This paper examines the mechanical behavior of fiber reinforced polymer (FRP)-confined concrete under cyclic compression using the 3D cohesive zone model (CZM). A numerical modeling method was developed, employing zero-thickness cohesive elements to represent the stress-displacement relationship of concrete potential fracture surfaces and FRP-concrete interfaces. Additionally, mixed-mode damage plastic constitutive models were proposed for the concrete potential fracture surfaces and FRP-concrete interface, considering interfacial friction. Furthermore, an anisotropic plastic constitutive model was developed for the FRP composite jacket. The CZM model proposed in this study was validated using experimental data from plain concrete and large rupture strain (LRS) FRP-confined concrete subjected to cyclic compression. The simulation results demonstrate that the proposed model accurately predicts the mechanical response of both concrete and FRP-confined concrete under cyclic compression. Lastly, various parametric studies were conducted to investigate the internal failure mechanism of FRP-confined concrete under cyclic loading to analyze the influence of the inner friction plasticity of different components.

The fiber-reinforced polymer (FRP) is a lightweight, high-strength, easy-to-construct, and corrosion-resistant material with promising applications in the construction industry [

The abovementioned studies, while advancing the understanding of FRP-confined concrete structures, have a notable weakness regarding the failure mechanism on their long-term performance and durability under cyclic and fatigue loading. This deficiency restricts the ability to fully assess how these structures will withstand repetitive stress over time, a crucial factor in real-world construction scenarios. Addressing this gap is essential for a comprehensive understanding of the structures’ resilience, especially in environments prone to regular loading and unloading cycles.

In recent years, there has been an emergence of new types of FRP materials for seismic reinforcement of concrete columns. Apart from traditional materials like aramid FRP (AFRP), carbon FRP (CFRP), and glass FRP (GFRP), which have rupture strains of less than 3%, 1.5%, and 2.5%, respectively [

While there has been significant research on FRP-confined concrete, most of it has focused on the macroscopic scale. Limited attention has been given to studying the mechanistic aspects of this structure at the mesoscopic scale, which considers the interaction within the concrete fracture surface and the FRP-concrete interface. Therefore, it is important to establish a mesoscale model to gain a better understanding of the internal fracture mechanisms of FRP-confined concrete under cyclic compression conditions. Since FRP-confined concrete is a composite structure that relies on the transfer of internal forces through interfaces, the cohesive zone model (CZM) is a suitable choice. Because CZM can accurately describe the normal and tangential mechanical damage behavior between interfaces, as well as detailed friction behavior between interfaces, it has significant advantages in characterizing interface problems compared to traditional continuous or contact elements, including the interface properties between FRP and concrete [

In order to understand the internal fracture mechanisms of FRP-wrapped concrete under cyclic compression conditions, this study developed an FE model based on the CZM. Zero-thickness cohesive elements were used to represent the potential fracture surfaces of concrete and the interface between FRP and concrete. Damage plastic constitutive models were proposed to account for the interface’s damage, plastic behavior, and friction effect. The proposed model was validated using different experiments, and subsequent analyses were conducted to investigate the internal fracture and failure mechanisms.

The 3D modeling method used in this study is based on the insertion of cohesive elements. To characterize the mechanical behavior of the concrete potential fracture surfaces and FRP-concrete interface, coherent elements (COH3D6) were adopted, as shown in

In the CZM model, solid elements are assumed to be linear elastic, while all damage, plasticity, and interface friction behaviors occur within the cohesive elements. Therefore, this section will provide a detailed introduction to the constitutive model used for the cohesive elements.

Single-mode damage plastic relation

To characterize the loading, unloading, and reloading mechanical behavior of the FRP-concrete interface, the exponential softening relationship and linear unloading and reloading relationship were adopted, as shown in

For mode I, the interface was consumed undamaged under compression. In monotonic loading conditions, the normal stress σ can be expressed as follows:

where _{n} is the normal stiffness; _{n} is the normal displacement; _{n0} and _{nf} are the damage initial displacement and failure displacement in the normal direction, respectively;

As shown in

where _{np} is the plastic displacement in the normal direction, which can be given as follows according to the geometry relation in _{max} is the historical maximum nominal damage factor; _{nmax} is the corresponding normal displacement to _{max}.

