurring from the front end of a node andthe plasticizing of concrete at the front side of thenode. Consequently, it is expected that the analyticalresults give a macroscopic bond model.

105Figure 4. Tensile bond specimen for FEA to perform meso-scale analysis. The cracks with the interval of approximately 500mm
were observed in the loading test. (unit: mm)
1000

125
Reinforcing bar

100

Stress of reinforcing bar (MPa)

載荷端鉄筋応力（N/mm2）

Tension

Comp.

A
B

Normal direction

Shear direction

4200.1Distancefrom load
載荷端からのend (x D)
距離(×D)
0.5
1.5
2.5
3.5
4.55.5
6.5
Shima
0.5

Bondstress(N/mm(MPa)2)付着応力

2Bondstress(MPa)
付着応力(N/mm)

6600
400
20000

解析結果
FEA
実験結果
Experiment
246Wholeelongation (mm)
伸び（mm）
Figure 7. Stress – elongation relationships.

Figure 6. Constitutive laws for boundary elements.
8

Boundaryelement B

Boundaryelement A

Reinforcing bar

Concrete

Figure 5. FE model of specimen and reinforcing bar, boundary elements864
20-2-4-6-8

8

10Distancefrom load
載荷端からのend (x D)
距離(×D)
6.5
7.5
8.5
9.5
10.5
11.5
12.50.2
0.3
0.4
-0.2
-0.1
00.1
0.2
相対すべり
(mm)
相対すべり
(mm)
Relative slipS(mm)RelativeslipS(mm)Figure 8. Bond stress – relative slip relationships plotted by the positions from the loaded end of specimen.

for the boundary elements are shown in Figure 6.
The enough-lower stiffness for axial direction surface is set for the boundary element A.
Figure 7 shows the relationship between stress ofreinforcing bar and whole elongation comparing experimental results and FEA. Crack stress differs between experiment and FEA. The reason is considered that the shrinkage stress occurs in the specimen.
However outline of FEA curve agrees with the ex-perimental result. Figure 8 shows bond stress versus
relative slip curves between reinforcing bar elements
and concrete elements. The curves are plotted by thepositions from the loaded end of the specimen. Except for the curves of 0.5D, 1.5D (D=bar diameter)
curves, curves behave similarly. After the crack occurs, the bond stresses decrease and become showing negative bond stresses (opposite direction). The
differences of 0.5D and 1.5D curves from other107

Figure 9. Effect of tension stiffening model for uniaxial tensile specimen. Double counted stress is included by tension stiffeningand bond link model.

curves are due to cone shaped crack which takes
place at the end of specimen.
3 ACTUAL APPLICATIONS OF BOND
MODELS INTO FEA
The results of two series of FEA are reported in thischapter. Both FEAs are conducted to study the effectof bond models to the behavior of RC members
comparing the experimental results. At first, an uniaxial tensile test is investigated. This is a basic experimental method to investigate the bond characteristics between a reinforcing bar and concrete..
3.1 FEA of uniaxial tensile test for prism specimen
Engineers and researchers often use the bond linkelements or other similar elements in FEA to express
the bond slip between reinforcing bar and concrete.
On the other hand, the bond behavior is indirectly
expressed by the tension stiffening model of concrete in case of smeared crack model. The tension

Figure 10. Assumption of bond stress –slip curve.

stiffening model is boldly modeled of tensile stressof concrete transmitted by the bond. If the bond linkelements and tension stiffening model are simultaneously used, it is anxious that the effect of bond isdouble counted as shown in Figure 9. In this section,“double counted effect” is investigated by the FEA
using both bond link elements for discrete reinforcing bar and tension stiffening model for concrete
comparing with the experimental results.
3.1.1 Experiments and target specimens
The target specimens for FEA are uniaxial tensile
prism specimens tested by Kanakubo et al. (2009)
with square section of 80 mm, 100 mm and 120 mm.
A deformed bar of 10 mm (D10) in diameter is arranged at the center of the section, and the reinforcement ratios () are 1.23 %, 0.79 % and 0.55 %,respectively. The length of specimen is 1600 mm.
The four-node plane elements, two-node truss elements and four-node bond link elements are used.
Before the investigation of double counted stress,
the tension stiffening curve is modeled by an integration calculation based on the assumption of bondstress – slip relationship as shown in Figure 10. The

Figure 11. Comparison of tensile load – elongation curve between test results
and analytical results.

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Figure 12. Tension stiffening model from integration calculation results. Tensile stress of concrete is modeled by multi linear.

