Geometric quality evaluation of three-dimensional printable concrete using computational fluid dynamics

Abstract

The importance of geometrical control of three dimensional (3D) printable concrete without the support of formwork is widely acknowledged. In this study, a numerical model based on computational fluid dynamics was developed to evaluate the geometrical quality of a 3D printed layer. The numerical results were compared, using image analysis, with physical cross-sectional sawn samples. The influence of printing parameters (printing speed, nozzle height, and nozzle diameter) and the rheological behavior of printed materials (yield stress), on the geometrical quality of one printed layer was investigated. In addition, the yield zone of the printed layer was analyzed, giving insights on the critical factors for geometrical control in 3D concrete printing. Results indicated that the developed model can precisely describe the extrusion process, as well as the cross-sectional quality.

Graphical abstract

Keywords

digital fabrication / 3D concrete printing / geometric quality / computational fluid dynamics / printing parameters / yield stress

1 Introduction

Three dimensional concrete printing (3DCP) is a technique used in construction to produce concrete structures by adding layers of material through 3D printing technology [1–3]. The printing process starts with a digital model of the aimed structure, which is then used to generate instructions for the layer-by-layer deposition of concrete materials, with the option to include reinforcement where required by the design specifications [4,5]. This method allows for the production of intricate designs and shapes that would be challenging or impossible to achieve using conventional mold casting [6,7]. Other advantages over mold casting include faster construction speed, lower labor consumption, and reduced costs [8–10].

It is essential to ensure that material properties in 3DCP are consistent, to prevent structural defects and reduced durability caused by variations in material composition and to maintain proper bonding between layers to avoid delamination and cracking [11,12]. 3DCP also poses challenges such as preserving geometric accuracy throughout the process and finding a balance between printing speed and efficiency while maintaining quality, since slow printing speeds can lead to increased production costs while faster speeds may introduce imperfections and affect the performance of structures [13].

Therefore, developing materials with appropriate flowability, extrudability, and buildability is a significant requirement for 3DCP. This challenge has been the focus of recent research efforts in the field. Flowability pertains to the concrete mixture’s capacity to flow. Extrudability refers to the ability of fresh concrete to be extruded through the nozzle of 3D printer with minimal energy needed [14]. Buildability is the ability of the concrete to hold its shape and form during the printing process without the support of formwork, and is crucial in meeting the design specifications of the final structure [15,16]. High buildability makes it possible to control the geometrical quality of each printed layer, and is strongly related to further material properties such as yield stress, viscosity, and thixotropy [17–19].

Changes in process parameters can significantly affect the morphology of the printed object. Different process parameters can result in a concave or convex shape of the printed body cross-section, or even cause violent lateral deformation of the material. In addition, during the printing process, the high extrusion stress applied by the printing nozzle on the material may cause larger deformation and weak interlayer bonds. Therefore, the process parameters need to be evaluated based on their impact on the surface traction distribution of the printed material, which refers to how forces are distributed across the surface. Unfortunately, the unpredictable nature of the printing process and the material waste associated with trial-and-error experiments make it necessary to use numerical tools to select proper process parameters and material properties for 3DCP. However, obtaining the desired layer height and width during printing is a complex issue due to the interaction of various printing factors. For instance, changing the printing height leads to changes in the layer height of the material, while the printed layer width changes without altering the printing speed [20].

Numerical simulations have emerged as an effective method for gaining insights into the characteristics of freshly printed concrete [21–23]. Several computational strategies have been employed in this context, with the finite element method being a prominent choice. This approach involves modeling both the extrusion process and the behavior of the printed material, including various failure patterns [24]. Notably, Vantyghem et al. [25] have developed a Grasshopper plug-in for conducting voxel-based numerical simulations of 3D concrete printing. Additionally, the discrete element method has been utilized to simulate the processes of concrete extrusion and deposition [26]. A novel simulation model for concrete flow has been introduced, which represents fresh concrete as a collection of particles consisting of rigid, spherical grains representing aggregates, encased within concentric layers that symbolize mortar or cement paste [27]. Furthermore, the lattice model, incorporating geometric nonlinearity, has been employed to mimic elastic buckling phenomena in 3D concrete printing [28]. Computational fluid dynamics (CFD) presents an alternative approach to simulating the extrusion process [29–31]. It is particularly valuable because it has been widely applied to model the mixing and pumping stages of fresh concrete [32,33]. In a recent study, Comminal et al. [17,34–36] employed CFD to predict the cross-sectional shape of a 3D-printed layer through virtual printing simulations. They compared various constitutive laws and discussed plastic deformation resulting from the self-weight of 3D-printed concrete structures [37]. Subsequently, Spangenberg et al. [38,39] utilized an elastic-viscous-plastic constitutive model to simulate the flow behavior of 3D-printed layers and to predict regions where the mortar yielding takes place during printing. In addition, Liu et al. [40,41] employed a support vector machine to study various factors in the flow mechanism and the deformation of the printed filament. He et al. [42] investigated the influence of interlayer notch and shear stress on the interlayer strength of a 3D printed filament. Unfortunately, limited existing studies have investigated the influence of various printing parameters and rheological properties on geometric profiles and plastic-yielded regions. Moreover, limited analysis of the stress state of 3D printed material, which can reveal the mechanism of deformation during 3DCP, has been carried out.

