mechanical beha3dted lightweight concrete structure … › content › pdf › 10.1007 ›...

Vol.:(0123456789)1 3

Archives of Civil and Mechanical Engineering (2020) 20:16 https://doi.org/10.1007/s43452-020-00017-1

ORIGINAL ARTICLE

Mechanical behaviors of 3D printed lightweight concrete structure with hollow section

Li Wang1,2 · Hailong Jiang1 · Zhijian Li3 · Guowei Ma1

Received: 7 March 2019 / Accepted: 15 December 2019 / Published online: 18 February 2020 © Wroclaw University of Science and Technology 2020

AbstractA practical revolution in construction could be realized by combining the potential of 3D concrete printing with lightweight cementitious materials to fabricate adeptly hollow structures. In this study, five concrete mixtures with different replacement rates of lightweight ceramsite sand to silica sand are prepared for extrusion-based 3D printability evaluation. To reduce the water absorption induced shrinkage and micro-cracks, the ceramsite sands were coated with polyvinyl alcohol. An optimized cementitious material was identified by harmonizing the fresh properties to the continuous printing process. Cubic and beam elements with four different types of interior hollow structures were designed and 3D printed based on the optimized lightweight mixture. The interior structures include cellular-shaped structure, truss-like structure, lattice-shaped structure with a square topology, as well as gridding shaped structure with triangle topology. The mechanical capacities of the printed samples were measured and evaluated by compressive tests for the cubic samples and four-points flexural bending tests for the beam specimens. Basing on the results, the rectangular lattice hollow structure demonstrates the best mechanical resist-ance to compression and the truss-shaped prism structure ensues the highest flexural properties. The stress distribution and failure process were also explored through discrete element method.

Keywords 3D concrete printing · Mechanical testing · Ceramsite sand · Hollow concrete structure · Lightweight structure · DEM simulation

1 Introduction

Conventional construction faces criticism for over-reserved safety margins in design thus yielding bulky structural com-ponents besides the excessive construction wastes. This excessive self-weight of structural components renders cumbersome, costly, and dangerous construction processes [1]. To make amendments, 3D concrete printing (3DCP) technologies gain rapid development in recent years due to

the distinct advantages in structural optimization and sparing the formworks in the conventional construction [2–5]. Com-pared to conventional fabrication methods, this advanced technique possesses a series of advantages, such as increased efficiency, automation of construction, minimized pollution of the environment and reduced labors and injuries, which is a promising enabler for the revolution of the construction industry in near future [6–8]. 3DP technology adeptly offers almost unlimited potential for arbitrary geometric complex-ity. Studies demonstrate that additive manufacturing is able to provide distinct benefits to achieve additional complexity without extra costs [9]. Practical engineering applications have proven the applicability of 3DCP in constructing lar-gescale building components.

Largescale 3DP coupled with printable cementitious materials revolutionizes implementation of construction projects [10]. Lower density cementitious materials based concrete, known as lightweight concrete (LWC), has been widely applied due to its excellent performance, in view of lightweight, high strength, and thermal insulation, etc. [11]. Different from the ordinary or heavyweight concrete

* Li Wang [email protected]

1 School of Civil and Transportation Engineering, Hebei University of Technology, 5340 Xiping Road, Beichen District, Tianjin 300130, China

2 State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology at Beijing, D11 Xueyuan RD, Beijing 100083, China

3 College of Architecture and Civil Engineering, Beijing University of Technology, Pingleyuan 100, Chaoyang District, Beijing 100084, China

http://crossmark.crossref.org/dialog/?doi=10.1007/s43452-020-00017-1&domain=pdf

Archives of Civil and Mechanical Engineering (2020) 20:16

1 3

16 of 17

in adopting coarse aggregate and high-density gravels, LWC are produced with expanded clay, ceramsite sand, etc., as aggregates. Ceramic concrete prioritizes itself with small dry bulk density, building energy conservation, high strength, low thermal conductivity, good permeability resist-ance, good fire resistance, etc. [12]. Structural lightweight concrete plays an important role in the construction industry, especially for the high-rise buildings [11]. It is expected that a combination of lightweight ceramic concrete with 3DP can optimize the structural designs in the construction indus-try. Structural self-weight can be reduced to the minimum by rationalizing appropriately the component ratios of the cementitious materials and smartly manipulating the archi-tectural form with the 3DP technology. Construction cost should be reduced greatly as well.

On the other hand, systematic investigations on the prepa-ration and manufacturing of lightweight concrete materials by extrusion-based 3DP are lacking. It is understood that the fresh properties of manufactured cementitious materi-als should be reconcilable with the 3DP process with regard to pumping transportation, material extrusion, and vertical stacking, etc. [3, 13, 14]. It is prerequisite for the cementi-tious materials to be flowable to travel the long distance of pumping pipe, extrudable to pass the narrow opening of nozzles. It is also expected that its green stiffness is suf-ficiently high for shape retention and dormant strength is sustainable enough for the self-weight of the subsequent lay-ers and yet stay viscous enough to bond the adjacent layers through the formation of cold joints. Thus, it still remains a big challenge to coordinate the material properties with the printing process parameters to substantialize the advantages of 3DP with cementitious materials [15]. Although a series of researches have been conducted to fabricate lightweight concrete using ceramsite sand, the feasibility of ceramsite concrete for 3D printing is yet to be explored [16, 17]. For the potential general application, it is imperative to exposit how the particle grading of ceramsite sand influence the flowability and extrudability of the concrete materials, and how to optimize the content of ceramsite sand for favorable buildability.

