Finite element model for the FRP strengthened RC beams under static loading with consideration of bond-slip effect between concrete-adhesive-FRP adhesive.

1. Finite Element Simulation for Nonlinear Finite Element Analysis of FRP
Strengthened RC Beams with Bond-Slip Effect
PATHAK Prabin a
, ZHANG Y. X. b *
School of Engineering and Information Technology, University of New South Wales, Australian
Defence Force Academy, Canberra, ACT 2600, Australia
E-mail: a
Prabin.Pathak@student.adfa.edu.au; b
y.zhang@adfa.edu.au
Keywords: Bond-slip; Fibre Reiforced Polymer; Nonlinear Finite Element Analysis; RC Beams.
Abstract. A new simple, efficient and accurate finite element model denoted as FEM-B is
developed for the analysis of structural behavior of FRP strengthened RC beams with bond-slip
effect. Geometric nonlinearity and material nonlinear properties of concrete and steel rebar are
accounted for this model. Concrete, steel, FRP and adhesive are modelled as Solid 65, Link 180,
Shell181 and Solid 45 respectively. Concrete is modelled using Nitereka and Neal’s model for
compression, isotropic and linear elastic model before cracking for tension and strength gradually
reduces to zero after cracking, whereas steel is assumed to be elastic perfectly plastic material. The
material of FRP is considered to be linearly elastic until rupture, and adhesive is assumed to be
linearly elastic. The bond slip between concrete, adhesive and FRP is based on the bilinear law,
which is modelled using spring element Combin 39.The developed new finite element model FEM-
B is validated against experimental results, and demonstrates to be effective for the structural
analysis of FRP strengthened RC beams.
Introduction
In recent decades, there is an increasing interest in using high strength composites for the
strengthening of concrete structures. Steel-rebar reinforced structures are subjected to structural
deterioration, which might be caused by design and construction defects, environmental effects,
extreme loadings such as earthquake, fire, impact loadings. Fiber reinforced polymers are of
superior characteristics such as high strength to weight ratio, ease of application, immunity to
corrosion, fatigue resistance, good durability, and are being used increasingly to reinforce and
strength the concrete structures [1].
A large number of experimental and numerical studies have been carried out on FRP
strengthened RC beams and many finite element models have been developed and employed for the
structural analysis of FRP strengthened RC beams. However, majority of these models focused on
the structural behavior of FRP strengthened RC beam with perfect bonding between FRP and
concrete interface [2-6], and the debonding failure between FRP and concrete, which is the one of
the typical failure mode [7], was neglected. In fact, as a result of the debonding, the strength
utilization ratios are sometimes only 15–35%, depending on the cause of debonding due to the FRP
debonding failures [8]. So, consideration of bond slip effect between FRP, adhesive and concrete is
utmost important for accurate prediction of the structural behavior of FRP strengthened RC beams.
Several finite element models considering the bond-slip effect were reported. For example, Wu
et al. [9] conducted a finite element analysis of FRP strengthened RC beam under three point load
using DIANA where material properties of concrete was based on Drucker-Prager plasticity model,
and steel rebar and FRP were assumed as linear elastic–perfectly plastic material and linear elastic
material until rupture respectively. Concrete was modelled as four-node plane stress element, and
the steel rebar and FRP were modelled as two-node linear truss elements. A zero thickness interface
element was used to model the bond slip between FRP and concrete according to bond-slip law
developed by Niu et al. [10]. Sayed et al. [11] analyzed the structural behavior of FRP strengthened
RC beams using ANSYS under four-point loading. The concrete, steel reinforcement and FRP were
modelled as SOLID65, LINK8 and SOLID46 elements respectively. The material properties of
concrete was based on the Mac Gregor and Plight’s model [12] for concrete in compression,