This paper aims to systematically investigate the effect of printing parameters and rheological properties on the geometric profiles and plastic-yielded regions in 3DCP, incorporating a stress state analysis based on CFD. The rheological properties of 3D printable materials were obtained based on flow curve measurements. Graphic recognition techniques were adopted for the analysis of cross-sections of one printed layer, providing an experimental reference for validation. The effect of different process parameters including printing speed (20, 30, 40 mm/s), layer height (10, 15, 20 mm), and nozzle diameter (15, 20, 25 mm) on the geometrical quality of one printed layer was analyzed. In addition, the paper discusses the effect of yield stress of 3D printed material and analyzes the shear stress and strain rate of the material immediately after extrusion.

2 Experimental program

2.1 Materials and sample preparation

P.O 52.5 Portland cement (Tab.1) and quartz sand (0–2 mm) were used. Admixtures included hydroxypropyl methyl cellulose ether (0.15% of mass of cement) and polycarboxylic acid (0.1% of mass of cement). The water-cement ratio was 0.35 and the sand-to-cement ratio was 1. The material was prepared according to the following procedure. First, quartz sand and other dry materials were mixed at 60 r/min for 60 s. Afterwards, polycarboxylic acid was dissolved in water. Then, water with polycarboxylic acid was added to dry materials and mixed at 60 r/min for 120 s. After scraping and resting for 60 s, the materials were continuously mixed for 240 s. The total mixing period lasted 480 s.

2.2 Rheological measurements

The eBT-V rheometer (Schleibinger) equipped with a 6-blade vane was used in this study. The maximum rotational speed of the rheometer was 40 r/min. The diameter and height of the blade were both 103 mm. The inner diameter and height of the container were 244 and 290 mm, respectively. To conduct the measurement, the sample was placed into the measuring container and the instrument holder with the mounted device was inserted. As the Vane probe rotated, the torque exerted on it was recorded. There were three main stages during flow curve measurements. The first stage was the pre-shear stage, to reach a reference state of the tested material. The second stage was the flow curve measuring stage, and the third stage was the evaluation of the rheological behavior of the material. The pre-shearing lasted for 10 s, with a rotational speed increasing gradually from 0 to 35 r/min. After reaching the maximum speed, continuous shear was maintained for 5 s. The second stage involved a total of 6 steps, with the maximum speed set to 35 r/min and the minimum speed set to 2 r/min. At each step, the rotational speed decreased gradually, with a measurement interval of 5 s. As speed and torque could fluctuate during the transition period of speed change (usually the first 1.5 of 5 s), only data points from the last 3.5 s of each interval were collected. Approximately 50 stable data points were collected for each step, and any unstable data points caused by external factors were excluded. In the third stage, the rotational speed was increased from 0 to 35 r/min within 10 s, and the torque value was recorded and compared to the torque value obtained during the second testing period at the same speed, for the evaluation of the segregation of the tested material. The testing protocol and one example of the torque evolution are shown in Fig.1 (a) and 1(b), respectively.

During the pumping and extrusion process, the material exhibited high viscosity and low Reynolds number, due to laminar flow throughout the whole 3DCP process. The Herschel-Bulkley model was utilized, as expressed:

(1)\tau ={\tau }_0+k{\dot{\gamma }}^n,

where \tau denotes the shear stress, {\tau }_0 is the yield stress, \dot{\gamma } is the shear rate, k is the consistency index, and n is the power index.

Flow curve measurements were conducted twice. The obtained values for the yield stress, consistency index, and power index were 405.7, 74.07, and 0.81, respectively. Understanding time-dependent behavior was of paramount importance in the context of 3DCP. In this study, we accounted for the time-dependent behavior by assigning different yield stress values to the printed filament based on previous studies [16,43]. In addition, the critical shear rate was set at a small value of 0.1 s⁻¹, following the study carried out by Mollah et al. [35].

2.3 three dimensional printing tests

A gantry 3D printer with a maximum size of 2 m (in length, width, and height) was utilized. The gantry 3D printer had two main components, the printing part and the mechanical part. The printer part included the control system, print head, and stepping device, while the mechanical part comprised the overall frame, printing platform, and other related elements. The programmable logical controller (PLC) governed the overall device stepping. With the servo motor’s accuracy of 0.01mm, the single-axis stepping speed ranged between 0 and 50 mm/s, and it enabled three-axis linkage. The printer was equipped with a printhead that was compatible with the largest particle size of the printing material (2 mm). Circular printheads with different diameters were selected.

To validate the model, single paths with different printing parameters were printed (Fig.2). The design-to-production 3DCP framework included a customized algorithm developed in Rhino/Grasshopper. The algorithm converted toolpath designs into G-code files that included crucial information, such as point coordinates, orientation vectors, and nozzle travel speeds, necessary for the end-effectors to execute the designated path.

