# Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review

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## Abstract

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## 1. Introduction and Background

## 2. Finite Element Model Development Strategies

#### 2.1. Considerations for Element Types

#### 2.2. Considerations for Material Parameters

#### 2.2.1. Concrete

_{c}= concrete compressive stress in MPa corresponding to a specified strain value ε

_{c}, ${f}_{c}^{\prime}$ = concrete compressive strength in MPa.

_{t}. Once the value of the tensile strength of concrete is reached, stress relaxation is simulated with a steep drop of 40% of f

_{t}and then followed by linear descending curve up to a strain value of 6ε

_{t}, where ε

_{t}is the concrete strain value at f

_{t}as shown in Figure 2 [28,48,52]. From this view, the tensile strength of concrete f

_{t}is computed as per Equation (4). Knowing this value, as well as modulus property of concrete, then the strain at this particular tensile strength can be estimated in addition to that at failure. Other properties of concrete include Poisson’s ratio, which can vary between 0.18–0.22 [53].

#### 2.2.2. Steel Reinforcement

_{r}the diameter of the mentioned reinforcements in (mm), N

_{r}the number of reinforcements bars and L

_{1}and L

_{2}is the lengths of two adjacent reinforcement link elements in (mm).

#### 2.2.3. FRP and Adhesive

_{u}is the ultimate slip at ${\tau}_{u}$ in (mm).

_{u}, for the steel reinforcement and the values of ${\tau}_{u}\mathrm{and}$s

_{u}for the GFRP and CFRP materials can be assumed to roughly be 20.25 MPa, 10.1 MPa, 0.42 mm, 0.33 mm, respectively.

_{max}) value. This τ

_{max}corresponds to a slip (s

_{u}) value. Beyond this point, a softening response is registered until the ultimate attained slip (assumed to equal to four times the slip corresponding to the ultimate shear stress) is reached. For transparency, τ

_{max}for round deformed FRP bars can be evaluated using the following expression proposed by Hassan and Rizkalla [60].

_{ct}is the concrete tensile strength in MPa, μ the coefficient of friction. A value of μ = 1 is used as proposed by De Lorenzis and Teng [61] and G

_{1}is a constant taken as 1.0.

#### 2.3. Considerations for Boundary Conditions and Loadings

#### 2.3.1. Monotonic and Cyclic Loading

#### 2.3.2. Fire Loading

^{2}K for standard fire conditions and in the range of 40–50 W/m

^{2}K for hydrocarbon fires [69]. The value of the same coefficient is 4 W/m

^{2}K the unexposed cold surfaces. Heat transfer via radiation requires the input of emissivity (ε) and Stefan-Boltzman radiation (σ) coefficientS with values of 0.7–0.9 and 5.669 × 10

^{−8}W/m

^{2}K

^{4}, respectively [70,71].

#### 2.4. Considerations for Failure Criteria and Convergence Limits

- Yielding of steel reinforcement in tension is followed by concrete crushing when strain in the top compression fibers exceeds 0.003.
- Shear/tension delamination of the concrete cover may occur once the filling layer or substrate cannot sustain the forces induced in the reinforcing steel/cfrp rebars.
- Debonding of the FRP systems from the concrete substrate (delamination of plates/sheets or NSM bar pull-out).

#### 2.5. Considerations for Post-Processing of Results

## 3. Challenges, and Future Research Needs

- Experimental and numerical studies on the thermal and mechanical response of FRP-strengthened beams under cold and hot temperatures.
- Experimental and numerical studies on the creep-rupture behavior and endurance times of FRP-strengthened RC beams.
- Modeling the effects of high concrete strength on the shear and flexural performance of FRP-strengthened beams.
- Experimental and numerical studies on the effects of lightweight concrete on the shear and flexural performance of FRP-strengthened beams.
- Experimental and numerical studies on the long-term deflection behavior of flexural members strengthened with different types of FRP systems.
- Modeling the performance of externally strengthened RC beams anchored with FRP splay anchors under static, cyclic, and fire loadings.

