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Intricacies of various printing parameters on mechanical behaviour of additively constructed concrete

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Abstract

Extrusion-based three-dimensional (3D) printing has seen rapid growth in the last few years, including in the construction sector owing to its reduced construction cost, minimal labour intervention, freeform design, implementation of complex architectural structural design and more. However, like other technologies, additive construction or 3D concrete printing has several limitations such as additional requirement of printing performance of the material along with hardened mechanical properties, construction challenges of the additive construction in the case of large-scale reinforced concrete structures, accuracy and performance of the digital 3D print model are the few. Moreover, the lack of understanding about the effect of various printing-related parameters on the load capacity of additively manufactured structural element is another barrier in the popularisation of such technology. Consequently, in this article, a finite-element (FE)-based framework is utilised and the load–deflection of additively constructed concrete beam under 4-point loading is simulated. In the model, measured geometrical specifications of additively manufactured specimen (length and sectional curvatures, varying width and thickness at different layers along the beam depth), are utilised. Each concrete filament is modelled using coupled damage-plasticity-based material behaviour, whereas cohesive zone-based constitutive behaviour is used to represent the interfacial bond characteristics between two printed filaments. In the model, the input properties such as mechanical properties of concrete (e.g. compressive and tensile strength) and the tensile bond strength value of the interfaces are obtained from the respective experiments conducted. A detailed sensitivity analysis for the various printing-related parameters, e.g. tensile and shear bond strength, bond stiffness, plastic or failure displacement of bond, pores or gaps that exist between two consecutive printed filament and the number of printed layers, have been conducted. In the simulation, one parameter at a time is varied keeping all other fixed and the resultant effect on the load–deflection behaviour is analysed. The simulated results of the concrete specimen for various above-mentioned printing parameters are also compared with the results obtained from the perfect bond condition. Consequently, simplified statistically fitted relations are proposed that helps in quick evaluation of the variability in load-carrying capacity of additively constructed concrete beam for variable bond or printing conditions. The results of such studies would be helpful for the research community in the design and prediction of load capacity of additively manufactured concrete beam.

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Data availability

Data will be made available on request.

Abbreviations

\({f}_{{\text{c}}}, {f}_{{\text{t}}}\) :

Uniaxial compressive and tensile stress

\({f}_{{\text{cu}}}, {f}_{{\text{tu}}}\) :

Uniaxial compressive and tensile strength

\({\varepsilon }_{{\text{c}}}, {\varepsilon }_{{\text{t}}}\) :

Compressive and tensile strain under uniaxial loading

\({\varvec{\sigma}}, \overline{{\varvec{\sigma}}}\) :

Total and stress tensor

\(\rho\) :

Mass density

\(\underline{b}\) :

Body force vector

\(\underline{u}, \underline{t}\) :

Displacement and tractor vector

\(d\) :

Damage in concrete

\({{\varvec{D}}}_{0}^{el}\) :

Initial elastic tensor

\({\widetilde{\varepsilon }}^{pl}\) :

Effective plastic strain

\({\varepsilon }_{{\text{c}}}^{pl},{\varepsilon }_{{\text{t}}}^{pl}\) :

Compressive and tensile plastic strain

\({\widehat{\tilde{\sigma }}}_{{\text{max}}}\) :

Maximum principal stress

\({f}_{{\rm b}0},{f}_{{\rm c}0}\) :

Biaxial and uniaxial compressive yield stress

\({K}_{{\text{c}}}\) :

Ratio of second stress invariant on the tensile meridian to that of the compressive meridian at initial yield point

\({\overline{f} }_{{\text{c}}},{\overline{f} }_{{\text{t}}}\) :

Effective compressive and tensile cohesion stress.

\(\psi\) :

Dilatation angle measured in the p-q plane,

\(\epsilon\) :

Eccentricity parameter used in flow potential

\({d}_{{\text{c}}},{d}_{{\text{t}}}\) :

Compressive and tensile damage variable of concrete layer

\({u}_{{\text{t}}}^{pl},{u}_{{\text{t}}}^{ck}\) :

Plastic and cracking displacement under tensile loading

\({E}_{0}\) :

Undamaged elastic modulus

t i, δ i :

Traction and separation associated with bond (i = n, s stands for normal and shear direction)

\({k}_{i}\) :

Bond stiffness in ith direction (i = n, s stands for normal and shear direction)

\({k}_{i,0}\) :

Initial bond stiffness in ith direction (i = n, s stands for normal and shear direction)

\({t}_{i,0}\) :

Bond strength in ith direction (i = n, s stands for normal and shear direction)

\({\delta }_{i,0},{\delta }_{i,{\text{f}}}\) :

Slip at damage initiation and failure of bond in ith direction (i = n, s stands for normal and shear direction)

\({d}_{{\text{b}}}\) :

Damage in bond element

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Acknowledgements

The authors thank the Ministry of Housing & Urban Affairs for financial support in conducting the research work. The authors also thank the Director, CSIR-Central Building Research Institute, Roorkee for permitting the publication of the paper.

Funding

This study was funded by Ministry of Housing and Urban Affairs under Project No.GAP-0152.

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  1. CSIR-Central Building Research Institute, Roorkee, Uttarakhand, 247667, India

    Biswajit Pal, Ajay Chourasia & Ashish Kapoor

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  1. Biswajit Pal
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All the authors contributed to the study conception; experimental works involved in this study. BP and AC designed and performed the numerical analysis. All the authors contributed in writing the manuscript.

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Correspondence to Biswajit Pal.

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Pal, B., Chourasia, A. & Kapoor, A. Intricacies of various printing parameters on mechanical behaviour of additively constructed concrete. Archiv.Civ.Mech.Eng 24, 41 (2024). https://doi.org/10.1007/s43452-023-00853-x

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