2.4 Image analysis

The geometry of the cross-sections of printed layers was processed using image analysis. The first step involved calibrating the filming device matrix, followed by contour detection using a custom image processing script that combined spatial filtering and image binarization. The detected contours were then denoised and smoothed before being positioned in the coordinate system and compared to simulated experimental results. Additionally, the extracted layer height, layer width, and cross-sectional area were automatically calculated based on the identified contours. After that, the data was calibrated to extract the coordinates of each corner point in the image. This was done by taking photographs of the calibration matrix board from different angles using the filming equipment and simulating the image information acquisition conditions using the calibration tool library in MATLAB, as illustrated in Fig.3.

The next step involved further binarization of the image [44]. This entailed converting the grayscale image into a binary image by assigning a value of 1 (white) to all pixels in the input image that had a brightness greater than a threshold value while assigning a value of 0 (black) to all other pixels.

Once the binary image was obtained, the object’s outline was tracked by identifying nonzero pixels as objects and zero-valued pixels as the background. The starting point on the object boundary and the initial search direction for the next object pixel was specified. The row and column coordinates of the region boundary pixels were then saved, and a smoother cross-sectional profile with more uniform profile data points was obtained (Fig.4).

3 Numerical model

3.1 Governing equations

The fundamental relevant laws mainly include the conservation of mass and the conservation of momentum. The conservation of mass can be written as:

(2)\mathrm{\nabla }\cdot \mathit{u}=0,

where \mathit{u} indicates the velocity vector field.

The conservation of momentum is expressed as follows:

(3)\rho \left(\frac{\mathrm{\partial }\mathit{u}}{\mathrm{\partial }t}+\mathit{u}\cdot \mathrm{\nabla }\mathit{u}\right)=-\mathrm{\nabla }p+\eta {\mathrm{\nabla }}^2\mathit{u}+\rho \mathit{g},

where \rho is the density of fluid, p is the pressure, \eta is the plastic viscosity of the fluid, g is the gravitational field strength vector, and t is time. The density was set constantly as 2100 kg/m³, and the rheological parameters were measured as described in Subsection 2.2. More details are summarized in Tab.2.

3.2 Simulation framework

To ensure better convergence, the fresh concrete was modeled as an incompressible fluid and the walls of the printing nozzle were set as slip-free interfaces in the whole computational domain. In addition, temperature variation was not taken into account. The computational fluid domain of the model consisted of the printing nozzle, the planar component surface, the printing path, and the corresponding region (Fig.5). The printing nozzle was cylindrical, with an inner diameter of 20 mm and a wall thickness of 2 mm. The length, width, and height of the planar component surface measured 350, 80, and 50 mm, respectively. The printing path was established using Rhino/Grasshopper software and included in the computational domain.

For grid settings, a tetrahedral grid was used for the metal solid wall of the print nozzle, while a hexahedral grid was used for the computational fluid domain, with appropriate grid refinement in the nozzle region. The grid resolution in the fluid region was set to 1, resulting in a total of 496767 cells and 90017 nodes in the vertical grid spacing (Fig.6).

Upon importing the mesh model into Fluent, no-slip boundary conditions were applied, due to the particle size used in the material being closely matched to the roughness of the wall surface. Additionally, due to volume conservation, the volume of the extrudate had to be identical to the volume of the printed material, as schematically indicated in Fig.7. The cross-sectional area was determined by the velocity ratio S_R=V/U, which was the ratio of printing speed (V) to material extrusion flux (U). The material extrusion volume flux could be calculated using the following equation:

(4)\frac{1}{4}\text{π}{D}^{2}U=AV,

where U is the material extrusion flux (mm/s), D is the nozzle diameter (mm), A is the cross-sectional area of one printed layer (mm²), and V is the printing speed (mm/s). It should be noted that the material extrusion flux may not be constant during the whole printing process. Thus, the actual extrusion flux was calculated based on the cross-sections of the sawn samples.

Other parameters in Fig.7 include the layer height H_{\mathrm{L}} (defined as the height at the middle of the cross-section), the layer width W_{\mathrm{L}} (defined as the maximum width of the extruded layer), and the nozzle height H_{\mathrm{N}} (defined as the distance between the nozzle outlet and the building plate).

The boundary conditions are shown in Fig.6(b). The computational domain had continuous boundary conditions set on its lateral sides, allowing for the unrestricted flow of the material within. Once the boundary conditions were established, the SIMPLE solution algorithm initialized the flow field, with local initialization at the printing nozzle for calculation purposes. Real-time monitoring ensured the convergence of the calculation, with particular attention paid to changes in pressure and flow velocity within the domain’s field.

When information about the behavior of mortar slip inside the nozzle was unavailable, a no-slip boundary condition was applied to all solid surfaces, including the nozzle wall and build surface. This choice was justified by the amplitude of roughness of the layered surface of the nozzle, which was similar in size to the particle size of the sand. The remaining boundaries of the computational domain had continuous boundary conditions, allowing materials to exit the boundary freely during the simulation.