The explanation of the damage factor _{n} should always be much higher than the one (1 − _{n} without considering plasticity. This indicates that the damage factor ^{n}, ensuring that

For mode II, as shown in _{0} is the shear strength; _{s} is the normal stiffness, _{s} = _{0}/_{s0}; _{s} is the tangential displacement, in 3D condition, _{s} = (^{2}_{sx} + ^{2}_{sy})^{1/2}; δs0 and _{sf} are the damage initial displacement and failure displacement in the tangential direction, respectively;

In unloading and reloading conditions, the isotropic plastic and damage behavior was adopted to characterize the shear stress in the tangential direction (2D) or tangential plane (3D). As shown in _{n}, same as mode-I, _{sp} is the plastic displacement in the tangential direction or tangential plane, it is a positive value, which can be expressed as follows:_{smax} is the corresponding tangential displacement to _{max}.

Mixed-mode damage plastic relation

In the mixed-mode condition (mode I and mode II), the damage and plastic behavior can be explained through

_{t} is the tensile strength of the interface.

Thus, according to the geometry relation in _{n0r} and _{s0r} [_{n0r} and _{s0r} are the projections of the initial damage displacement in normal and tangential directions under a mixed-mode loading path.

Similarly, the relative damage initial displacements _{nfr} and _{sfr} [_{nfr} and _{sfr} are the projections of the failure displacement in normal and tangential directions. _{n} and _{s} are the fracture energies in the normal and tangential directions, which can be obtained by calculating the area under the stress-displacement curves in

According to the red line in _{0} and failure displacement _{f} in mixed-mode loading conditions can be expressed as follows:

Thus, the damage factor

In addition, based on the projection, the expression for plastic displacements can be written as:

Friction effect

Once the damage initiates in the interface, the friction stresses would be involved in the tangential stresses under the interface compression condition. According to the friction law, the friction stress can be calculated under the interface non-slippage condition and interface slippage condition.

Interface non-slippage condition

In the interface non-slippage condition, as shown in _{f} in this condition can be expressed as follows:

where _{fmax} is the maximum friction stress that the interface can provide, which can be given as follows:

Interface slippage condition

In the interface slippage condition, as shown in _{sx}^{slide} and _{sy}^{slide} are the projections of the slip displacement in the tangential plane.

Besides, in the interface slippage condition, when the maximum frictional stress is unable to prevent further slippage, an update to the slip displacements _{sx}^{slide} and _{sy}^{slide} should be implemented:_{sx}^{slide*} and _{sy}^{slide*} are the updated slip displacements.

Stress expressions

Based on the damaged plastic relation and friction effect of the interface, the stress expression for the interface can be formulated as follows:

Elastic stage:

Non-linear stage:

For normal stress:

For shear stresses:

To implement the damage plastic constitutive model proposed in this study into the FE model, a VUMAT subroutine for EXPLICITE/ABAQUS [

The constitutive model for concrete potential fracture surfaces is similar to the FRP-concrete interface. The only difference is that the stress-displacement envelope curve of the potential fracture surfaces follows the bilinear relationship, as shown in

In mixed-mode conditions, the damage initiation of the interface follows the square stress criterion, which can be given as follows:

Similar to the FRP-concrete interface, the damage initial displacements in the mixed-mode can be expressed as follows:

Besides, the failure displacements can also be similarly calculated by:

Finally, the damage factor

Except for the parameters mentioned above, all other parameters, such as _{np}, _{sp}, _{sp}, _{f}, and so on, can be calculated using

Finally, the stresses of the potential fracture surfaces in the mixed-mode condition can be formulated as follows:

Elastic stage:

Nonlinear stage:

As mentioned earlier, the stresses can be calculated using

The FRP composite is cast by combining FRP fabric and epoxy resin, making its mechanical response more complex than a single material. According to the previous studies [

