Abstract
Fiber-reinforced polymer (FRP) sheet bonding methods are used in practice as a way of strengthening reinforced concrete (RC) structural members under static and quasistatic loading. The applicability of RC members under impact loading has been investigated since 1990. Generally, carbon FRP (CFRP) sheets and aramid FRP (AFRP) sheets have been used in Japan as strengthening materials for FRP sheets in RC infrastructure. Although only one material is normally used for an AFRP sheet, three types of materials are used for a CFRP sheet: high strength, medium elasticity and high elasticity. Usually, a high-strength sheet is applied for strengthening RC members because it has the largest fracture strain of the three types, and medium- and high-elasticity sheets are used for steel members because their Young’s modulus values are more than twice those of steel members. In this work, static and drop-weight impact loading tests for flexurally strengthened RC beams with medium-elasticity bonding (Beam ME) were conducted to investigate the applicability of this sheet to flexurally strengthened RC beams. RC beams with high-strength (Beam HS) bonding sheets of similar axial stiffness to Beam ME and without the bonding FRP sheet (Beam N) were also tested to compare the load-carrying behavior of the RC beams. The results are as follows: Beams ME and HS fail by sheet rupturing and debonding, respectively, under static loading and impact loading; Beam ME can assure the calculated load-carrying capacity statically; however, this beam reaches the ultimate state under a lower impact energy than Beam HS does.
Keywords
Introduction
Recently, the steel-plate jacketing method, the concrete enlargement method, and the fiber-reinforced polymer (FRP) sheet bonding method have been applied to strengthen and/or upgrade existing reinforced concrete (RC) structures subjected to static and/or quasistatic loads. Specifically, in the case of the FRP sheet bonding method, its applicability to strengthened RC bridge piers subjected to collisions by vehicles and/or ships and RC infrastructures subjected to rock impact has been investigated because of the improved material properties of the FRP sheet, namely, its noncorrosive properties, high strength‒weight ratio, and better adjustability in situ.
There are two ways to strengthen RC structural members by applying the FRP sheet bonding method: (1) flexural strengthening of the members by bonding the sheet to the tension-side surface and (2) increasing the shear capacity of the members with winding and/or U-shaped bonding of the FRP strip at even intervals.
By focusing on the flexural strengthening method using an FRP sheet, the bonding effects of the FRP sheet/laminate on the impact resistance capacity of concrete beams were experimentally investigated by Eriki and Meier (1999), Tang and Saadatmanesh (2003, 2005), Kantar and Anil (2012), Kishi et al. (2020), Ye et al. (2020), and Zhang et al. (2023). Eriki and Meier (1999) conducted an impact test on RC beams by bonding a carbon FRP (CFRP) sheet to the upper and lower surfaces while freely dropping one end. Tang and Saadatmanesh (2003, 2005) conducted drop-weight impact loading tests on RC beams by bonding CFRP and/or aramid FRP (AFRP) laminates to the upper and lower surfaces. Kantar and Anil (2012) performed cyclic impact loading tests on plain concrete beams bonding a CFRP strip to the tension-side surface. These studies confirmed that the impact resistance capacity of the beams can be enhanced by bonding the sheet/laminate and/or strip to the tension-side surface. Kishi et al. (2020) experimentally reported that the impact resistance behavior, including FRP sheet debonding, of RC beams strengthened in flexure by bonding the sheet to the tension surface may be similar regardless of the material properties of the FRP sheet when the axial stiffness and tensile failure strain of the sheet are similar. Ye et al. (2020) conducted drop-weight impact loading tests for RC beams strengthened in flexure by bonding large-rupture-strain FRP (LRS-FRP) laminates, in which LRS-FRP has a large rupture strain that is greater than 5% and is recyclable and an environmentally friendly material. When end-anchored polyethylene naphthalene (PEN) FRPs are used as LRS-FRP, the maximum deflection and damage of the beams can be reduced. Zhang et al. (2023) conducted tests of drop-weight impact and subsequent quasi-static loading for flexural strengthened RC beams with CFRP sheets to investigate the residual load-carrying performance of the beams after impact loading. From the experiments, it is seen that the residual resistance of the beams can be significantly enhanced by bonding with the CFRP sheets.