4 Results and discussion

4.1 Model validation

Fig.8 presents a visual comparison of the cross-sections of printed layers obtained from 3D printing experiments and numerical simulation. It is shown that the model calculation results align with the actual cross-sections from experiments, demonstrating that the numerical model can accurately represent 3DCP prints. In particular, for the cases with a nozzle height (H_N) of 15 mm, the overall cross-sectional area error is merely 4%, with less than 1% error for both height and width.

Results showed that increasing the printing speed resulted in the print nozzle dragging the extruded material, leading to smaller cross-sectional layer width. Conversely, decreasing the printing speed led to over-extrusion of the material, resulting in larger layer width. As the material flow rate remained constant, changing the printing speed would alter the layer height and layer width accordingly. In practical situations, it is easy to adapt the printing speed in real time to modify the cross-sectional shape of the printed layer. Even, a visualizing system can be equipped with a printing system to capture the geometry of the printed layer, thus adapting the flow rate and achieving real-time geometrical control of the printed layer [45].

Fig.9 and Fig.10 further provide quantitative comparison of the layer height and width variation pattern at nozzle heights of 5 and 15mm. The results further indicated that the experimental outcomes aligned with the numerical simulation results utilizing the H–B model. In addition, results showed that a lower velocity ratio S_{\mathrm{R}} (i.e., the ratio of printing speed V to material extrusion flux U), would lead to a greater layer height. In the case of using the nozzle with a height of 5 mm (Fig.9), the layer height amounted to around 12 mm as the velocity ratio S_{\mathrm{R}} was 0.4. When the velocity ratio S_{\mathrm{R}} slightly exceeded 1.2, the layer height remained similar to the nozzle height of 5 mm. Unlike what happened in the case where nozzle height was 5 mm, the change in the velocity ratio S_{\mathrm{R}} had limited influence on the layer height when increasing the nozzle height to 15 mm. This was due to less shear stress being applied to the extruded layer where the gap between the printing plate and the nozzle was large enough (e.g., 15 mm in the current study) [16,46]. Still, it should be noted that the filament’s cross-sectional shape remained constant when a balance between the flow rate of the material and the printing speed was reached, which is the case in the current study. However, when the process settings deviate from this norm, such as when the flow exceeds the printing speed, it leads to filament buckling [21,28]. Conversely, when a very low flow rate was set, filament tearing would occur [21].

4.2 Geometrical profile

Numerical simulations can aid in understanding the process parameter interactions in the printing process. This section explores the impact of process parameters on the single-layer printed component to estimate the magnitude of the effect of various processes on printing. To avoid the excessive overlap of the geometrical profiles, only partial results are presented for the geometrical profiles, while more detailed analysis can be found in the stress state analysis shown in Subsection 4.3.

4.2.1 Influence of nozzle height

Fig.11 illustrates the influence of the nozzle height on the cross-sectional shape. The nozzle diameter was set constant at 20 mm and the yield stress was set constant at 405.7 Pa. As the nozzle height rose, the height of the cross-section of the extruded layer also increased proportionally, which was consistent with real experimental observations. Furthermore, the top surface of the printed layer was flatter when using a lower nozzle height, while the surface of the printed layer using a higher nozzle height tended to be convex. Since the material flow rate remained constant, the width of the cross-section of the extruded layer decreased as the nozzle height increased. Therefore, to increase the layer height while keeping the layer width constant, one feasible strategy is to adjust of printing speed or the material extrusion speed.

4.2.2 Influence of nozzle diameter

To investigate the influence of nozzle diameter, the nozzle height was set constant at 10 mm and the yield stress was set constant at 405.7 Pa. As shown in Fig.12, the extrusion speed was adjusted to match the nozzle diameter, and the cross-section of the printed layer remained mostly unchanged, with minor variations toward a more rectangular or curved shape. Changing the nozzle diameter while keeping the extrusion speed constant resulted in changes to the width of the printed object. As compared to the results shown in the previous section where the nozzle height was adapted for different layer widths, the surface of the printed layer tended to be flatter when adapting the nozzle diameter, especially for those with greater layer height. When the diameter change was small and within the range that matched the extrusion speed change (such as reduction of the nozzle diameter from 25 to 20 mm), the layer height of the printed object was almost unaffected. However, if the change in diameter was larger (such as a reduction of the diameter further to 15 mm), the layer height was affected to some extent. This was because a larger radius required more material to be printed, and if the diameter was too large, there was not enough time to fill the space under the extrusion nozzle.