## 4. Summary and Conclusions

- FRP materials offer unique solutions to aging and new structures that exceed those constructed by traditional materials.
- Developing appropriate modeling techniques is warranted given that the performance of FRP-strengthened concrete structures is complicated and complex.
- There is a need for development of appropriate and validated FE models since they provide more economical solutions than testing. It is beneficial in design oriented parametric studies and could be used in lieu of tests in the laboratory.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Rasheed, H.A. Strengthening Design of Reinforced Concrete with FRP, 1st ed.; CRC Press: Boca Raton, FL, USA, 2014. [Google Scholar]
- Hollaway, L.C. A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties. Constr. Build. Mater.
**2010**, 24, 2419–2445. [Google Scholar] [CrossRef] - Naser, M.Z.; Hawileh, R.A.; Abdalla, J.A. Fiber-reinforced polymer composites in strengthening reinforced concrete structures: A critical review. Eng. Struct.
**2019**, 198, 109542. [Google Scholar] [CrossRef] - Oliveira, D.V.; Basilio, I.; Loureņo, P.B. Experimental behavior of FRP strengthened masonry arches. J. Compos. Constr.
**2010**, 14, 312–322. [Google Scholar] [CrossRef] [Green Version] - Czaderski, C.; Meier, U. EBR Strengthening Technique for Concrete, Long-Term Behaviour and Historical Survey. Polymers
**2018**, 10, 77. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hawileh, R.; Abdalla, J.A.; Naser, M.Z.; Tanarslan, M. Finite element modeling of shear deficient RC beams strengthened with NSM CFRP rods under cyclic loading. ACI Spec. Publ.
**2015**, 301, 1–18. [Google Scholar] - Firmo, J.P.; Correia, J.R. Fire behaviour of thermally insulated RC beams strengthened with NSM-CFRP strips: Experimental study. Compos. Part B Eng.
**2015**, 76, 112–121. [Google Scholar] [CrossRef] - Zhu, H.; Wu, G.; Zhang, L.; Zhang, J.; Hui, D. Experimental study on the fire resistance of RC beams strengthened with near-surface-mounted high-Tg BFRP bars. Compos. Part B Eng.
**2014**, 60, 680–687. [Google Scholar] [CrossRef] - ACI Committee 440. Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440. 2R-17); American Concrete Institute: Farmington Hills, MI, USA, 2017. [Google Scholar]
- International Federation for Structural Concrete. FRP Reinforcement in RC Structures; Technical Report; International Federation for Structural Concrete: Lausanne, France, 2007. [Google Scholar]
- Sonobe, Y.; Mochizuki, S.; Matsuzaki, Y.; Shimizu, A. Guidelines for Structural Design of FRP Reinforced Concrete Building Structures. In Rilem Proceedings; Chapman & Hall: London, UK, 1997. [Google Scholar]
- Yuan, C.; Chen, W.; Pham, T.M.; Hao, H. Bond behaviour between hybrid fiber reinforced polymer sheets and concrete. Constr. Build. Mater.
**2019**, 210, 93–110. [Google Scholar] [CrossRef] - Naser, M.; Hawileh, R.; Abdalla, J.A.; Al-Tamimi, A. Bond behavior of CFRP cured laminates: Experimental and numerical investigation. J. Eng. Mater. Technol. Trans. ASME
**2012**, 134, 021002. [Google Scholar] [CrossRef] - Mosallam, A.; Allam, K.; Salama, M. Analytical and numerical modeling of RC beam-column joints retrofitted with FRP laminates and hybrid composite connectors. Compos. Struct.
**2019**, 214, 486–503. [Google Scholar] [CrossRef] - Chellapandian, M.; Prakash, S.S.; Sharma, A. Experimental and finite element studies on the flexural behavior of reinforced concrete elements strengthened with hybrid FRP technique. Compos. Struct.