However, since the relationships between the sheet volume and load-carrying capacity of RC beams, between the sheet volume and failure mode of RC beams, including sheet debonding/rupturing, and the applicability of each sheet material, have not been clarified, a strengthening design procedure for the FRP sheet bonding method has not yet been established.
In Japan, CFRP and AFRP sheets are generally used as strengthening materials for RC infrastructure. Even though one material is normally used for an AFRP sheet, three materials are used for a CFRP sheet: high-strength materials (tensile strength f f = 3.4 GPa, Young’s modulus E f = 245 GPa, and fracture strain ε uf = 1.39%); medium-elasticity materials (f f = 2.4 GPa, E f = 440 GPa, and ε uf = 0.545%); and high-elasticity materials (f f = 1.9 GPa, E f = 640 GPa, and ε uf = 0.3%) (Toray, 2025). Typically, a high-strength CFRP sheet is used to strengthen RC members because it has the largest fracture strain of ε uf = 1.39% of the three materials, whereas medium- and high-elasticity materials are used to strengthen steel members because of their easy increase in axial stiffness of the sheet without increasing the number of piles. Although the fracture strains are less than 0.6%, the Young’s modulus values are more than twice those of the steel members. Although CFRP sheets might be applicable for strengthening RC members, their applicability has not been investigated.
Therefore, in this work, to investigate the applicability of medium- and high-elasticity CFRP sheets to strengthen RC beams in flexure, static and drop-weight impact loading tests were conducted for flexurally strengthened RC beams by bonding a CFRP sheet of medium elasticity placed on the tension-side surface. RC beams strengthened with and without a high-strength CFRP sheet were also tested to compare the strengthening effects of the sheets. Although the RC beams were strengthened, usage of high-elasticity CFRP sheets should be tested, and medium-elasticity CFRP sheets were only used, excluding high-elasticity CFRP sheets. Because the dynamic response characteristics of the RC beams strengthened using these medium- and high-elasticity sheets may be like each other because the fracture strain is less than 0.6 %. The drop-weight impact loading tests were performed using a 300 kg steel weight and a new RC beam for each test while varying the drop height of the weight (hereafter referred to as the drop height) H up to the beam reaching the ultimate state.
Experimental overview
Test specimens
Figure 1 shows the dimensions, rebar arrangement, and strengthened area when a CFRP sheet was used for the tested RC beams with a rectangular cross section. The dimensions (width × height × clear span length) of the beams were 200 × 250 × 3000 mm. Two D19 axial rebars were cast in the upper and lower fibers and were welded to the 9 mm thick steel plates at the ends of the beam to reduce the anchoring length. The D10 rebars for the stirrup were placed 100 mm apart. A 200 mm wide CFRP sheet was bonded to the tension-side surface up to 50 mm from the support point (see Figure 1) because when a crack occurs at the lower fiber of the beam at or near the sheet end, concrete cover delamination and/or sheet end interfacial debonding may occur without any anchorage system (Smith and Teng 2002). Therefore, the sheet should be bonded as close to the support point as possible to decrease the tensile stress of the lower-fiber concrete as much as possible and not disturb the support condition of the beam. The foil strain gauges were glued on the sheet in the axial direction to measure the strain distribution of the sheet during the experiment. Dimensions and rebar arrangement of the RC beams.
In addition, the sheet was bonded to the tension-side surface of the beams via the following process: (1) the surface was grit-blasted to a depth of approximately 1 mm; (2) an epoxy resin-type primer was applied on the blasted surface, and touch drying was performed for the primer; and (3) the CFRP sheet was bonded by applying an epoxy-type impregnating resin while defoaming. The bonding resin was hardened, with a curing time of approximately 1 week.
List of specimens.
The calculated static flexural load-carrying capacities P usc for both beams were estimated via a multilayered method (Kaklauskas et al., 1999) with consideration of the stress‒strain relationship for each material following the Japan Concrete Standard (JSCE 2018) and the assumption of a plane section for the cross-section during bending, perfect bonding between the concrete and reinforcements (rebar and CFRP sheet), and the ultimate compressive strain of the concrete ε cu = 0.35%. The estimation procedure using this method can be found in Kishi et al. (2020). On the basis of these numerical estimations, although Beam HS numerically reached the ultimate state in the concrete compression failure mode, Beam ME failed by sheet rupturing. The calculated static shear load-carrying capacity V usc for each beam was estimated in accordance with the standard (JSCE 2018). In this table, since the shear‒flexural load-carrying capacity ratio V usc /P usc for each beam was greater than 1, all the beams considered in this study would usually reach the ultimate state in the flexural failure mode statically.