Figure 13. Elements for FEA, (a) smeared concrete elements with bond link, (b) discrete elements in which only central element
behaves under tension stiffening model.

calculation method is the integration of the onedimensional elements under the force equilibrium
condition and compatibility condition including slip
between reinforcing bar elements and concrete. The
calculated region is between cracks. If the tensilestress of concrete elements becomes bigger than thetensile strength of concrete, new crack takes place at
the center of the region, and the length of calculated
region is set to half length. The calculation is continued until the new crack does not occur. The results of calculation are shown in Figure 11 comparing with the test results. The shape of tensile load –elongation curves from the calculation almost agrees

with the test results. Figure 12 shows the analyticalresults of tensile concrete stress which is obtained bythe subtraction of the force of reinforcing bar fromthe whole tensile load, and its modeling by multilinear model.
3.1.2 FEA modeling and results
Two series of FEAs by smeared model and discretemodel are performed. Figure 13 shows the modelingfor both cases. In the smeared-based analysis, thetension stiffening model shown in Figure 12 isadopted for all concrete elements. The bond linkmodel is also used. The sizes of elements range from109

Figure 14. Analysis results by smeared-based model shown by concrete stress.

Figure 15. Analysis results by discrete-based model shown by concrete stress.

12.5 mm to 1600 mm (8 cases). In the discrete-based
analysis, only the central element behaves under thetension stiffening model. The other elements are set
to show elastic manner without bond link. After thecracking at the central element, the half length
model is newly adopted. The same progress is continued until no crack occurs.
The analysis results are shown in Figures 14 and
15 for the smeared-based model and the discretebased model, respectively. From the results of thesmeared-based model, it is observed that FEA results show the almost similar curves with tension

stiffening model shown in Figure 12. This meansthat “double count” of tension stiffening effect does
not occur. In case of smeared model, all elements forconcrete show the same strain, so that bond link
does not work. The use of combination of smeared
concrete element, discrete bar element and tension
stiffening model is effective only for expressing thelarge scale of slip of reinforcing bar such as slip outof bar from concrete. From the results of the discrete
based model, the obtained curves show almost thesame tendency with the tension stiffening model.
However, the crack spacing by the analysis (25 mm

110

in case of =1.23%) differs from the experimental
result (100 mm). This difference is due to the “double count” of tensile stress. Thus, the effect of double count appears as the difference of crack spacing.

considered the fracture energy. To express the interaction between the concrete and the longitudinal reinforcing bar, a trial analysis was performed under
the condition that the bond characteristic is assumed
as perfect bond, using the τ-s curve proposed byShima et al. (1987) and Suga et al. (2001).
Figure 16 shows examples of analytical results. In
the analysis for DB408, many slant cracks occur atthe center of beams. Since the yield of stirrup is observed at the peak load, the analysis presumably canpursue the failure mode similar to experiment. On
the other hand, for DB608 and DB808, bending
shear cracks and cracks along the longitudinal direction of the reinforcing bar occur. However, manyslant cracks are observed at the center of the beam,
showing a crack pattern different from that observedin the experiment.

3.2 FEA of RC beams failed by bond splitting
FEAs for RC beam specimens having a small shear
span ratio (a/d) under an anti-symmetrical bending
moment are conducted to investigate the adaptabilityof bond models. It is known that small span ratio
beams under anti-symmetrical bending momentshow the cracks along the longitudinal bars withsplitting crack of concrete. This failure is called as
bond splitting failure. The objective is to solve thebehavior of bond splitting beams considering bondstress transmission mechanism between reinforcing
bar and concrete. The sectional size of beams is 400
mm in effective height and 300 mm in width. The
shear span ratios are 1 (DB408), 1.5 (DB608) and 2(DB808), respectively. Four deformed longitudinalbars of 29 mm in diameter are arranged while deformed stirrups of 13 mm in diameter are used with
100 mm spacing. The concrete compressive strength
ranges from 28.9 MPa to 29.3 MPa.

3.2.2 Analysis by FINALFEA is conducted applying the bond model of Goto,
Morita and Fujii (1981) to four-node bond link elements, and coercive bond splitting cracks. The bondmodel is a multi-linear curve expressing the bondbehavior which accompanies the bond splitting
strength and slip based on many experimental results. In FEA, the simplest method for expressing
the deterioration of bond is to insert the bond link
between the reinforcing bar elements and the concrete elements. However, the deteriorating of bondwhich actually propagates around the reinforcing bar
in three-dimension is not modeled by bond link. In
this FEA, a user subroutine to cause coercive bondsplitting cracks linking to the Goto, Morita and Fujii
model is applied to the bond link.
Figure 17 shows the relationships between theshear force and the displacement and the crack pat-3.2.1 Analysis by DIANAThe analysis uses the commercially available FEA
software DIANA, and applies the model of smeared
cracks - discrete reinforcing bars. The model applied
to the concrete is the fixed crack model in which theshear stress - shear strain relation is used considering
compatibility with the loading experiment. The
nonlinear constitutive law for the concrete adopted
the Thorenfeldt model and the Hordijk model, which