**2019**, 208, 466–478. [Google Scholar] [CrossRef] - Kachlakev, D.; Niller, T.; Yim, S.; Chansawat, K.; Potisuk, T. Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates; California Polytechnic State University: San Lius Obispo, CA, USA; Oregon State University: Corvallis, OR, USA, 2001. [Google Scholar]
- Hawileh, R.A.; Abdalla, J.A.; Tanarslan, M.H.; Naser, M.Z. Modeling of nonlinear cyclic response of shear-deficient RC T-beams strengthened with side bonded CFRP fabric strips. Comput. Concr.
**2011**, 8, 193–206. [Google Scholar] [CrossRef] - Ibrahim, A.M.; Mahmood, M.S. Finite element modeling of reinforced concrete beams strengthened with FRP laminates. Eur. J. Sci. Res.
**2009**, 30, 526–541. [Google Scholar] - Shahverdi, M.; Mohammadi, S. Fracture analysis of FRP composites using a meshless finite point collocation method. In Proceedings of the Fourth International Conference on FRP Composites in Civil Engineering (CICE2008), Zurich, Switzerland, 22–24 July 2008. [Google Scholar]
- Lu, X.Z.; Ye, L.P.; Teng, J.G.; Jiang, J.J. Meso-scale finite element model for FRP sheets/plates bonded to concrete. Eng. Struct.
**2005**, 27, 564–575. [Google Scholar] [CrossRef] - Kadhim, M.M.A.; Jawdhari, A.R.; Altaee, M.J.; Adheem, A.H. Finite element modelling and parametric analysis of FRP strengthened RC beams under impact load. J. Build. Eng.
**2020**, 32, 101526. [Google Scholar] [CrossRef] - Bouziadi, F.; Boulekbache, B.; Haddi, A.; Hamrat, M.; Djelal, C. Finite element modeling of creep behavior of FRP-externally strengthened reinforced concrete beams. Eng. Struct.
**2020**, 204, 109908. [Google Scholar] [CrossRef] - Godat, A.; Challal, O.; Obaidat, Y. Non-linear finite-element investigation of the parameters affecting externally-bonded FRP flexural-strengthened RC beams. Results Eng.
**2020**, 8, 100168. [Google Scholar] [CrossRef] - Nie, X.F.; Zhang, S.S.; Chen, G.M.; Yu, T. Strengthening of RC beams with rectangular web openings using externally bonded FRP: Numerical simulation. Compos. Struct.
**2020**, 248, 112552. [Google Scholar] [CrossRef] - Hawileh, R.A. Nonlinear finite element modeling of RC beams strengthened with NSM FRP rods. Constr. Build. Mater.
**2012**, 27, 461–471. [Google Scholar] [CrossRef] - Kodur, V.K.R.; Bhatt, P.P. A numerical approach for modeling response of fiber reinforced polymer strengthened concrete slabs exposed to fire. Compos. Struct.
**2018**, 187, 226–240. [Google Scholar] [CrossRef] - Dal Lago, B.; Taylor, S.E.; Deegan, P.; Ferrara, L.; Sonebi, M.; Crosset, P.; Pattarini, A. Full-scale testing and numerical analysis of a precast fibre reinforced self-compacting concrete slab pre-stressed with basalt fibre reinforced polymer bars. Compos. Part B Eng.
**2017**, 128, 120–133. [Google Scholar] [CrossRef] [Green Version] - Hawileh, R.A.; Naser, M.Z.; Abdalla, J.A. Finite element simulation of reinforced concrete beams externally strengthened with short-length CFRP plates. Compos. Part B Eng.
**2013**, 45, 1722–1730. [Google Scholar] [CrossRef] - Chen, G.M.; Teng, J.G.; Chen, J.F.; Xiao, Q.G. Finite element modeling of debonding failures in FRP-strengthened RC beams: A dynamic approach. Comput. Struct.