2. whereas in tension the stress and strain relation was assumed to be linear and elastic until the
maximum tensile strength is reached, after which it gradually reduced to zero. Steel rebar was
modelled as isotropic, elastic and perfectly plastic material that behaves identically in tension and
compression, and the FRP was assumed to be linear and elastic. The contact between FRP and
concrete was modeled using a set of TARGE170 and CONTA174 contact elements, which
functioned on the basis of Coulomb’s friction model, and the bond-slip was modelled based on of
the model by Lu et al. [13]. However, the modelling of adhesive has been neglected in most of the
developed finite element models leading to inaccurate prediction of structural behavior of FRP
strengthened RC beams. Molina et al. [14] stated that the effect of adhesive could not be neglected
in a finite element model because it can be susceptible to damage. Gao et al. [7] mentioned that the
efficient analysis of FRP strengthened RC beams depends upon proper bonding of FRP and
concrete with an epoxy adhesive.
In this paper, a simple finite element model with bond-slip effect is developed for accurate and
effective numerical modelling of the structural behavior of FRP strengthened RC beams. A finite
element model (FEM-P) assuming perfect bond between adhesive, FRP and concrete interfaces was
developed by the authors[15]. The FEM-P element is further developed in this paper to form the
new finite element model FEM-B, with bond slip between concrete, adhesive and FRP accounted
for. To model the bond slip between FRP, adhesive and concrete, spring elements are used with the
nonlinear bond stress-slip relationship developed by Lu et al. [13]. The developed finite element
model is validated by comparing the computed results with available experimental results.
Finite Element Model
A finite element model FEM-B is developed using finite element package ANSYS under static
loading which includes the bond-slip between FRP, adhesive and concrete. Concrete, steel, FRP are
modelled as solid, link, shell elements respectively and FRP/adhesive/concrete interfaces are
modelled using spring element with appropriate bond stress slip law. A perfect bond is assumed
between steel rebar and concrete.
The three-dimensional eight-node Solid65 element, which is characterized by three translational
(translation in the x, y and z directions) degree of freedom at each node, is used to represent the
concrete. This element is capable of modelling concrete cracking in tension and compression.
Link180 element with three degrees of freedom (translation in the x, y and z directions) at each
node is used to model steel reinforcement. The FRP strips are smeared as thin plates and four-node
SHELL181 element with six degrees of freedom at each node, i.e. translations in the x, y, and z
directions, and rotations about the x, y, and z axes is used for modelling the FRP plate. Solid45
element, which has three degrees of freedom at each node, i.e. translation in the x, y and z
directions are used to model epoxy adhesive. Two-node nonlinear spring element COMBIN39,
which has no physical mass and dimension, is used to model FRP, adhesive and concrete interfaces.
Material Model
Concrete is a quasi-brittle material with different behavior in tension and compression. The
nonlinear stress-strain relationship by Nitereka and Neal [16] is used for compressive uniaxial
stress–strain relationship of concrete, which consists of an ascending curve and linear descending
branch as shown in Fig. 1(a) and Eq. (1).
𝜎𝑐=fc [
𝜀 𝑐
𝜀0
(2 −
𝜀 𝑐
𝜀0
)] for (𝜀 ≤ 𝜀0)
𝜎𝑐=fc [1 − 0.15 × (
𝜀 𝑐−𝜀0
𝜀 𝑐𝑢−𝜀0
)] for ( 𝜀0 ≤ 𝜀 ≤ 𝜀 𝑐𝑢) (1)

3. Where fc is the compressive strength of the concrete and 𝜀 𝑐𝑢 is the ultimate compressive strain of
the concrete. The corresponding compressive strain ε0 at the compressive strength is calculated by
the equation proposed by Coronado and Lopez [17] as
ε0= 1.71 × (fc/Ec) (2)
in which Ec is the Young’s modulus of concrete.
The stress-strain curve of concrete in tension is assumed to be isotropic, linear and elastic up to
the maximum tensile strength after which concrete crack occurs and strength gradually reduces to
zero as shown in Fig.1(b) in which, Tc is the multiplier for the amount of tensile stress relaxation
whose default value is 0.6 in ANSYS.
The required input data to describe the material properties of concrete in ANSYS are elastic
modulus (Ec), Poisson’s ratio, uniaxial compressive stress, shear transfer coefficient (βt), uniaxial
tensile stress (ft). The value of βt can vary from zero to one and zero refers to a smooth crack
whereas one refers to a rough crack. These factors are used to determine how much shear force can
be transferred across open or closed cracks. For this model, closed crack is assumed as 1 and open
crack is assumed as 0.3.
Fig. 1. Stress-strain relationship of concrete: (a) compression [14]; (b) tension [18]
The steel rebar is assumed to be bilinear, isotropic, elastic and perfectly plastic material which
behaves identically in tension and compression with stiffness only in axial direction. FRPs are
assumed to be linear and elastic until the tension stress reaches its ultimate strength which causes
brittle rupture and then reduces to zero. The epoxy is assumed to be linearly elastic.
A bilinear bond-slip model under static developed by Lu et al. [13] as shown in Fig. 2 is adopted
for the bond slip behaviour between FRP, concrete and adhesive where 𝜏 𝑚𝑎𝑥 is the maximum local
bond stress, 𝑠0 is a local slip at 𝜏 𝑚𝑎𝑥 , 𝑠𝑓 is a local slip .
Fig. 2. A bilinear bond stress-slip model [13]
Numerical Validation
A FRP strengthened RC beam is analysed using the developed FE model and the computed load-
central deflection relationship is compared to that obtained from the experimental study. Due to
𝜏 𝑚𝑎𝑥(MPa)
𝑠0 𝑠𝑓
Slip (mm)
Bond stress
(unit(MPa)
Stress
Strain
ε0
fc
𝜀 𝑐𝑢
Stress
Strain
ε0 6ε0
ft
Tc ft