Described by the conventional construction method of block casting, the solid and heavy structural components inevitably render the practical construction processes cum-bersome and sometimes dangerous for humans or even robots to handle [18]. 3DP technology can be employed to fabricate structural components with arbitrary geometry and even interior hollow structures. Development of new types of hollow concrete structural units can minimize its weight through topological optimization and smart design. Particu-larly, 3DP hollow structures will be lighter with sustainable structural resistance. Thus, smartly architected hollow struc-tures have gained significant interests in building sectors due to their unique and superior properties that cannot be

approached by natural bulk solids [19]. For example, inte-riorly honeycomb-configured structures are used as special damping, packaging, and energy-absorbing elements [20]. Sandwich plates with periodic lattice cores possess superior bending stiffness, strength and shock resistance compared to the monolithic plate of the same mass [21]. It has been envisioned that hollow structures are preferred candidate for constructing oversized lightweight structures. It is noticeable that the above prioritized mechanical and functional proper-ties strongly depend upon the appropriate architectural and topological design of the hollow structures. A comprehen-sive approach should be developed to evaluate systematically the mechanical resistance of the different configurations to choose the optimum hollow structure.

However, mechanical capacities may be severely sacri-ficed when a relatively larger hollow section is designed. A better alternative solution would be to fabricate lightweight structures by coupling the hollow configuration with light-weight materials. Therefore, in the current study, a light-weight cementitious material is proposed for 3DP by opti-mizing the replacement ratio of ceramsite sand to fine sand. The 3D printability is evaluated by the slump flow test and penetration resistance test. The identified optimum light-weight ceramsite mixture is applied to 3DP hollow samples. The mechanical properties of the printed hollow structures are accessed by compression and flexural bending tests. A numerical discrete element model (DEM) has been imple-mented to reproduce the characteristic mechanical response of the loaded models to further elaborate the deformation and failure mechanisms. The systematic investigations and results from this study credit itself an innovative solution to construction through the lightweight design of both materi-als and structures.

2 Materials and methods

2.1 Raw materials and mix proportions

The mixture comprises various cementitious powders including rapid hardening Portland cement P. O 42.5R and silica fume as the binder component. The chemical com-position of cement and silica fume are shown in Table 1. A high-efficiency polycarboxylate-based superplasticizer with a water-reducing rate of more than 30% and a solid content fraction of 37.2% is adopted to lower the water/binder ratio, to increase its workability and strength, and to achieve the required flowability. A small quantity of viscosity modify-ing admixture (VMA) is added to increase water-retaining property, and thus, prevent the formation of bleeding and segregation of cement pastes. Fine silica sand with a specific surface area of 0.11 m2/g and an average size 0.25 mm is


1 3

of 17 16

selected as the fine aggregate. Particularly, fine ceramsite sand is used to induce the lightweight properties.

The physical property and particle grading for the fine ceramsite sand are illustrated in Fig. 1. The chemical specifications are listed in Table 2. The ceramsite sand features by porous characteristics, which renders superior water-absorbing behavior. To access the water absorption property, the ceramsite sand was dried in the oven at a temperature of 60 °C for 3 days. Then the dried sands were immersed in water for different time intervals before weighing by a digital scale with 0.1 g accuracy. Figure 1a depicts the measured water absorption rates of the applied

ceramsite sand. The free water required for consistency, flowability, and hydration process will be consumed due to the water-absorbing property of ceramsite sand. It should be noted that improper addition of lightweight sand to the cementitious materials may result in conspicuous shrink-age and even micro-cracks. To prevent any water absorb-ing or release in the manufacturing process, which may unbalance the designed water content of the cementitious composite, the lightweight ceramsite sand is coated with a polyvinyl alcohol (PVA) based coating. The used PVA is in the form of a 98–98.8% hydrolyses powder with an average molecular weight of 146,000–186,000. The PVA solution is uniformly sprayed on the outer surfaces of cer-amsite sand before naturally dried at ambient temperatures for one day. The coated lightweight sands are stored in a plastic container until used.

In this study, five replacement ratios of ceramsite sand to silica sand are designed to manufacture different light-weight cementitious materials to derive an optimal mix-ture for the extrusion-based 3DP. The various lightweight composites are denoted by C10, C15, C20, C25 and C30 representing 10%, 15%, 20%, 25% and 30% mass ratio of silica sand replacement by ceramsite sand, respectively. The ratios by weight of the raw materials used for mixture preparation are presented in Table 3. The dry powders, i.e., cement, silica fume, both silica, ceramsite sand, and PP fibers are firstly mixed and blended for six minutes to obtain a uniform mixture. Then, the superplasticizer is mixed with water to produce a liquid solution, which is

Table 1 Chemical composition of cement P.O 42.5R

Composition Weight percentage (w%)

SiO2 19.4–21.5Al2O3 4.1–4.9Fe2O3 2.8–2.9CaO 61.9–64.2MgO 1.1–1.2SO3 3.0–3.2K2O 0.6–0.7Na2O 0.2Cl 0.02–0.05Loss of ignition 2.3–4.1

Fig. 1 a Water absorbing prop-erty and b particle grading of adopted ceramsite sand

Table 2 Chemical specifications of ceramsite sand

SiO2 Fe2O3 Al2O3 CaO K2O TiO2 MgO CuO

50.12 19.48 17.51 4.64 2.47 1.26 1.18 0.05

MnO Na2O BaO SO3 P2O5 Cl As2O3 ZnO

1.03 0.55 0.53 0.44 0.28 0.26 0.11 0.04


1 3

16 of 17

then poured into the dry mixtures and mixed for seven minutes.