**2015**, 158, 167–183. [Google Scholar] [CrossRef] [Green Version] - Bui, L.V.H.; Stitmannaithum, B.; Ueda, T. Mechanical performances of concrete beams with hybrid usage of steel and FRP tension reinforcement. Comput. Concr.
**2017**, 20, 391–407. [Google Scholar] - Kim, S.; Aboutaha, R.S. Finite element analysis of carbon fiber-reinforced polymer (CFRP) strengthened reinforced concrete beams. Comput. Concr.
**2004**, 1, 401–416. [Google Scholar] [CrossRef] - Shrestha, R.; Smith, S.T.; Samali, B. Finite element modelling of FRP-strengthened RC beam-column connections with ANSYS. Comput. Concr.
**2013**, 11, 1–20. [Google Scholar] [CrossRef] - Lu, X.Z.; Teng, J.G.; Ye, L.P.; Jiang, J.J. Bond-slip models for FRP sheets/plates bonded to concrete. Eng. Struct.
**2005**, 27, 920–937. [Google Scholar] [CrossRef] - Chen, G.M.; Chen, J.F.; Teng, J.G. On the finite element modelling of RC beams shear-strengthened with FRP. Constr. Build. Mater.
**2012**, 32, 13–26. [Google Scholar] [CrossRef] [Green Version] - Sakar, G.; Hawileh, R.A.; Naser, M.Z.; Abdalla, J.A.; Tanarslan, M. Nonlinear behavior of shear deficient RC beams strengthened with near surface mounted glass fiber reinforcement under cyclic loading. Mater. Des.
**2014**, 61, 16–25. [Google Scholar] [CrossRef] - Hawileh, R.A.; Musto, H.A.; Abdalla, J.A.; Naser, M.Z. Finite element modeling of reinforced concrete beams externally strengthened in flexure with side-bonded FRP laminates. Compos. Part B Eng.
**2019**, 173, 106952. [Google Scholar] [CrossRef] - Liu, Y.; Zwingmann, B.; Schlaich, M. Nonlinear progressive damage analysis of notched or bolted fibre-reinforced polymer (FRP) laminates based on a three-dimensional strain failure criterion. Polymers
**2014**, 6, 949–976. [Google Scholar] [CrossRef] [Green Version] - Ameli, M.; Ronagh, H.R.; Dux, P.F. Behavior of FRP strengthened reinforced concrete beams under torsion. J. Compos. Constr.
**2007**, 11, 384–390. [Google Scholar] [CrossRef] - Mahini, S.S.; Ronagh, H.R. Numerical modelling of FRP strengthened RC beam-column joints. Struct. Eng. Mech.
**2009**, 32, 649–665. [Google Scholar] [CrossRef] - Hassan, N.Z.; Sherif, A.G.; Zamarawy, A.H. Finite element analysis of reinforced concrete beams with opening strengthened using FRP. Ain Shams Eng. J.
**2017**, 8, 531–537. [Google Scholar] [CrossRef] [Green Version] - El-Kashif, K.F.O.; Adly, A.K.; Abdalla, H.A. Finite element modeling of RC shear walls strengthened with CFRP subjected to cyclic loading. Alexandria Eng. J.
**2019**, 58, 189–205. [Google Scholar] [CrossRef] - Zeng, J.; Guo, Y.; Li, L.; Chen, W. Behavior and Three-Dimensional Finite Element Modeling of Circular Concrete Columns Partially Wrapped with FRP Strips. Polymers
**2018**, 10, 253. [Google Scholar] [CrossRef] [Green Version] - Yu, H.; Bai, Y.L.; Dai, J.G.; Gao, W.Y. Finite element modeling for debonding of FRP-to-concrete interfaces subjected to mixed-mode loading. Polymers
**2017**, 9, 438. [Google Scholar] [CrossRef] [Green Version] - Gribniak, V.; Misiūnaitė, I.; Rimkus, A.; Sokolov, A.; Šapalas, A. Deformations of FRP–Concrete Composite Beam: Experiment and Numerical Analysis. Appl. Sci.
**2019**, 9, 5164. [Google Scholar] [CrossRef] [Green Version] - Willam, K.; Warnke, E. Constitutive model for the triaxial behavior of concrete. Proc. Intl. Assoc. Bridge Structl. Engrs.
**1975**, 19, 1–30. [Google Scholar] - Lazzari, B.M.; Filho, A.C.; Lazzari, P.M.; Pacheco, A.R. Using the element-embedded rebar model in ansys to analyze reinforced concrete beams. Comput. Concr.