Static loading test
Figure 2 shows the setup for a static loading test for strengthened RC beams with a CFRP sheet. The static load was surcharged by using a hydraulic jack with a capacity of 500 kN and placing a loading jig 100 mm wide in the span direction. In the case of Beam N, since the surcharged load gradually increased after rebar yielding because of the plastic hardening effect of the rebar, the load was increased to a deflection of approximately 80 mm, which corresponds to approximately 2.5% of the clear span length, whereas for Beams ME and HS, the load was increased until the beams reached the ultimate state with the sheet debonded and/or ruptured. Experimental setup for static loading.
Drop-weight impact loading test
Figure 3 shows the drop-weight impact loading apparatus used in this study. The impact load was surcharged by freely dropping a 300 kg steel weight with a diameter of 200 mm and a 2 mm high spherical nose from the predetermined height. The drop height was increased step by step, i.e., H = 1, 2, and 2.5 m, for each unused beam up to the beam reaching the ultimate state with sheet debonding and/or rupturing. Although Beam ME failed because of sheet rupturing at the drop height H = 2 m, as described later, the beam was impacted at the drop height H = 2.5 m for comparison with the experimental results for Beam HS, which failed at the same drop height H = 2.5 m. Beams N were impacted at the drop heights H = 1 and 2.5 m for comparison with the reference test results. In addition, since the support points of the beams can rotate, the supports have to be pinned, and any rebound or horizontal movement is restrained by tightening with steel cross beams. Experimental setup for drop-weight impact loading.
Measured items at impact loading
In this work, the impact force P, total reaction force (hereafter referred to as the reaction force) R, midspan deflection (hereafter referred to as the deflection) δ, and axial strain (hereafter referred to as the strain) distributions were measured at impact loading for the beams. The impact force P and reaction force R were measured by using load cells for impact loading, and the deflection δ was measured by a laser-type linear variable differential transformer (LVDT).
Static loading test results
Load‒deflection curves
Figure 4 shows comparisons of the static load‒deflection curves for the three beams, ME, HS, and N, obtained from the experimental results and numerical results via the multilayered method (Kakulauskas et al., 1999) together with Mohr’s integral technique (Kishi et al., 2020). In addition, the main rebar yield load (hereafter referred to as the rebar yield load), the maximum load, and the deflection at that load are listed in Table 2. In this table, the maximum load for Beam N was evaluated when the deflection reached 40 mm because Beam HS reached the ultimate state at a deflection of 37.5 mm and Beam ME at a smaller value. The ratio for each value of Beam N is also indicated in parentheses. Static load‒deflection curves. Experimental results at static loading. Note: The parentheses indicate the ratios with respect to the corresponding values of Beam N; and the maximum load for Beam N is the value at deflection of 40 mm.
This figure shows that Beams ME and HS failed because the sheets ruptured and debonded, respectively. The sheet rupturing occurred for Beam ME possibly because the tensile fracture strain of the bonded CFRP sheet of medium elasticity was less than 0.6%. A comparison of the experimental and numerical load-carrying capacities of Beam ME revealed that the experimental results agree with the calculated capacity, although the sheet ruptured. In the case of Beam HS, the experimental results disagree with the calculated results, and after rebar yielding, the difference between the experimental and calculated results increased with an increase of the deflection. From these results, it is revealed that the CFRP sheet may gradually debond after rebar yielded. Therefore, the static load-carrying capacity of flexurally strengthened RC beams bonded with a CFRP sheet of medium elasticity (Beam ME) can be evaluated on the safe side via the multilayered method. However, the performance of Beam HS with bonding of the high-strength CFRP sheet cannot be evaluated properly via the calculated results.
In the table, the rebar yield loads of Beams ME and HS improved by more than 60% and 50%, respectively, and the maximum loads increased by more than 90% because of flexural strengthening of the RC beams with the bonding CFRP sheet. The maximum deflection of Beam ME can be restrained by approximately 1% of the clear span length.