2.2 Printability determination for cementitious materials

2.2.1 Flowability evaluation

Desirable followability implies that the prepared cementi-tious material transports smoothly from the material tank/container to the nozzle, which is a key parameter to char-acterize the printability of cementitious materials. In this study, the flowability of the prepared lightweight materials is measured through mini-slump tests, which is preferable in laboratories and on sites due to its simplicity and immediate

results. Mini-slump cone is commonly used to determine the flowability of cement mortars. The freshly mixed cement paste is first filled in the mini-cone, the drop-in height is then measured to characterize the flowability of mixtures when the cone is lifted. The recommended range of flowability to render smooth 3D printing has been specified in previous investigations [22]. Thus, the manufactured materials that keep a flowability in the recommended range is expected to meet the requirement for extrusion-type 3DP.

2.2.2 Early age stiffness evaluation

The early age stiffness immediately after deposition is cru-cial to govern the buildability to ensure the stability of the stacked layers and retention of shape. The higher the early

Fig. 2 Digital design of 3D model of a prism and b cubic samples with different hollow structures. The width of each filament is equal to the diameter of print nozzle

Table 3 Mix proportions of raw materials for 3D printing (unit: kg/m3)

C10, C15, C20, C25 and C30, respectively, refers to the lightweight composites with 10%, 15%, 20%, 25% and 30% mass ratio of silica sand replaced by lightweight sand

No. Ceramsite sand Silica sand Cement Water Silica fume VMA PP fiber Super plasticizer

C10 72.3 650.3 722.6 289.0 43.4 0.22 1.81 0.36C15 108.5 614.1 722.6 289.0 43.4 0.22 1.81 0.36C20 144.6 578.0 722.6 289.0 43.4 0.22 1.81 0.36C25 180.8 541.8 722.6 289.0 43.4 0.22 1.81 0.36C30 216.9 505.7 722.6 289.0 43.4 0.22 1.81 0.36


1 3

of 17 16

age stiffness or the faster the hydration process, the more sustainable are fresh materials to the compression induced by the weight of subsequent layers [23]. In this study, the stiffness of various cementitious materials was measured through the penetration resistance method to access the build-up behavior. The experiments were conducted accord-ing to the Chinese industry testing standard JGJ/T-2009. The prepared mixtures are firstly filled into a cylindrical mould of 150 mm diameter and 150 mm in height. Then a steel nail with a cross-sectional area of 100 mm2 is pressed into the mortar to a depth of 25 ± 2 mm. The penetration resist-ance force exerted on the bottom of the nail is measured to characterize the hydration degree of tested mixtures [24]. The penetration resistance force divided by the area of nail is identified as the penetration resistance. The recommended range of penetration resistance to qualify the 3DP printing has been specified.

2.3 Additive manufacturing of hollow concrete structures

2.3.1 Computer model design for hollow concrete structures

The first step to start 3DP is digital model design. In this study, various types of hollow structures are established tentatively in 3D modelling software. AutoCAD is applied for the digital. The constructed digital 3D model is then exported to a 3D data exchange format, i.e., stereolithogra-phy (STL), which is the most popular format in 3D printing design. The STL data is then processed to decompose the model into a series of two-dimensional slices [25]. The noz-zle printing path, which is the 2D contour line, is designed based on the geometry of 2D slices. As a result, a G-code program file is created for the printer controlling system to read. In this study, four different hollow structures are designed, including cellular shaped structure, truss-like structure, lattice-shaped structure with a square shape, as well as gridding shaped structure with triangle topology, which are schematically shown in Fig. 2a–d. There are two main reasons for the design of these four flexible shapes, one is to validate the feasibility of applying ceramsite sand cementitious composite for the extrusion-based 3D print-ing, and the other is to further investigate the failure perfor-mances of hollow concrete structures to access the mechani-cal behaviors. The yellow lines in the figure indicate the printing path design. Fresh mixtures are smoothly deposited in the form of small filament to be stacked up under the controlling of operational program to achieve the designed 3D models.

2.3.2 Additive manufacturing of hollow concrete structures

A self-developed 3D printer for cementitious materials extrusion is applied to fabricate samples for mechanical testing as illustrated in Fig. 3. The proposed system com-prises of a steel gantry, motion sliders, step motors to drive motions in X, Y and Z directions. A material containing tank equipped with a mixing blade is used for the material storage and extrusion, and a platform is applied for the placement of models. Driven by the stepping motors, the steel gantry moves freely in the x direction along with the motion slid-ers; a lifting beam fixed on the frame gantry can move in the y direction; the material tank fixed on the lifting beam can move along the z direction. The construction of 3D mod-els is realized in the coordinated moving of frame gantry and lifting beam, which digitally controlled by the software operating system. The rotation speed of the screw blade is adjustable to coordinate the fresh property of cement mor-tars to ensure the fluent depositions. The proposed desktop 3D printer can produce 3D models with a maximum dimen-sion of 0.7 m (L) × 0.4 m (W) × 0.3 m (H).

The material for 3D printing is mixed through a conven-tional mixer before it is transferred to the material storage tank. It is then conveyed to the bottom of the printing nozzle through the rotation of mixing blade. The nozzle diameter is designed as 12 mm. To avoid twisting of extruded filaments and simplify the control of machine, nozzle with an oval cross-section is applied [26]. In the printing process, the fresh mortar is smoothly and continuously deposited from the nozzle. The extrusion rate and horizontal printing speed are set as 5.4 L/min and 4.5 m/min, respectively, in the print-ing processes. The nozzle standoff distance is designed as 5 mm to consolidate the concrete to enlarge the bonding surface. Particularly, to relieve the weak bonding, no time interval is set in the printing process to retain the chemical activity of extruded materials. As a result, the lateral stiff-ness is increased by the pressing effect.

Figures 4 and 5 illustrate the 3D printed hollow structures. The cubic samples are in dimensions of 150 mm × 150 mm × 150 mm. The sizes of prism samples are 100 mm × 100 mm × 400 mm. The size of each sample is introduced in the corresponding figures.