4. symmetry, only a quarter of the beam is analysed. A convergence study is carried out to study the
mesh sensitivity of the developed model.
A CFRP Strengthened RC Beam Tested by Arduini et al. [2]
A CFRP strengthened RC beam of size 320 mm 160 mm 1500 mm  strengthened with FRP under
four-point bending loading is modelled using the developed finite element model. The details of
steel reinforcement and FRP are shown in Fig. 3. The tension face of the RC beam is externally
strengthened with 1000 mm long, 300 mm wide and 1.2 mm thick CFRP plates using epoxy
adhesive. The material parameters of concrete, steel, FRP and epoxy are given in Table 1.
(a) Longitudinal section
(b) Cross-section
Fig 3. A CFRP-strengthened RC beam tested by Arduini et al. [2] (Dimensions: mm)

5. Table 1: Material parameters
Material Young
modulus
[GPa]
Compressive
strength
[MPa]
Tensile
strength
[MPa]
Yield
strength
[MPa]
Poisson’s
ratio
Concrete 27 36 2.7 0.2
Steel 200 550 0.3
CFRP 235 3510 0.35
Epoxy 2.0 0.38
The load-deflection relationship of the FRP strengthened RC beam under static loading obtained
from FEM-P [15] and FEM-B and experiment [2] is shown in Fig. 4. Very good agreement between
numerical results from developed finite element model and the experiment is achieved. The two
curves obtained from FEM-B and FEM-P are nearly identical before the load reaching 80 kN where
no obvious bond slip occurs, but after that when bond slip occurs, the FEM-B model predicts the
structural behavior of FRP strengthened RC beam more accurately. At 112 kN, the maximum
central deflection of the beam obtained from the FEM-B model and FEM-P [16] is 4.098 mm and
3.886 mm respectively, while the central deflection obtained from the experiment [2] is 4.45 mm.
This demonstrates the effectiveness and accuracy of the model in the nonlinear finite element
analysis of the FRP-RC beams and the capability of the FEM-B to model the structural behavior of
the beams with bond-slip effect.
Fig 4. Load-central deflection of the FRP strengthened RC beam
Conclusion
A new and simple finite element model FEM-B is developed with bond slip effect between
concrete, adhesive and FRP considered in this paper. In the finite element model, material
nonlinearities are considered, and concrete, steel, FRP components and adhesive are modeled using
Solid65 element, Link180 element, Shell181 elements, and Solid45 element respectively. Concrete
is modelled using Nitereka and Neal’s model for compression, isotropic and linear elastic model
before cracking for tension and strength gradually reduces to zero after cracking. Material property
of steel is assumed to be elastic-perfectly plastic, whereas the FRP is assumed to be linearly elastic
until rupture occurs, and adhesive is assumed to be linearly elastic. Spring element Combin39 is
used for the bond-slip behavior of concrete, FRP and adhesive based on a bilinear bond stress-slip
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6
Load(KN)
Central Deflection(mm)
FEM-P
Experiment
FEM-B

6. law. The computed results agree very well with those obtained from experimental results, and the
numerical results from FEM-B model are closer to the experimental results than those obtained
from finite element model FEM-P with perfect bond, especially after the load reaches certain value
where bond slip starts to occur. This demonstrates the efficiency, accuracy and capability of the
developed finite element model in the finite element analysis of FRP strengthened RC beams with
bond-slip effect.
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