Crack patterns after static loading
Figure 5 shows the crack patterns of the RC beams after static loading. This figure shows that in the case of Beam N, the flexural cracks began from the lower concrete cover near the loading area and developed toward the loading point, after which the loading area reached the ultimate state in the compression failure mode. Among the strengthened RC beams with the CFRP sheet, Beams ME and HS had flexural cracks distributed largely over the entire span, and the diagonal cracks did not develop. Moreover, the sheet ruptured near the loading area of Beam ME, and sheet debonding progressed toward the left-hand side of the support point of Beam HS. Crack patterns after static loading: (a) Beam N, (b) Beam ME, and (c) Beam HS.
Drop-weight impact loading test results
Dynamic response waves
Figure 6 shows comparisons of the dynamic response waves: the impact force P, the reaction force R, and the deflection δ for all the tested beams. In this figure, each wave was drawn with the origin as the time when the steel weight first impacted the upper surface of the beam. The reaction force in the upward direction was defined as positive, similar to that at static loading. Additionally, at time t from the beginning of impact (hereafter referred to as time t), the sheet debonded or ruptured, as indicated in Figure 6(c). Time records of the dynamic responses: (a) impact load P, (b) reaction force R, and (c) deflection δ.
Figure 6(a) shows comparisons of the impact force time records over durations of 50 ms and 5 ms after impact. This figure shows that the waves were composed of a primary impact force and a subsequent force plateau, which may belong to the type III impact force profile proposed by Li et al. (2020). Since the primary impact force wave had a similar shape distribution for all the beams with same drop height H, the maximum impact force may depend on the material properties of the impacted concrete (Kishi et al., 2020). The wave had a duration of approximately 1 ms for all drop heights H, and its maximum amplitude tended to increase with H.
Focusing on the force plateau, when the drop height H = 1 m, in which both strengthened RC beams did not reach the ultimate state, the waves had similar shapes, even though the material properties of the sheets were different. However, in the case of the unstrengthened Beam N with a CFRP sheet, the duration of the wave was extended by approximately 10 ms compared with those of the strengthened beams. At drop heights H = 2 and 2.5 m, the waves of Beam ME had smaller amplitudes and longer durations than those of Beam HS because sheet rupturing caused Beam ME to fail (see Figure 6(c)) prior to the impact force wave shifting to the force plateau. The difference in the duration of the wave between Beams ME and HS tended to increase with drop height H, possibly because of damage to Beam ME. Comparing the plateau wave between Beams ME and N at a drop height H = 2.5 m, although the amplitude for Beam ME was larger than that for Beam N, the durations for both beams were similar.
Figure 6(b) shows comparisons of the reaction force time records for 150 ms and 50 ms from the beginning of impact. This figure shows that the negative reaction forces were exerted at the beginning of impact regardless of the presence of the CFRP sheet, the material properties of the CFRP sheet and the magnitude of the drop height H. This type of behavior of the reaction force was reported by Cotsovos (2010), Pham et al. (2017), Wang et al. (2021), and Kishi et al. (2012, 2020, 2022). This behavior may be due to the tendency of the area near the support points to rebound and move in an upward direction at the beginning of impact. The reaction force waves were composed mainly of the reaction force wave part in the loading stage and the damped free vibration part in the unloaded stage.
A comparison of the behavior of the waves of three beams at a drop height H = 1 m revealed that (1) the positive main reaction force part has similar characteristics to those of the abovementioned force plateau of the impact force wave; the waves of Beams ME and HS behaved similarly, and the wave of Beam N was prolonged compared with those of the strengthened RC beams; (2) the vibration period in the damped free vibration state of Beam ME was shorter than that of Beam HS because the axial stiffness of the sheet of the former was slightly greater than that of the latter, as mentioned above; and (3) the period for Beam N was a few ms longer than that for the strengthened beams because of the absence of the CFRP sheet. In addition, the negative reaction force can be measured by taking zero balance for the amplifier units of the load cells, including the load cells with the steel cross beams shown in Figure 3, after the RC beams are tightened. The reaction force waves in the damped free vibration state were distributed in the region of approximately −40 kN for all the beams considered in this study. This distribution may be due to the zero level of the load cells shifting to the negative side because the tightening force for the cross beams through the bolts may be released when the beams are impacted.