**2017**, 19, 347–356. [Google Scholar] [CrossRef] - Al-Azzawi, A.A.; Abdul Al-Aziz, B.M. Behavior of reinforced lightweight aggregate concrete hollow-core slabs. Comput. Concr.
**2018**, 21, 117–126. [Google Scholar] - Hawileh, R.A. Finite element modeling of reinforced concrete beams with a hybrid combination of steel and aramid reinforcement. Mater. Des.
**2015**, 65, 831–839. [Google Scholar] [CrossRef] - Dahmani, L.; Khennane, A.; Kaci, S. Crack identification in reinforced concrete beams using ANSYS software. Strength Mater.
**2010**, 42, 232–240. [Google Scholar] [CrossRef] - Zhou, L.; Zheng, Y.; Taylor, S.E. Finite-Element Investigation of the Structural Behavior of Basalt Fiber Reinforced Polymer (BFRP)-Reinforced Self-Compacting Concrete (SCC) Decks Slabs in Thompson Bridge. Polymers
**2018**, 10, 678. [Google Scholar] [CrossRef] [Green Version] - Hognestad, E.; Hanson, N.W.; McHenry, D. Concrete Stress Distribution in Ultimate Strength Design. ACI J. Proc.
**1955**, 52, 455–480. [Google Scholar] - Hawileh, R.A.; El-Maaddawy, T.A.; Naser, M.Z. Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites. Mater. Des.
**2012**, 42, 378–387. [Google Scholar] [CrossRef] - Naser, M.Z. Behavior of RC Beams Strengthened with CFRP Laminates Under Fire-A Finite Element Simulation. Master’s Thesis, American University of Sharjah, Sharjah, UAE, 2011. [Google Scholar]
- Nie, J.; Fan, J.; Cai, C.S. Stiffness and deflection of steel-concrete composite beams under negative bending. J. Struct. Eng.
**2004**, 130, 1842–1851. [Google Scholar] [CrossRef] - Obaidat, Y.T.; Heyden, S.; Dahlblom, O. The effect of CFRP and CFRP/concrete interface models when modelling retrofitted RC beams with FEM. Compos. Struct.
**2010**, 92, 1391–1398. [Google Scholar] [CrossRef] - Hawileh, R.A.; Naser, M.; Zaidan, W.; Rasheed, H.A. Modeling of insulated CFRP-strengthened reinforced concrete T-beam exposed to fire. Eng. Struct.
**2009**, 31, 3072–3079. [Google Scholar] [CrossRef] - Martinelli, E.; Napoli, A.; Nunziata, B.; Realfonzo, R. RC Beams Strengthened with Mechanically Fastened Composites: Experimental Results and Numerical Modeling. Polymers
**2014**, 6, 613–633. [Google Scholar] [CrossRef] [Green Version] - Comite Euro-International Du Beton. CEB-FIP Model Code 1990: Design Code; Default Book Series; Thomas Telford Ltd.: London, UK, 1993. [Google Scholar]
- Nakaba, K.; Kanakubo, T.; Furuta, T.; Yoshizawa, H. Bond behavior between fiber-reinforced polymer laminates and concrete. ACI Struct. J.
**2001**, 98, 359–367. [Google Scholar] - Hassan, T.K.; Rizkalla, S.H. Bond mechanism of near-surface-mounted fiber-reinforced polymer bars for flexural strengthening of concrete structures. ACI Struct. J.
**2004**, 101, 830–839. [Google Scholar] - De Lorenzis, L.; Teng, J.G. Near-surface mounted FRP reinforcement: An emerging technique for strengthening structures. Compos. Part. B Eng.
**2007**, 38, 119–143. [Google Scholar] [CrossRef] - CEN. Design of Concrete Structures—Part 1–2: General Rules—Structural Fire Design (EN 1992-1-2); CEN: Brussels, Belgium, 2004. [Google Scholar]
- Bisby, L. Fire Behaviour of Fibre-Reinforced Polymer (FRP) Reinforced or Confined Concrete. Ph.D. Thesis, Queen’s University, Kingston, ON, Canada, 2003. [Google Scholar]
- Naser, M.Z. Properties and material models for modern construction materials at elevated temperatures. Comput. Mater. Sci.