2.4 Mechanical capacity evaluation

The printed hollow concrete samples are then prepared for testing to evaluate the shape efficiency on the mechani-cal capacity. The mechanical properties are measured for both printed cubic and prism specimens after the 28-day curing. The cubic samples are loaded by uniform vertical compression and the prism samples were subject to flexural bending through four points bending test. In this study, the


1 3

16 of 17

Fig. 3 a Extrusion based 3D printer for cementitious material, b printing process of hollow sample, and the printed solid c prism and d cubic samples

Fig. 4 3D printed hollow prism samples (unit: mm)


1 3

of 17 16

compressive and flexural tests were carried out in accord-ance with the Chinese national standard [27] for test method of mechanical properties on ordinary concrete due to there is still no specific standard or guideline for 3DP. Three identi-cal specimens are measured for each test.

A servo-hydraulic universal testing machine with load-ing capacity of 1500 kN is used to load the specimens., The loading rate is set as 0.5 mm/min until failure. While in the flexural test, the loading rate is set as 0.05 mm/min. The

supporting span and loading span of four points bending test are 300 mm and 100 mm, respectively. In the compres-sion test, strain gauges are attached on the left and right side of the cube samples to evaluate the deformation resistance of various structures under compressions. In the flexural bending test, strain gauges are bonded on the middle bottom surfaces to measure the tensile strain. Three displacement meters are deployed on the top surfaces of prims samples to monitor the deflection evolution. The schematics of both

Fig. 5 3D printed hollow cube samples (unit: mm)

Fig. 6 Schematic of compres-sive and flexural bending tests


1 3

16 of 17

compression and flexural tests are shown in Fig. 6. The load-ing force and deformation data are measured and recorded in the testing process. The test results will reflect the effect of the various hollow shapes on the mechanical performances of 3D printed structures.

3 Results and discussion

3.1 3D printability evaluation

The printability of various cementitious material contain-ing different ceramsite sand is evaluated through the mini-slump method to test the flowability and the penetration resistance to test the structural built-up. Based on our pre-vious research, the recommended range of slump in height for feasible printability is determined as 32–88 mm, and the recommended range of penetration resistance lies in 13–40 kPa [22]. The materials that keep up the fresh prop-erties in the recommendation range depict good printabil-ity. Figure 7 depicts the results to check if the five cemen-titious lightweight material meet the requirement for 3D printing. From Fig. 7a, material C10 presents larger slump than the high critical vault value, demonstrating the mate-rial of interest is excessively flowable to retain the shape after immediate deposition. The flowability decreases with the increasing replacement of ceramsite sand to the silica sand. The slump value of materials C15 and C20 are in the optimized range, which implies that the materials can be smoothly and continuously extruded without blockage. On the other hand, when the replacement ratio increases to 25% and even 30%, the materials yield relatively small slump and is also less than the lower limit to pass print-ability. It demonstrates that the materials of C25 and C30 cannot meet the requirement for smooth extrusion, which may result in interruption or blockage. High content of ceramsite sand may form a structural skeleton to make the

cementitious materials more stable. Therefore, the slump value is reduced with increasing ceramsite sand.

From the results as shown in Fig. 7b, the penetration resistance of cementitious materials increases with the content of ceramsite sand. The C10–C25 all keep up the required green stiffness to facilitate smooth vertically stacking process since the penetration resistance values are all in the optimized range, i.e. 13–40 kPa. On the other hand, the material C30 has a larger stiffness than the higher critical value. It means that C30 is not suitable for printing and may result in blockage in the nozzle opening. Therefore, from the measured results of mini-slump and penetration tests, the materials of C15 and C20 are proved to be applicable for extrusion-based printing. To maximize utilization of ceramsite sand, C20 is identified as the most favorable material to fabricate the hollow structures.

3.2 Mechanical property of printed hollow cube samples

The various printed hollow structures are loaded with con-tinuous compression by applying uniformly vertical dis-placement on the top surfaces of samples. Figure 8 depicts the tested relationship of compressive force and vertical displacement of the top surface of cellular, lattice, truss, and triangle-shaped hollow structures. From the results, it can be seen that the differences in the hollow shapes influence the mechanical resistant properties substantially. The peak loads of hollow samples are low due to the small bearing areas. The compressive strength of 3DP cubes with cellular, truss, triangle, and lattice hollow configura-tion were calculated as 30.8 MPa, 18.1 MPa, 22.6 MPa, and 36.0 MPa, respectively. Net area is used for the calcu-lation of compressive strength. The truss shaped structure incurs the lowest capacity, whereas the lattice structure shows the highest capacity. The respective peak compres-sion value of cellular, triangle and lattice-shaped struc-ture is approximately 35.8%, 24.6% and 58.7% higher than

Fig. 7 a Slump in height and b penetration resistance of various cementitious materials


1 3

of 17 16

that of the truss shaped one. From the measured results, the compressive strength of various hollow specimens is approximately 45.3–90% of the solid one. The mechanical behaviors of printed solid samples are significantly influ-enced by the designed printing path, which may affect the stress transfer and, therefore, influence overall mechanical property. For instance, the sample with triangle hollow configuration performs 56.5% of the strength using 48.0% of the materials, compared with the solid one. The lat-tice hollow configuration sample performs 90.0% of the strength using 53.3% of the materials, compared with the solid one. From this point of view, it is promising to opti-mize the material cost and strength by printing hollow structures.