4.2.3 Influence of yield stress

The above sections focus on how process parameters (nozzle height, and nozzle diameter) affect shape during printing. The following discussion examines how changing only the yield stress affects form deformation during printing under identical process parameters. The nozzle height was set constant at 10 mm and the nozzle diameter was set constant at 20 mm. As pointed out by Liu et al. [40], it is mainly the material’s yield stress that contributes to the deformation of the printed filament. In the current study, Fig.13 indicates that modifying the yield stress did not significantly impact the cross-sectional changes in the print body while maintaining a constant extrusion flow rate. This could be due to only one layer being printed, so that the yield stress of the material is still able to support the geometrical profile, according to the individual strength-based stability of one layer [47]. Increasing the yield stress of the material is expected to require more energy consumption to maintain a constant discharge flow, such as the torque of the screw rod inside the extrusion nozzle, assuming that the material layer height and width remain unchanged. Consequently, altering the yield stress primarily impacts the shear stress distribution within the material during printing. Considering this, the yield stress can be adapted according to the maximum printing height of the element. In case a low element is printed, the fresh material with a low yield stress can be used to save energy, giving the precondition of high geometrical quality. There is no doubt that a high yield stress is beneficial for higher printing height [48–50], while the high yield stress can increase the possibility of crack formation in the printed filament and reduce interlayer bond strength during multi-layer printing [34].

4.3 Stress state analysis

This section presents a numerical simulation-based investigation of the shear stress distribution within the material during the 3DCP process. The primary focus was on the extrusion stress that occurred under the printing nozzle during material extrusion. This stress may cause excessive deformation of the substrate layer and can also affect the interlayer bond strength by influencing the material build-up. Therefore, it is essential to understand the unique properties of this force through numerical simulations to improve the printing process. As circular printed sections’ working conditions are complex, this section uses 3D model calculations to explain the stress-strain variations by intersecting 3D model sections.

4.3.1 Influence of nozzle height

Fig.14 illustrates the effect of nozzle height. The nozzle diameter was fixed at 20 mm, and the yield stress remained constant at 405.7 Pa. Fig.14(a) shows results of the extrusion of printed material around the printing nozzle at different nozzle heights under the given standard working parameters. The numerical simulation showed that a protrusion was formed in the direction of nozzle travel, which decreased as the printing height increased. However, if the printing height was too high, the protrusion resembled a steep slope, resulting in incomplete filling of the space below the nozzle or dragging. Furthermore, as the printing height decreased, the protrusion increased due to the accumulation of material in front of the printing nozzle. This protrusion affected the contact area between the layers during multi-layer stacking, which is crucial for printing circular bodies. The numerical simulations of different working conditions revealed that a higher printing height formed a more suitable protrusion for the material used in this study, resulting in a better printing effect and more favorable interlayer bonding in multilayer printing.

Fig.14(b) shows the effect of different printing heights on the surface traction of the material at the nozzle. Note that the surface traction was exported from the surface of the printed filament at the time interval when the nozzle moved to the central position of the computational domain. At smaller printing heights, the peak of the surface traction appeared on the travel side of the printing head due to mutual compression by the printing nozzle and the substrate. With the increase in printing height, the peak gradually became smaller and smoother, and the stress distribution changed, with the maximum peak appearing in a smoother position. The graph indicates that at the right printing height, the peak stress caused by extrusion pressure was about twice the gravitational stress, implying that the lower layer needs to withstand twice the gravitational stress localized in the printing nozzle during the printing process. Thus, it is essential to ensure that the lower layer has sufficient load-bearing capacity to withstand the upper material gravity and local pressure load requirements for successful layer stacking.

4.3.2 Influence of nozzle diameter

Fig.15 compares the effect of different printing nozzle diameters on the surface traction of the material. The nozzle height was maintained at a constant value of 10 mm, and the yield stress was kept at a constant value of 405.7 Pa. To keep the printing height scaled according to the diameter of the printing nozzle, the printing speed and material inlet flow rate were kept constant. It was speculated that the magnitude of the traction force would vary according to the width. However, it was observed that the peak value of the surface traction of the material under the printing nozzle was almost the same for different diameter variations, independent of the printing nozzle diameter. The change in diameter only affected the range of force on the material, with a wider range of action for larger diameters resulting in a wide-area stress distribution, and a more localized stress distribution for smaller diameters, with the surface traction acting more on the base or lower layer of the material. When the nozzle diameter exceeded a reasonable range of variation, the force below the nozzle appeared to decrease. The material surface traction changed more slowly, indicating that the material entered another flow state. This was because a large diameter results in a small material inlet flow, and the material is in a drag state during printing, with no extrusion protrusion in the direction of travel.

4.3.3 Influence of yield stress

The preceding discussion focused on process parameters, while the subsequent discussion examines a crucial material parameter, namely, yield stress. To study the effect of the yield stress of the extruded material, the nozzle maintained a constant height of 10 mm, and the nozzle diameter remained fixed at 20 mm. Fig.16 demonstrates that, as yield stress increased, the surface traction in the material at the printing nozzle increased in the direction of printing travel, owing to the need for greater energy and extrusion pressure to produce the printing. Furthermore, yield stress had a substantial impact on stress pattern, which became broader and flatter. The flow behavior of the material depended on both process and material parameters and their impacts on stress distribution.