When the drop height is H = 2 m, the sheet of Beam ME ruptured, causing the wave of this beam to be more prolonged than that of Beam HS. When H = 2.5 m, although Beam HS failed in the sheet debonding mode, the duration of the wave was shorter than that of Beam N, and only Beam ME failed because of sheet rupturing. Because the sheet for Beam HS debonded after this beam reached the maximum deflection, as described later, the strengthening effect of the sheet may be greater than that of Beam ME.
Figure 6(c) shows comparisons of the deflection time records between two and/or three beams for 150 ms from the beginning of impact for each drop height H. This figure shows that the waves were composed of a sinusoidal half wave during impact loading and that the damped free vibration state had a residual deflection after unloading, and the duration of the sinusoidal half wave corresponded to those of the impact force and the reaction force waves.
A comparison of waves in the case of a drop height of H = 1 m revealed that since the input impact energy was lower and the strengthened RC beams did not reach the ultimate state, the strengthened RC beams had similar maximum and residual deflections because both beams had similar axial stiffnesses of the CFRP sheets. Additionally, it is confirmed that the maximum and residual deflections can be decreased by bonding the CFRP sheet to the tension-side surface of the beams compared with those of Beam N.
When H = 2 m, although Beam HS was still in a structurally healthy state, Beam ME reached the ultimate state in the sheet rupturing mode. Therefore, the maximum and residual deflections of Beam ME were larger than those of Beam HS. Additionally, the damped free vibration period of Beam ME was similar to that of Beam N at a drop height H = 1 m. When the impact force and deflection time histories were used, the absorbed energies for both the beam ME and the HS up to time t = 9 ms when the beam ME failed were estimated as 2.64 and 2.19 kJ, which were 46% and 38%, respectively, for the total input impact energy. At this time, since these midspan axial strains of the sheet reached 0.59 and 0.67%, respectively, the beam HS was still in a healthy state, but the beam ME failed, as mentioned above, because the fracture strain of the sheet for the Beam ME was a nominal value of ε uf = 0.545%.
When H = 2.5 m, Beam ME failed, with the sheet rupturing earlier, and Beam HS failed, with the sheet debonding occurring after the maximum deflection was reached. The maximum and residual deflections of Beam ME were approximately 20 mm larger than those of Beam HS. This difference is obtained possibly because the sheet for the Beam ME ruptured during the early stage before its strengthening effect was sufficient. However, the deflections of Beam ME were smaller than those of Beam N because the strengthening effect of the sheet for Beam ME was more or less apparent.
Temporal transition of the axial strain distribution of the CFRP sheet at H = 2.5 m
Figure 7 shows comparisons of the temporal transitions of the strain distributions of the CFRP sheets for Beams ME and HS at drop height H = 2.5 m. This figure shows that the strain distributions of both beams were similar up to time t = 8.3 ms, when the sheet for Beam ME tended to rupture; up to time t = 2.5 ms, the positive strains were distributed near the loading area, the negative strains were distributed in the outer areas, such as a beam fixed at both ends with a short span length, the positive strain area tended to expand toward the support points and the span length tended to increase; at time t = 5 ms, the strain distributions corresponded to those of a simply supported beam, and the maximum strains were less than 0.5%; and at time t = 8.3 ms, the strains near the loading area gradually increased by approximately 0.75% even though the fracture strain of Beam ME had a nominal value of ε
uf
= 0.545%. Temporal transition of the CFRP sheet strain distributions at drop height H = 2.5 m.
At time t = 8.4–10 ms, since the strains near the left-hand side edge of the loading area of Beam ME tended to decrease toward zero over time, the sheet ruptured near this area and lost its strengthening effect throughout the span. In contrast, the strains in the sheet for Beam HS gradually increased by more than 0.75% in the midspan area to form a dome-shaped distribution, and the main rebar in the area may be in the plastic state.
At time t = 15–23 ms, even though the strains of the sheet for Beam HS did not reach 1%, the strain distribution in the midspan area was flattened, and the sheet tended to debond toward the right-hand side of the support point. The strengthening effect of the sheet was lost in the right half of the beam at time t = 23 ms. After time t = 23 ms, the strengthening effect of the sheet for Beam HS was almost completely lost throughout the beam span.