From the curves in the figures, there is a stable increase stage of compressive force before the steep increase phase starts, which may be caused by the uncompleted contact between the loading end with the sample surfaces. An increasing line is drawn with the two stress points 30% and 60% of peak loads, and a parameter D0, the cross point of the increasing line extended to the horizontal axis, is defined as the initial value to bear the applied loads. The displacement of sample under peak load is defined as Dult. The difference between D0 and Dult can be used to characterize the mechani-cal deformation-resistant capacity. From the measured data, this displacement difference of cellular, truss, triangle, and

lattice-shaped hollow structures are 1.12 mm, 1.34 mm, 1.17 mm, and 1.67 mm, respectively. Although the truss-like prism specimen performs the lowest bending strength, its flexural deformation capacity is 19.6%. It is 14.5% higher than the counterparts of cellular and triangular configured prism specimens. Similar to the strength, the lattice meshed sample incurs the highest vertical strain. The test results demonstrate that the mechanical behaviors of 3DP speci-mens are governed by the interior hollow geometries.

Figure 9 shows the failure patterns of the different hol-low structures. The weak interlayers will reduce the overall mechanical capacities to some extent and are prone to initi-ate cracks. In this study, the print speed is set as 4.5 m/min. Then the time difference between the adjacent two layers is much less than 1 min, which may not produce obvious cold joints between layers. Meanwhile, from the failure status of the printed samples, no delamination failure was observed, demonstrating the acceptable interfacial bond.

For the cellular one, the cracks propogate approximately horizontally along with the interface between the printed filaments, where the bearing area is relatively small because of incomplete contact between neighboring filaments. For the truss shaped structures, the cracks start at the left edge, to run through the truss member to reach the contact point of the truss structure to the top edge, which is marked as the yellow line in Fig. 9b. The damage at the left edge may

Fig. 8 The relationship of verti-cal compression vs. deformation of 3D printed cubes: a cellular, b truss, c triangle, and d lattice hollow structures


1 3

16 of 17

be yielded by torture due to the hollow structure asym-metricity. The reason cracks initiated at the contact point may be attributed to the stress concentration at that point. On the other hand, cracks are also observed at the bottom edge, which experiences tensile stress beyond the tensile strength. Cracks are produced at the left edge of gridding shaped structure with triangle topology (see Fig. 9c), which may also be induced by torture due to the inner structural asymmetricity. As the failure pattern shown in Fig. 9d, the cracks are parallel to the loading directions. The vertical filaments in the lattice hollow structure are prone to undergo and transfer the most compression.

To assess the different deformation resistances of vari-ous hollow structures, the vertical strains under compres-sion derived from the displacement at the top surfaces and measurements of strain gauge are depicted and compared in Fig. 10. The strain data presented in Fig. 10a are calculated from the ration of displacement at the loading end to the height of the specimen. From Fig. 10, the strain of all hol-low structures increases with increasing compression force. The lattice structure performs the highest deformation than those of all other types subject to similar pressure, while the truss shaped structure behaves the smallest strain. The results demonstrate that the structure with lattice topology shows the best mechanical deformation resistance capacity,

Fig. 9 Failure patterns of differ-ent 3D printed hollow structures

Fig. 10 Comparison of vertical strain of different hollow struc-tures subject to compression measured by the displacement of a top surfaces and b strain gauge


1 3

of 17 16

whereas the truss structure performs the worst properties. From the strain data depicted in Fig. 10b, which are meas-ured directly through the strain gauge attached on the edges of tested samples, similarly, the lattice structure yields the highest deformation. The strain at the edge of most struc-tures increase with the increasing pressure, whereas the strain of hollow structure with triangular topology increases firstly and then maintains a plateau before increasing again to reach the peak value. Based on the experimental obser-vation, it is because that a small crack in the loading pro-cess occurs before the peak load is reached. For the lattice structure, the attached gauge is damaged when the load is higher than 80 kN. The strain data in Fig. 10a reflects the overall deformation behavior of the printed structures, while the strain measured by gauges in Fig. 10b dictates the local deformation behavior. The remarkable differences in both the overall and local deformation behaviors imply the con-spicuous influences of the different topologies of the interior structures.

3.3 Mechanical property of printed hollow prism samples

Figure 11 shows the failure patterns of various hollow struc-tures subject to four-point flexural test. For the beam with cellular topology, the cracks extend along the line of loading and supporting points, which may be induced by shear stress (see Fig. 11a). For the other cases, i.e., the triangle meshed, truss shaped, and lattice hollow structures, the cracks start

from the mid-span and propagate upward. In the bending process of printed beam specimen, the bottom part under-goes significant tensile stresses. Once the tensile strength is reached, the cracks will occur. For the different cases shown in Fig. 11b–d, the tensile strength is first reached at the mid-span area before the shearing strength in the load-ing and supporting points is reached. Most cracks of hollow structure start from the contact point of the filament to the bottom edge. Different interior hollow topology incurs dif-ferent crack propagation path.

To further demonstrate the influence of different hollow topology on the mechanical responses of the printed beam specimens, the loading curves and mechanical characteris-tics of different hollow structures are depicted in Fig. 12. From Fig. 12, all the beams perform distinct brittle failure process. The reason could be that the printed structures are not reinforced with either steel bar or fiber. The strains at peak bending loads are given in Fig. 12b. The strains of various printed beam at peak loads are measured to be 98, 115, 90, 137 με for the cellular, triangular, lattice, and truss topological hollow structures, respectively. The truss shaped beam shows the highest strain, which is 39.8%, 19.1% and 52.2% higher than the respective counterparts cellular, trian-gular, and lattice-shaped ones, indicating the lowest bending deformation resistance. The lattice beam shows the smallest tensile strain at the peak load, crediting the best flexural deformation-resistant capacity. On the other hand, the lattice structure shows the smallest deformation resistance in the compressive testing.