To summarize, the impact of process and material parameters on the surface traction beneath the printing nozzle during 3D-printed concrete printing was examined. The substrate or the subsequent layer experiences localized pressure from the printing nozzle during printing, with the pressure values being several times larger than those caused by gravitational stress. Regarding process parameters, smaller printing heights and faster printing speeds generated higher local forces. The numerical simulation also indicated that smaller printed layers led to a lower degree of stress concentration, whereas changing the printing nozzle diameter could produce similar peak forces at a constant material inlet flow rate. Two states of material flow were identified: first, full compression, resulting in stress concentration and a more noticeable protrusion in the printing direction, and, secondly, the material tending to be dragging with a more diffuse stress distribution that showed a steep slope in the direction of printing travel and gentler local material stress trends.

4.4 Strain rate

The numerical simulation demonstrated the distribution of strain rate under default working parameters (Fig.17). It is shown that printing parameters (such as the yield stress of the printed material, the nozzle diameter, the printing speed, and the layer height) should be coordinated and consistent. As shown in Fig.17(b), the distribution indicated a significant increase in pressure beneath the nozzle, which could even be transferred to the printing substrate or the next layer. On the contrary, the increase in the layer height would decrease the pressure, resulting in reduced interlayer bond, see Fig.17(c). This highlighted the importance of using a material with appropriate yield stress during printing to prevent excessive lateral deformation and ensure the lower layer can withstand the transfer of this force. It was essential to ensure that the lower layer could withstand the upper material gravity and local pressure load requirements to ensure smooth layer stacking during the printing process.

To modify the layer height of a printed body, adjusting the printing height is the only available option. However, it’s important to ensure a constant width of the printed body by adjusting the inlet flow rate accordingly, as this is the most predictable method for achieving an appropriate layer width. Modifying the printing speed can negatively impact printing efficiency and lead to uneven surfaces due to excessive pressure on the material at the printing head. Alternatively, changing the printing head diameter can significantly alter both the printing height and width. Increasing the printing diameter results in a flatter upper surface and a printed cross-section that’s closer to rectangular, which is a more suitable approach for both single and multi-layer printing. Fig.18 illustrates the various deformation states observed for different combinations of working conditions. Nevertheless, it should be noted that the current study was limited to the effect of different process parameters on a single printed layer, while a multi-layer print needs to be targeted in future research. Some trials have been carried out by Spangenberg et al. [38] and Mollah et al. [35] using the elastic–viscoplastic constitutive law. An interesting research point is the effect of different printing parameters on the geometrical parameters of 3D printed filaments; the parameters can serve as a basis for optimizing the multi-layer 3D printing process.

5 Conclusions

This study focuses on the impact of process parameters and the yield stress of the material on the geometrical quality of the printed layer and the shear stress state of the material using CFD. Based on the results and discussion, the following conclusions can be drawn.

1) Changing the printing height is the only effective strategy by which to alter the layer height of the printed body, and controlling printing height and adjusting the extrusion flow rate of the inlet material are the most effective process parameters for regulating the shape of the final concrete layer.

2) Although it is possible to print wider layers with smaller printheads, over-extrusion can lead to inhomogeneity in the printed body, and the lower layer can be subjected to huge local stress.

3) The use of larger printing nozzles can lead to more regular printed body shapes, provided that the extrusion flow is matched accordingly.

4) The internal shear stress state is crucial for changing the printing height of the same layer. The difference in yield stress of the material leads to the change in the distribution of shear stress distribution in the printed material.

5) The peak surface traction of the material remains relatively constant between process parameters, but changing the printing height causes a large change in the peak surface traction.

References

[1] Wangler T, Pileggi R, Gürel S, Flatt R J. A chemical process engineering look at digital concrete processes: Critical step design, inline mixing, and scaleup. Cement and Concrete Research, 2022, 155: 106782

[2] Mechtcherine V, van Tittelboom K, Kazemian A, Kreiger E, Nematollahi B, Nerella V N, Santhanam M, de Schutter G, van Zijl G, Lowke D, Ivaniuk E, Taubert M, Bos F. A roadmap for quality control of hardening and hardened printed concrete. Cement and Concrete Research, 2022, 157: 106800

[3] Tao Y, Lesage K, Van Tittelboom K, Yuan Y, de Schutter G. Twin-pipe pumping strategy for stiffening control of 3D printable concrete: From transportation to fabrication. Cement and Concrete Research, 2023, 168: 107137

[4] Gebhard L, Esposito L, Menna C, Mata-Falcón J. Inter-laboratory study on the influence of 3D concrete printing set-ups on the bond behaviour of various reinforcements. Cement and Concrete Composites, 2022, 133: 104660

[5] Marchment T, Sanjayan J. Reinforcement method for 3D concrete printing using paste-coated bar penetrations. Automation in Construction, 2021, 127: 103694

[6] Ma G, Buswell R, Leal da Silva W R, Wang L, Xu J, Jones S Z. Technology readiness: A global snapshot of 3D concrete printing and the frontiers for development. Cement and Concrete Research, 2022, 156: 106774

[7] Mohan M K, Rahul A V, de Schutter G, Van Tittelboom K. Extrusion-based concrete 3D printing from a material perspective: A state-of-the-art review. Cement and Concrete Composites, 2021, 115: 103855