Shear force - displacement
curve

Crack pattern Crack pattern(Analysis)(Experiment)

DB408

DB608

DB808

275
150201201175210232
132191

191

132232700

解析結果 (kN)Shear force
せん断力(kN) (kN)

700

600
500
400
300
200
1000051015
層間変位 (mm)Displacement (mm)20

Shear force
せん断力(kN) (kN)

700

600

600

500

500

400

400

300

300

200

200

100

1000010203040

Shear
せん断力force(kN) (kN)50

層間変位 (mm)Displacement(mm)60Figure 16. Analysis results of bond splitting failed beams by DIANA.

111

Experiment
Analysis001020304050

層間変位 (mm)Displacement
(mm)

60

DB608

Shear force –disp. curve

DB408- - - - Analysis with split crack

DB808

Analysis

At 5% angle(Analysis)

At max.
(Analysis)

Experiment

Figure 17. Analysis results of bond splitting failed beams by FINAL.

terns. In the shear force-displacement relationships,
the thin lines represent the test results, the thick lines
the analyses without the splitting cracks, and the dotted lines the analyses with the splitting cracks. Since
the splitting cracks appear after the peak load, thepre-peak behaviors are the same whereas the postpeak behaviors differ. The differences, however, arenot significant in the shear force-displacement relationships. Regarding the cracks at the peak loads, theexperiments showed regions without the cracks near
the center of the beam. In the analysis, however,cracks are generated over the entire span.
In the experiment, before growing the shear
cracks over the entire region of the span, splitting
cracks were presumably generated along the longitudinal bars, thus a region of no cracks remained.
The objective of introducing splitting cracks in theanalysis is to reproduce the above phenomenon. Asillustrated in Figure 17, however, many shear cracks
have already formed at the point of reaching maximum load, and an effect of suppressing shear cracks
by introducing splitting cracks is not observed.
4 CONCLUSIONSIn the meso-scale analyses of the reinforcing bar andsurrounding concrete, a possibility is found to understand the bond behavior and the bond models by
RBSM and FEA. By the FEA of uniaxial tensile testof RC prism, the "double count" tensile stress byadopting both the tension stiffening model and thebond link element is discussed. In the FEA for thebond splitting beams, it is difficult to simulate thecrack patterns caused by the bond splitting although
the shear force-displacement behaviors are wellsimulated.

5 ACKNOWLEDGEMENT
The authors fully acknowledge the members of Japan Concrete Institute Technical Committee on
Bond in Concrete Structures for their dedicated activities.
6 PREFERENCES
Goto, S., Morita, S., Fujii, S., Tokuno, M., and Fukui, K.,
1981: Influence of Lateral Reinforcement on Bond Splitting
Failure Modes. Annual Reports of Architectural Institute ofJapan, Kinki Branch, Vol. 21, 197-200
Ingarffea, A.R. et.al., 1984: Fracture Mechanic of Bond in Reinforced Concrete, ASCE Structural Division, Vol.110,No.4, pp.871-890
Kanakubo, T., Yamato, N., 2009: Prediction Me-thod of Crack
Width in Reinforced Concrete Members, Journal of Structural and Construction Engineering, Transactions of Architectural Insti-tute of Japan, Vol.74, No.640, pp.1137-1143
Kokusho, S., Hayashi, S. and Yoshida, H., 1981: Study on
Bond between Deformed Bar and Con-crete, Summaries ofTechnical Papers of Annual Meeting, Architectural Instituteof Japan, pp.1513-1514
Muto, S., Nakamura, H., Tanabe, T., Srisoros, W. and Lee,S.H., 2004: Analysis of Bond Character-istics Between
Concrete and Deformed Bar by Meso-Scale Analysis, Journal of Applied Me-chanic, JSCE, Vol. 7, No. 2, pp. 767-774
Reinhardt, H.W. et.al., 1984: Prediction of Bond between Steeland Concrete by Numerical Analy-sis, Material and Structures, Vol.17, No.100, pp.311-320
Shima, H., Chou, L., and Okamura, H., 1987: Bond-Slip-Strain
Relationship of Deformed Bars Embedded in Massive Concrete, Journal of Japan Society of Civil Engineers, No. 378,Vol. 6，pp.165-174
Suga, M., Nakamura, H., Higai, T, and Saito, S., 2001: Effectof Bond Properties on The Mechanical Behavior of RC
Beam, Proceedings of the Japan Concrete Institute,Vol.23，No.3，pp.295-300

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