Fig. 11 Failure patterns of different 3D printed structures: a cellular, b triangle meshed, c truss shaped, and d lattice hol-low structures


1 3

16 of 17

The deflection for various printed beams in the bending test is also illustrated in Fig. 12b from the displacement meter connected on the top surface of beams. The deflection is calculated by the displacement difference between the side and center displacement measurements. From the measured results, the deflection shows similar trend to that of the bot-tom strain. Specifically, the deflections of various printed beam at peak load measures 0.54, 0.75, 0.51, 0.86 mm for the cellular, triangular, lattice and truss topological hollow structures, respectively. The truss shaped beam shows the highest strain, which is 60.3%, 14.3% and 68.1% higher than that of the cellular, triangular and lattice shaped ones, indi-cating the lowest bending deformation resistance. Whereas the lattice beam shows the smallest deflection at the peak loading, demonstrating the best flexural deformation-resist-ant capacity. It is noticeable that contradictory optimizing results are ensued from both strain and deflection results with the different resistant capacity to the flexural bending.

3.4 Numerical simulation of 3D hollow structures

3.4.1 DEM modelling

To further elaborate on the mechanical resistance and failure mechanisms of various hollow structures, numeri-cal simulation was employed. Discrete element method (DEM) has been validated to be an effective approach to simulate the mechanical behaviors of various engineering structures/materials [28]. Particle flow code (PFC), a com-mercially available software, is employed in this section

to predict the deformation and failure process of the 3D printed hollow samples with consideration of their inter-nal geometrical topology. In the PFC program, 2D discs and 3D spheres elements are adopted for the calculation, which minimize computation intensity and time due to its simple contact search algorithm. In PFC calculations, the contact force between adjacent contacting balls, i.e., the formation of force chain, comply with the force–displace-ment laws. While the movement of each single ball follow the Newton’s laws of motion [29].

For simplicity, 2D simulation models with assumption of plane stress in view of the uniform thickness is adopted for the hollow structures. PFC models are constructed to encompass the geometrical information of the CAD mod-els as shown in Fig. 2. For the cubic model, a quadrate model with dimension of 150 mm × 150 mm is created by randomly distributing the small balls into the correspond-ing area formed by four walls. The radius of all generated balls is set as approximately 0.1 mm to guarantee the accu-racy of calculated results. The geometrical information of a specific hollow structure is then imported into the cre-ated quadrate model. The balls outside the geometrics are deleted. The DEM rectangular models are also built simi-larly. However, it should be noted that there is difference between the numerical models and the practical 3D printed structures. It could be attributed to the unproficiency of the printer in view of the distinct flowability. Thus, the width of the extruded filaments is wider than the design specification, which is adopted in the numerical models. In the PFC2D models, the contacts of particle groups are

Fig. 12 a Loading curves, b mechanical characteristics of different hollow structures

Table 4 Particle/bond parameters assigned to cluster of each individual phase of PFC2D models

E and kn/ks are the effective modulus and normal-to-shear stiffness ratio of the linear contact, respectively. E and kn∕k

s are the effective modu-

lus and normal-to-shear stiffness ratio of the parallel bond contact, respectively. μ is the friction coefficient. �c , c and � are the tensile strength,

cohesion angle, and friction angle of the parallel bond contact, respectively

E kn∕k

s E kn∕k

s� �

cc �

30e9 0.3 30e9 0.3 0.8 5e6 30e6 15


1 3

of 17 16

assigned with the parallel bond contact model (PBCM). The assigned meso parameters of the assembled balls to replicate the concrete materials are presented in Table 4. E and E are effective modulus of linear contact and parallel bond contact, respectively. kn/ks and k

n∕k

s refer to the nor-

mal-to-shear stiffness ratio of linear contact and parallel bond contact, respectively. � accounts for the friction coef-ficient. �

c , c , � represent the tensile strength, cohesion,

and friction angle of parallel bond contact, respectively.In the uniaxial compression simulation, the top walls are

used as loading platens and set with a velocity of 0.5 mm/min as compression load on the numerical models. For the four points bending models, four circular walls with a diam-eter of 10 mm are created. The upper two are applied with 0.05 mm/min downward velocity while the bottom two are fixed. The loading conditions in DEM simulation replicate mechanically the test scenario.

3.4.2 Simulation results

Different from the finite element method, the stress field in discrete element method is characterized by the value of the contact force between adjacent contacted balls. Figure 13 illustrates the force chain distribution of various DEM mod-els subject to compression loading. The force chain in com-pression and tension demonstrate the deformation and fail-ure processes. From Fig. 13, failure initiates in the particles that sustain the highest degree of stress concentration, which will drive the cracks to propagate. The numerical crack pat-terns of the specimens indicated by the breakage of contact bond, as red marks in the figure, are also presented. It could be noted that some of the meso cracks nearby may close up in the later on loading process due to redistribution of the stress following crack formation.

For the compression cellular specimen in Fig. 13a, the corner regions in the hexagon sustain highly concentrated tensile stresses, the cracks initiate in these areas. For the compression truss-like samples in Fig. 13b, the top left corner and the bottom right corner experience the highest stress due to the topological asymmetricity. Whence, cracks converge. For the triangle meshed sample in Fig. 13c, the side boundaries and the inclined filaments transfer the most compressions, while the horizontal filaments sustain ten-sile stresses. Due to the axial compressive load, the verti-cal deformation is much larger than the transverse defor-mation. The side boundaries are damaged under excessive compression. The damage in the crossed filaments are prob-ably induced by the torque induced by the incompatible deformation of the horizontal and inclined filaments. From Fig. 13d, it is evident that the four vertical filaments of the lattice meshed samples transfer the most compressions and

the main cracks are prone to progress comfortably with the stress propagation.