[8] Weng Y, Li M, Ruan S, Wong T N, Tan M J, Ow Yeong K L, Qian S. Comparative economic, environmental and productivity assessment of a concrete bathroom unit fabricated through 3D printing and a precast approach. Journal of Cleaner Production, 2020, 261: 121245

[9] Xiao J, Zou S, Yu Y, Wang Y, Ding T, Zhu Y, Yu J, Li S, Duan Z, Wu Y, Li L. 3D recycled mortar printing: System development, process design, material properties and on-site printing. Journal of Building Engineering, 2020, 32: 101779

[10] Tao Y, Vantyghem G, Lesage K, Yuan Y, Corte W D, Tittelboom K V, Schutter G D. Adhesion properties of printable polymer-modified concrete for rock tunnel linings. ACI Materials Journal, 2021, 118(6): 61–73

[11] de Schutter G, Lesage K, Mechtcherine V, Nerella V N, Habert G, Agusti-Juan I. Vision of 3D printing with concrete—Technical, economic and environmental potentials. Cement and Concrete Research, 2018, 112: 25–36

[12] Buswell R A, Leal de Silva W R, Jones S Z, Dirrenberger J. 3D printing using concrete extrusion: A roadmap for research. Cement and Concrete Research, 2018, 112: 37–49

[13] Lu B, Weng Y, Li M, Qian Y, Leong K F, Tan M J, Qian S. A systematical review of 3D printable cementitious materials. Construction and Building Materials, 2019, 207: 477–490

[14] Nair S A O, Panda S, Santhanam M, Sant G, Neithalath N. A critical examination of the influence of material characteristics and extruder geometry on 3D printing of cementitious binders. Cement and Concrete Composites, 2020, 112: 103671

[15] BhattacherjeeSSanthanamM. Enhancing buildability of 3D printable concrete by spraying of accelerating admixture on surface. In: Proceedings of Second RILEM International Conference on Concrete and Digital Fabrication: Digital Concrete 2020. Eindhoven: Springer, 2020

[16] Tao Y, Ren Q, Lesage K, van Tittelboom K, Yuan Y, de Schutter G. Shape stability of 3D printable concrete with river and manufactured sand characterized by squeeze flow. Cement and Concrete Composites, 2022, 133: 104674

[17] Comminal R, Leal da Silva W R, Andersen T J, Stang H, Spangenberg J. Modelling of 3D concrete printing based on computational fluid dynamics. Cement and Concrete Research, 2020, 138: 106256

[18] Rahul A V, Mohan M K, De Schutter G, van Tittelboom K. 3D printable concrete with natural and recycled coarse aggregates: Rheological, mechanical and shrinkage behaviour. Cement and Concrete Composites, 2022, 125: 104311

[19] Yuan Q, Li Z, Zhou D, Huang T, Huang H, Jiao D, Shi C. A feasible method for measuring the buildability of fresh 3D printing mortar. Construction and Building Materials, 2019, 227: 116600

[20] Buswell R, Xu J, de Becker D, Dobrzanski J, Provis J, Kolawole J T, Kinnell P. Geometric quality assurance for 3D concrete printing and hybrid construction manufacturing using a standardised test part for benchmarking capability. Cement and Concrete Research, 2022, 156: 106773

[21] Roussel N, Spangenberg J, Wallevik J, Wolfs R. Numerical simulations of concrete processing: From standard formative casting to additive manufacturing. Cement and Concrete Research, 2020, 135: 106075

[22] Perrot A, Pierre A, Nerella V N, Wolfs R J M, Keita E, Nair S A O, Neithalath N, Roussel N, Mechtcherine V. From analytical methods to numerical simulations: A process engineering toolbox for 3D concrete printing. Cement and Concrete Composites, 2021, 122: 104164

[23] Reinold J, Nerella V N, Mechtcherine V, Meschke G. Extrusion process simulation and layer shape prediction during 3D-concrete-printing using the particle finite element method. Automation in Construction, 2022, 136: 104173

[24] Wolfs R J M, Bos F P, Salet T A M. Early age mechanical behaviour of 3D printed concrete: Numerical modelling and experimental testing. Cement and Concrete Research, 2018, 106: 103–116

[25] Vantyghem G, Ooms T, de Corte W. VoxelPrint: A Grasshopper plug-in for voxel-based numerical simulation of concrete printing. Automation in Construction, 2021, 122: 103469

[26] Ramyar E, Cusatis G. Discrete fresh concrete model for simulation of ordinary, self-consolidating, and printable concrete flow. Journal of Engineering Mechanics, 2022, 148(2): 04021142

[27] Remond S, Pizette P. A DEM hard-core soft-shell model for the simulation of concrete flow. Cement and Concrete Research, 2014, 58: 169–178

[28] Chang Z, Zhang H, Liang M, Schlangen E, Šavija B. Numerical simulation of elastic buckling in 3D concrete printing using the lattice model with geometric nonlinearity. Automation in Construction, 2022, 142: 104485