Therefore, the stress-strain envelope curve of the FRP composite jacket in its strengthening direction can be given as follows:_{x} and _{x} are the stress and strain in the strengthening direction; _{1} and _{2} are the elastic modulus in two batches; _{1} and _{1} are the stress and strain value of the turning point in

When an FRP composite jacket is under unloading and reloading, its stress-strain relation in the strengthening direction can be expressed as follows:_{re} is the unloading and reloading stiffness; _{p} is the plastic strain, which can be obtained according to the maximum stress _{max} and the corresponding strain _{max} during the loading history:

As shown in

The constitutive models of concrete potential fracture surfaces and FRP composite jackets were also implemented by user subroutine VUMAT in EXPLICITE/ABAQUS.

To ensure the accuracy of the established FE model for FRP-confined concrete in this study, it is essential first to ensure that the plain concrete FE model accurately reflects its mechanical characteristics under cyclic loading. The experimental study about low-strength concrete carried out by Ozcelik [

The FE model was built using the modeling method proposed in this study. Through mesh sensitivity analysis, a typical FE model contains about 35,000 nodes, 9000 solid elements, and 17,000 cohesive elements. Through the experimental results [

Material | Mode I | Mode II | |||||
---|---|---|---|---|---|---|---|

Concrete potential |
10^{6} |
0.70 | 45 | 10^{6} |
2.40 | 450 | 0.35 |

By calculation, the simulated stress-strain hysteresis curve of plain concrete under cyclic loading and the post-failure morphology (cracks were represented by deleting the cohesive elements whose damage factor

It is crucial to validate the accuracy of the proposed model under monotonic compression conditions before examining the cyclic behavior of FRP-confined concrete columns. The experiments carried out by Dai et al. [

Specimen | Concrete strength (MPa) | FRP type | FRP thickness |
_{1} (GPa) |
_{2} (GPa) |
---|---|---|---|---|---|

PET-600-1 | 32.5 | PET-600 | 0.848 | 18.9 | 7.4 |

PET-600-2 | 1.696 | 18.9 | 7.4 | ||

PET-600-3 | 2.544 | 18.9 | 7.4 | ||

PEN-600-1 | 39.2 | PEN-600 | 0.848 | 27.0 | 12.0 |

PEN-600-2 | 1.696 | 27.0 | 12.0 | ||

PEN-600-3 | 2.544 | 27.0 | 12.0 |

One typical FE model contains about 43,000 nodes, 10,500 solid elements, 22,000 cohesive elements, and 1500 shell elements. Through the experimental results [

Material | Mode I | Mode II | ||||||
---|---|---|---|---|---|---|---|---|

Concrete potential fracture surface (32.5 MPa) | 10^{6} |
2.60 | 120 | 10^{6} |
9.10 | 1200 | – | 0.35 |

Concrete potential fracture surface (39.2 MPa) | 10^{6} |
3.20 | 180 | 10^{6} |
11.50 | 1800 | – | 0.35 |

FRP-concrete interface | 2 ^{3} |
2.50 | 100 | 2 ^{3} |
8.75 | 1000 | 4.38 | 0.35 |

It should be noted that the FRP-concrete interface is composed of a mixture of epoxy resin and concrete surface mortar. Since the strength and fracture energy of epoxy resin are much greater than those of concrete surface mortar, the strength and fracture energy of the FRP-concrete interface should be taken as the parameter values of the concrete surface mortar. These parameters are generally chosen to be slightly weaker than the core concrete. Besides, the elastic modulus and Poisson’s concrete ratio are about 30 GPa and 0.22, respectively. The elastic modulus of CFRP is about 120 GPa. For the FRP jacket, considering the epoxy resin and the externally bonded fiber sheet [_{FRP} · _{FRP} of the FRP jacket has been uniformly increased by 15 GPa·mm. _{epoxy} (_{re} = 5_{1}.