Figure 14 displays the numerical results of four points bending tests. Both the deformation field and damage pat-terns are presented. For the flexural bending test, the top two walls move downwards, while the bottom two are fixed. For all the different types of hollow structures, the central regions of the beams produce relatively large deformation and the bottom central region in the middle span undergoes significant tensile stress. When the tensile stress exceeds the tensile strength of contact balls with the increasing applied loads, the bonds breaks and coalesces into macroscopic frac-tures to ensure separation of balls. The locations and crack pattern at failure conformably permeate the regions where the tensile strength of the material is exceeded.

Generally, it can be seen that the locations of simulated cracks coincide with the experimental tested results. It can be said that the DEM simulation approaches and the physical tests verify mutually. The comparison with the physical test results are shown in Table 5. For the compressive test, the compressive load is determined using the sum all of the ver-tical forces acting on the walls. For the flexural bending test, the vertical displacement is determined by the moving of the upper midpoint of prism samples. As shown in the table, the compressive loads and the displacement of the DEM results were broadly similar to those of the corresponding test results. The deviations are derived from the choosing of calculation algorithm, the setting of numerical parameters, etc. that are different with the physical conditions to a certain extent, as well as the influence of interfaces on the mechani-cal heterogeneous properties is ignored in this study.

4 Conclusions

This study develops a systematic approach to explore maxi-mum lightweight potential of extrusion-based 3DP cemen-titious hollow structures. Optimization of the mechanical capacity of hollow structural components are fulfilled by tests with different ratios of the cementitious components and different interior structural patterns. The present results shed light on the lightweight optimization of 3DP modular members for the assembly constructions.

(1) It is feasible to employ ceramsite sand to prepare 3DP concrete. Five lightweight cementitious materials are produced by incorporating different content of poly-vinyl alcohol (PVA) coated ceramsite sand. Based on the flowability and penetration resistance tests, the mix C20 is identified as the best choice for printing free-form components, in which 20% silica sand is replaced by ceramsite sand.


1 3

16 of 17

(2) The lattice meshed sample displays the best compres-sive resistant behaviors, while the truss-like hollow

prism displays the best flexural bending properties. It is promising to optimize the material cost and strength

Fig. 13 Force chain distribution by DEM simulation subject to axial compression and crack patterns under 70% peak load at the post-peak stage: a cellular, b truss shaped, c triangle meshed and d lattice hollow structures (unit: Pa)


1 3

of 17 16

Fig. 14 Numerical force chain distribution subject to four points flexural load and crack patterns of models under 70% peak load at the post-peak stage: a cellular, b truss shaped, c triangle meshed, and d lattice hollow structures (unit: mm)


1 3

16 of 17

by printing hollow structures. 56–90% of the strength can be obtained using 48–63% less material, compared with solid ones.

(3) DEM is demonstrated as an effective approach to access the mechanical behaviors of the hollow structures. The regions sustaining compression and tension are derived to explicate the failure mechanism. Position and orien-tation of macro-cracks formed by the breakage of the contact bond and separation of adjacent balls are very similar to those of the test results.

In simple summary, 3DCP has distinct advantages in the reduction of concrete volume and mass, saving complex and costly formworks, the easy transportability and instal-lation, etc. The presented method scarifies the mechanical strength of concrete structures by hollow section. How-ever, the hollow section coupled with lightweight concrete are benefit to the thermal and sound insulation, etc. Cur-rently, these lightweight blocks are suggested to serve as the masonry blocks, which have insignificant requirement for the mechanical strength. Even though the regular hol-low sections are applied in current study, the results will provide experimental basis and references for manufac-turing more complex and more flexible structures. It will be applicable to design some stress adaptable structures through topological optimization algorithm.

The advanced 3DCP is still under development with various restrictions, such as weaker strength than block casted counterpart, scale limitation by the printer dimen-sions, etc., to prevent its general practical applications. Currently, these structures can only be applied in the pure compression conditions or serve as the masonry blocks which are of insignificant requirement for the mechani-cal capacities. Automatic reinforcement, size effect, envi-ronmental degradation, smart feedback shall be further addressed to enhance the applicability of such a technol-ogy [30, 31]. Nevertheless, it is very promising for its general practical application in the real-life construction

sectors. Further research will be devoted to explore the frontiers of assembly construction method based on the 3DP structural components.

Acknowledgements The authors acknowledge the financial support of the Research Fund of The State Key Laboratory of Coal Resources and safe Mining, CUMT (SKLCRSM17KFA03), the National Natural Sci-ence Foundations of China (Nos. 51808183 and 51878241) and Hebei Science and Technology Department (18391203D).

References

1. Sousa LC, Sousa H, Castro CF, António CC, Sousa R. A new lightweight masonry block: thermal and mechanical performance. Arch Civ Mech Eng. 2014;14:160–9.

2. De Schutter G, Lesage K, Mechtcherine V, Nerella VN, Habert G, Agusti-Juan I. Vision of 3D printing with concrete—techni-cal, economic and environmental potentials. Cement Concr Res. 2018;112:25–36.

3. Ma G, Li Y, Wang L, Zhang J, Li Z. Real-time quantification of fresh and hardened mechanical property for 3D printing material by intellectualization with piezoelectric transducers. Constr Build Mater. 2020;241:117982.

4. Li Z, Wang L, Ma G. Mechanical improvement of continuous steel microcable reinforced geopolymer composites for 3D print-ing subjected to different loading conditions. Comp Part B: Eng. 2020;187:107796.

5. Ma G, Salman NM, Wang L, Wang F. A novel additive mor-tar leveraging internal curing for enhancing interlayer bonding of cementitious composite for 3D printing. Constr Build Mater. 2020;244:118305.