[29] Wolfs R J M, Salet T A M, Roussel N. Filament geometry control in extrusion-based additive manufacturing of concrete: The good, the bad and the ugly. Cement and Concrete Research, 2021, 150: 106615

[30] Pan T, Teng H, Liao H, Jiang Y, Qian C, Wang Y. Effect of shaping plate apparatus on mechanical properties of 3D printed cement-based materials: Experimental and numerical studies. Cement and Concrete Research, 2022, 155: 106785

[31] PanTGuoRJiangYJiX. How do the contact surface forces affect the interlayer bond strength of 3D printed mortar? Cement and Concrete Composites, 2022, 133: 104675

[32] Hanada T, Kuroda K, Takahashi K. CFD geometrical optimization to improve mixing performance of axial mixer. Chemical Engineering Science, 2016, 144: 144–152

[33] Jiang S, He Z, Zhou Y, Xiao X, Cao G, Tong Z. Numerical simulation research on suction process of concrete pumping system based on CFD method. Powder Technology, 2022, 409: 117787

[34] Mollah M T, Comminal R, Serdeczny M P, Šeta B, Spangenberg J. Computational analysis of yield stress buildup and stability of deposited layers in material extrusion additive manufacturing. Additive Manufacturing, 2023, 71: 103605

[35] Mollah M T, Comminal R, Serdeczny M P, Pedersen D B, Spangenberg J. Stability and deformations of deposited layers in material extrusion additive manufacturing. Additive Manufacturing, 2021, 46: 102193

[36] Mollah M T, Comminal R, Leal da Silva W R, Šeta B, Spangenberg J. Computational fluid dynamics modelling and experimental analysis of reinforcement bar integration in 3D concrete printing. Cement and Concrete Research, 2023, 173: 107263

[37] Mollah M T, Comminal R, Serdeczny M P, Pedersen D B, Spangenberg J. Numerical predictions of bottom layer stability in material extrusion additive manufacturing. Journal of the Minerals Metals & Materials Society, 2022, 74(3): 1096–1101

[38] Spangenberg J, Leal da Silva W R, Comminal R, Mollah M T, Andersen T J, Stang H. Numerical simulation of multi-layer 3D concrete printing. RILEM Technical Letters, 2021, 6: 119–123

[39] Spangenberg J, Leal da Silva W R. In: Buswell R, Blanco A, Cavalaro S, Kinnell P. Eds. Integrating reinforcement with 3D concrete printing: Experiments and numerical modelling. In: Proceedings of Third RILEM International Conference on Concrete and Digital Fabrication. Cham: Springer International Publishing, 2022, 379–384

[40] Liu Z, Li M, Weng Y, Qian Y, Wong T N, Tan M J. Modelling and parameter optimization for filament deformation in 3D cementitious material printing using support vector machine. Composites. Part B, Engineering, 2020, 193: 108018

[41] Liu Z, Li M, Tay Y W D, Weng Y, Wong T N, Tan M J. Rotation nozzle and numerical simulation of mass distribution at corners in 3D cementitious material printing. Additive Manufacturing, 2020, 34: 101190

[42] He L, Chow W T, Li H. Effects of interlayer notch and shear stress on interlayer strength of 3D printed cement paste. Additive Manufacturing, 2020, 36: 101390

[43] Mohan M K, Rahul A V, van Tittelboom K, de Schutter G. Rheological and pumping behaviour of 3D printable cementitious materials with varying aggregate content. Cement and Concrete Research, 2021, 139: 106258

[44] Tao Y, Rahul A V, Mohan M K, van Tittelboom K, Yuan Y, de Schutter G. Blending performance of helical static mixer used for twin-pipe 3D concrete printing. Cement and Concrete Composites, 2022, 134: 104741

[45] Lloret-Fritschi E, Quadranti E, Scotto F, Fuhrimann L, Demoulin T, Mantellato S, Unteregger L, Burger J, Pileggi R G, Gramazio F, Kohler M, Flatt R J. Additive digital casting: From lab to industry. Materials, 2022, 15(10): 3468

[46] Shantanu B, Smrati J, Manu S. Criticality of binder-aggregate interaction for buildability of 3D printed concrete containing limestone calcined clay. Cement and Concrete Composites, 2023, 136: 104853

[47] Roussel N. Rheological requirements for printable concretes. Cement and Concrete Research, 2018, 112: 76–85

[48] Tao Y, Rahul A V, Lesage K, Yuan Y, van Tittelboom K, de Schutter G. Stiffening control of cement-based materials using accelerators in inline mixing processes: Possibilities and challenges. Cement and Concrete Composites, 2021, 119: 103972

[49] Hou S, Duan Z, Xiao J, Ye J. A review of 3D printed concrete: Performance requirements, testing measurements and mix design. Construction and Building Materials, 2021, 273: 121745

[50] Chen Y, Chaves Figueiredo S, Li Z, Chang Z, Jansen K, Çopuroğlu O, Schlangen E. Improving printability of limestone-calcined clay-based cementitious materials by using viscosity-modifying admixture. Cement and Concrete Research, 2020, 132: 106040

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