**2019**, 160, 16–29. [Google Scholar] [CrossRef] - Yu, B.; Kodur, V. Effect of temperature on strength and stiffness properties of near-surface mounted FRP reinforcement. Compos. Part. B Eng.
**2014**, 58, 510–517. [Google Scholar] [CrossRef] - Kodur, V.K.R.; Bhatt, P.P.; Naser, M.Z. High temperature properties of fiber reinforced polymers and fire insulation for fire resistance modeling of strengthened concrete structures. Compos. Part. B Eng.
**2019**, 175, 107104. [Google Scholar] [CrossRef] - Kodur, V.K.R.; Shakya, A.M. Effect of temperature on thermal properties of spray applied fire resistive materials. Fire Saf. J.
**2013**, 61, 314–323. [Google Scholar] [CrossRef] - Džolev, I.M.; Cvetkovska, M.J.; Lađinović, D.; Radonjanin, V.S. Numerical analysis on the behaviour of reinforced concrete frame structures in fire. Comput. Concr.
**2018**, 21, 637–647. [Google Scholar] - Wang, Y.; Dong, Y.L.; Zhou, G.C. Nonlinear numerical modeling of two-way reinforced concrete slabs subjected to fire. Comput. Struct.
**2013**, 119, 23–36. [Google Scholar] [CrossRef] - Hawileh, R.A.; Kodur, V.K.R. Performance of reinforced concrete slabs under hydrocarbon fire exposure. Tunn. Undergr. Sp. Technol.
**2018**, 77, 177–187. [Google Scholar] [CrossRef] - CEN. Eurocode 1. Actions on Structures–Part 1–2: General Actions–Actions on Structures Exposed to Fire (EN 1991-1-2); BSI: London, UK, 2002. [Google Scholar]
- Kohnke, P.C. ANSYS Theory Reference; ANSYS Technology Drive: Canonsburg, PA, USA, 2013. [Google Scholar]
- Federation International Du Béton. Externally Bonded FRP Reinforcement for RC Structures: Technical Report on the Design and Use of Externally Bonded Fibre Reinforced Polymer Reinforcement (FRP EBR) for Reinforced Concrete Structures; International Federation for Structural Concrete: Lausanne, Switzerland, 2001. [Google Scholar]
- Gawil, B.; Wu, H.-C.; Elarbi, A. Modeling the Behavior of CFRP Strengthened Concrete Beams and Columns at Different Temperatures. Fibers
**2020**, 8, 10. [Google Scholar] [CrossRef] [Green Version] - Müzel, S.D.; Bonhin, E.P.; Guimarães, N.M.; Guidi, E.S. Application of the Finite Element Method in the Analysis of Composite Materials: A Review. Polymers
**2020**, 12, 818. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Typical finite element (FE) models developed in ANSYS for fiber-reinforced polymer (FRP)-strengthened Reinforced Concrete Beams (RC beams) showing different components.

**Figure 4.**Consideration for applied loading in ANSYS and ABAQUS: (

**a**) Monotonic loading; (

**b**) Cyclic loading.

**Figure 5.**Comparison between the failure modes of the experimental and FE models developed in ANSYS: (

**a**) Cover delamination; (

**b**) Debonding.

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**MDPI and ACS Style**

Naser, M.Z.; Hawileh, R.A.; Abdalla, J.
Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review. *J. Compos. Sci.* **2021**, *5*, 19.
https://doi.org/10.3390/jcs5010019

**AMA Style**

Naser MZ, Hawileh RA, Abdalla J.
Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review. *Journal of Composites Science*. 2021; 5(1):19.
https://doi.org/10.3390/jcs5010019

**Chicago/Turabian Style**

Naser, M. Z., Rami Antoun Hawileh, and Jamal Abdalla.
2021. "Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review" *Journal of Composites Science* 5, no. 1: 19.
https://doi.org/10.3390/jcs5010019