6. Li Z, Wang L, Ma G. Method for the enhancement of buildability and bending resistance of 3D printable tailing mortar. Int J Con-crete Structures and Materials. 2018;12:37–45.

7. Feng P, Meng X, Zhang H. Mechanical behavior of FRP sheets reinforced 3D elements printed with cementitious materials. Comp Struct. 2015;134:331–42.

8. Zhang Y, Zhang Y, She W, Yang L, Liu G, Yang Y. Rheological and harden properties of the high-thixotropy 3D printing concrete. Constr Build Mater. 2019;201:278–85.

9. Buswell RA, Leal WR, Jones SZ, Dirrenberger J. 3D printing using concrete extrusion: a roadmap for research. Cement Con-crete Res. 2018;112:37–49.

10. Gosselin C, Duballet R, Roux P, Gaudillière N, Dirrenberger J, Morel P. Large-scale 3D printing of ultra-high performance con-crete—a new processing route for architects and builders. Mater Des. 2016;100:102–9.

11. Zhao X, Liu C, Zuo L, Wang L, Zhu Q, Wang M. Investigation into the effect of calcium on the existence form of geopolymerized gel product of fly ash based geopolymers. Cement Concr Compos. 2019;103:279–92.

12. Zhou B, Wang L, Ma G, Zhao X, Zhao X. Preparation and proper-ties of bio-geopolymer composites with waste cotton stalk materi-als. J Clean Prod. 2020;245:118842.

13. Sanjayan JG, Nematollahi B, Xia M, Marchment T. Effect of surface moisture on inter-layer strength of 3D printed concrete. Constr Build Mater. 2018;172:468–75.

14. Zhang C, Hou Z, Chen C, Zhang Y, Mechtcherine V, Sun Z. Design of 3D printable concrete based on the relationship between flowability of cement paste and optimum aggregate content. Cem Concr Comp. 2019;104:103406.

Table 5 Comparison between the numerical modeling and physical test

Cellular Truss Triangle Lattice

Peak compressive load Numerical 72.2 kN 50.2 kN 69.9 kN 96.2 kN Test 82.0 kN 60.4 kN 75.2 kN 95.8 kN

Peak flexural displacement Numerical 0.62 mm 0.75 mm 0.76 mm 0.57 mm Test 0.58 mm 0.83 mm 0.75 mm 0.52 mm


1 3

of 17 16

15. Ma G, Li Z, Wang L, Wang F, Sanjayan J. Mechanical anisot-ropy of aligned fiber reinforced composite for extrusion-based 3D printing. Constr Build Mater. 2019;202:770–83.

16. Gong J, Zeng W, Zhang W. Influence of shrinkage-reducing agent and polypropylene fiber on shrinkage of ceramsite concrete. Con-str Build Mater. 2018;159:155–63.

17. Che T, Pan B, Ouyang J. The laboratory evaluation of incorporat-ing ceramsite into HMA as fine aggregates. Constr Build Mater. 2018;186:1239–46.

18. Agustí-Juan I, Müller F, Hack N, Wangler T, Habert G. Potential benefits of digital fabrication for complex structures: environmen-tal assessment of a robotically fabricated concrete wall. J Clean Prod. 2017;154:330–40.

19. Xiong C, Chu M, Liu J, Sun Z. Shear behavior of precast concrete wall structure based on two-way hollow-core precast panels. Eng Struct. 2018;176:74–89.

20. Monajemi H, Mazinani I, Ong ZC, Khoo SY, Kong KK, Karim R. Using local stiffness indicator to examine the effect of hon-eycombs on the flexural stiffness of reinforced concrete beams. Measurement. 2015;64:157–62.

21. Li F-H, Han B, Zhang Q-C, Jin F, Lu TJ. Buckling of a standing corrugated sandwich plate subjected to body force and terminal load. Thin-Walled Struct. 2018;127:688–99.

22. Ma G, Li Z, Wang L. Printable properties of cementitious material containing copper tailings for extrusion based 3D printing. Constr Build Mater. 2018;162:613–27.

23. Wu P, Wang J, Wang X. A critical review of the use of 3-D print-ing in the construction industry. Autom Constr. 2016;68:21–31.

24. Liao Y, Wei X. Penetration resistance and electrical resistivity of cement paste with superplasticizer. Mater Struct. 2014;47:563–70.

25. Xu J, Ding L, Love P. Digital reproduction of historical building ornamental components: from 3D scanning to 3D printing. Autom Constr. 2017;76:85–96.

26. Lim S, Buswell RA, Le TT, Austin SA, Gibb AGF, Thorpe T. Developments in construction-scale additive manufacturing pro-cesses. Autom Constr. 2012;21:262–8.

27. Chinese National Standard, Standard for test method of mechani-cal properties on ordinary concrete, GB/T 50081-2002.

28. Xu WJ, Wang S, Zhang HY, Zhang ZL. Discrete element model-ling of a soil-rock mixture used in an embankment dam. Int J Rock Mech Min Sci. 2016;86:141–56.

29. Skarzynski L, Nitka M, Tejchman J. Modelling of concrete frac-ture at aggregate level using FEM and DEM based on X-ray μCT images of internal structure. Eng Fract Mech. 2015;147:13–35.

30. Ma G, Li Z, Wang L, Bai G. Micro-cable reinforced geopoly-mer composite for extrusion-based 3D printing. Mater Lett. 2019;235:144–7.

31. Marchment T, Sanjayan J. Mesh reinforcing method for 3D con-crete printing. Autom Constr. 2020;109:102992.

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

mechanical beha3dted lightweight concrete structure … › content › pdf › 10.1007 ›...

Documents