In addition to stress-strain curves, the fracture pattern in the concrete during the cyclic loading process was analyzed, five typical states in

To validate the accuracy of the FRP-confined concrete FE model under cyclic compression conditions, the experiment carried out by Bai et al. [

As in

Material | Mode I | Mode II | ||||||
---|---|---|---|---|---|---|---|---|

Concrete potential fracture surface (35.6 MPa) | 10^{6} |
2.70 | 160 | 10^{6} |
9.80 | 1600 | – | 0.35 |

FRP-concrete interface | 2 ^{3} |
2.50 | 100 | 2 ^{3} |
8.75 | 1000 | 4.38 | 0.35 |

In order to gain a deeper understanding of the interaction between concrete and FRP jackets during the cyclic loading process of FRP-confined concrete columns, as shown in

Furthermore, during the unloading process transitioning from state B to state C, the overall radial displacement of the concrete surface gradually becomes smaller than the radial displacement of FRP. This indicates that the compressive effect between concrete and FRP is weak during this process. Therefore, the stress-strain relationship of concrete at this stage is essentially equivalent to that of unwrapped concrete. This internal mechanism explains why there is a turning point in the cyclic unloading and reloading process of FRP-confined concrete columns. This turning point is a crucial indicator for distinguishing whether there is a noticeable compressive effect between the concrete and the FRP jacket.

The CZM constitutive model proposed in this paper, compared to previous pure damage models, additionally considers plasticity and meticulously accounts for the friction effects between interfaces and potential fracture surfaces. As a result, the simulation results are closer to the experimental results. In order to better understand the internal mechanical behavior of FRP-confined concrete columns under cyclic loading, a series of parameter studies were conducted in this section. According to

Different from other classical fracture models, such as the CDP model [

The impact of the friction effect at the FRP-concrete interface was also investigated by calculating the model with

In previous literature [_{re} is an important parameter (in

Compared to the damage constitutive models proposed in the previous studies [

In this study, a modeling method for FRP-confined concrete was developed using zero-thickness cohesive elements. These cohesive elements were used to simulate the potential fracture surfaces of concrete and the FRP-concrete interface. The CZM constitutive models were proposed to characterize the mechanical behavior of the potential fracture surfaces and FRP-concrete interface, considering the damage relation, plasticity, and friction effect. Additionally, an anisotropic plastic constitutive model was established for the FRP composite jacket. The proposed FE model was validated by performing simulations on existing compressive cyclic loading tests for plain concrete and FRP-confined concrete. By comparing the simulation results with experimental data, the proposed model successfully replicated the mechanical response of both concrete and FRP-confined concrete. The simulated stress-strain hysteresis loops showed good agreement with the experimental results. Furthermore, parametric studies were conducted to investigate the internal failure mechanism of FRP-confined concrete under cyclic loading conditions. The findings of these studies can be summarized as follows:

(1) Internal friction in concrete plays a crucial role in the mechanical performance of FRP-confined concrete. It accounts for about half of its load-bearing capacity and also determines the energy dissipation, represented by the hysteresis loop area, during cyclic loading.

(2) The plasticity of FRP composite jackets has a significant impact on the energy dissipation of FRP-confined concrete during cyclic loading. If the plasticity of FRP is not taken into account, the confinement effect on concrete would be overestimated, resulting in increased internal compression and frictional energy dissipation.

(3) Without considering the plasticity of concrete, the load-bearing capacity of concrete is reduced due to the increased damage inside the concrete compared to the one considering plasticity.

(4) The shear performance of the FRP-concrete interface has minimal impact on the structure, while the friction and plasticity of the interface have little effect on the simulation results. This suggests that the main function of the FRP-concrete interface is to transmit normal compressive stress.

None.

This study was funded by the Natural Science Foundation of Fujian Province (2023J01938), the Scientific Research Startup Foundation of Fujian University of Technology (GY-Z21026).

The authors confirm contribution to the paper as follows: study conception and design: Wei Zhang, analysis and interpretation of results: Mingxu Zhang; draft manuscript preparation: Mingliang Wang. All authors reviewed the results and approved the final version of the manuscript.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare that they have no conflict of interest.