Crack patterns of the beams after impact loading
Figure 8 shows comparisons of crack patterns of all the beams considered in this study after impact loading. This figure shows that flexural cracks developed from the lower and upper fibers of the beams throughout the span regardless of the bonding and material properties of the CFRP sheet and the magnitude of the drop height H, which differed from those after static loading, as shown in Figure 5 (Hao et al., 2021; Kishi et al., 2012, 2020). This behavior may be why the flexural waves, which have the characteristics of a fixed beam at both ends with a short span length, travel toward the support points, as mentioned above. Additionally, diagonal cracks occurred near the loading area of all the beams considered in this study. However, under static loading, these results were not observed, as shown in Figure 5. Crack patterns after impact loading: (a) Beam N, (b) Beam ME, and (c) Beam HS.
The angles at the tips of the diagonal cracks of Beam HS were smaller than those of Beam ME, and correspondingly the former cracked region was wider than the latter. Since diagonal cracks essentially developed in the axial rebar yield region, the rebar yield region of the Beam HS was wider than that of the Beam ME. This can be identified from the results shown in Figure 7: the rebar yield region for the Beam HS tended to expand, resulting in the formation of a dome-shaped distribution of axial strain of the sheet, whereas that for the Beam ME was limited to the loading area because of sheet rupture. Therefore, Beam HS might fail by sheet debonding due to the peeling action of the tip of the diagonal crack and Beam ME by sheet rupturing because the beam tends to fold near the loading area.
Since the beam HS reaches the ultimate state in the sheet debonding mode, the impact resistance capacity of the RC beams flexurally strengthened with the high-strength CFRP sheet may be more enhanced because the sheet debonding is able to be restrained. However, when the medium-elasticity sheet is used, the capacity may not be effectively enhanced because of the brittle material properties of the sheet and the sheet rupturing before reaching maximum deflection with a fracture strain of less than 0.6 %.
Conclusions
In this work, to investigate the applicability of a CFRP sheet of medium elasticity to flexurally strengthened RC beams subjected to static and impact loads, static and 300 kg drop-weight impact loading tests for RC beams with bonding of the sheet to the tension-side surface (Beam ME) were conducted. RC beams strengthened by bonding with high-strength CFRP sheets (Beam HS) and without bonding a sheet (Beam N) were also investigated to compare the load-carrying behavior of the beams. The results obtained from this study are as follows:
The static loading test results are as follows: (1) Beam HS reached the ultimate state in the sheet debonding mode, with Beam ME in the sheet rupturing mode because the fracture strain of the sheet is less than 0.6%. (2) Since Beam ME ensures the calculated ultimate load-carrying capacity, it may be possible to conduct a flexural strengthening design using a CFRP sheet of medium elasticity for RC beams subjected to static loading on the safe side. However, since the sheet for Beam HS tends to gradually debond with increasing deflection after rebar yielding, the beam cannot confirm the calculated ultimate capacity. (3) When the CFRP sheet of medium elasticity is bonded to the tension-side surface, the flexural capacity of the beam can be enhanced by approximately twice that of Beam N, and the maximum deflection can be restrained to approximately 1% of the span length. (4) The strengthened RC beams with CFRP sheets had flexural cracks distributed over the entire span and the diagonal cracks did not develop.
The drop-weight impact loading test provided the following results: (1) Flexurally strengthened RC beams with a bonded CFRP sheet in a structurally healthy state had similar impact resistance behavior regardless of the material properties of the CFRP sheet having an equivalent axial stiffness. (2) Flexural cracks developed from the lower and upper fibers of the RC beams throughout the span, and diagonal cracks occurred near the loading area regardless of the bonding and material properties of the CFRP sheet and the magnitude of the drop height H. (3) Beam ME reached the ultimate state in the sheet rupturing mode and Beam HS in the sheet debonding mode similar to that under static loading. The sheet for the beam ME ruptured before reaching maximum deflection. (4) Since Beam ME reached the ultimate state under a lower impact energy than Beam HS did, the medium elasticity CFRP sheet should have a smaller strengthening effect than a high-strength sheet has because the medium elasticity type CFRP sheet has lower fracture strain less than 0.6% and than the high-strength type sheet has. (5) Therefore, the medium- and high-elasticity CFRP sheets may be unpreferable materials compared with the high-strength sheet for flexurally strengthening RC structures under impact loading.
Footnotes
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.