# Investigating the Poisson Ratio of 3D Printed Concrete
###### Abstract  
Poisson's ratio, defining the lateral to longitudinal strain of a material under uniaxial load, is an extensively used material property in engineering analysis and design. For conventionally cast concrete, an isotropic static Poisson ratio typically ranges between 0.15 to 0.25. However, no ratio has been established for 3D printed concrete, and is currently widely assumed to be 0.2 and isotropic in computational modelling applications. This layer-wise additive manufacturing technology is notorious for yielding orthotropic mechanical properties due to the presence of weak interlayer regions at the structural level and elongated oblate voids at the material level. This study therefore aims to characterise the static Poisson ratio of printed concrete. Specimens were prepared from a printed element and uniaxially tested both parallel and perpendicular to the printing direction. Digital image correlation technology was employed to facilitate the capturing of specimen strains, followed by micro-computed tomography scans to determine void topography. The results indicate larger Poisson ratios apply for 3D printed concrete compared to its cast counterpart; up to 17 and 33% increases were obtained when printed specimens were tested perpendicular and parallel to the printing direction, respectively. This orthotropic behaviour is ascribed to the oblate voids present in the printed specimens. 3D printed concrete; Poisson's ratio; experimental testing; digital image correlation; micro-computed tomography +
Footnote †: journal: Applied Sciences  
3D printed specimens are elongated, with their largest dimension in the printed direction followed by the transverse direction and the smallest in the vertical direction. As a premise for a follow-up study [8], it was demonstrated that (i) 3D printed concrete exhibits reduced mechanical performance compared to its cast equivalent, and (ii) orthotropic compressive strengths are prevalent in 3D printed concrete. This orthotropic mechanical nature of 3D printed concrete is widely reported in the literature [9; 10; 11; 12; 13; 14; 15]. The theoretical grounding of this study's hypothesis lies in the stress concentrations that develop around micro-voids in a continuum under uniaxial loading. A study by [PERSON] et al. [16] demonstrated that as a void becomes more oblate (as was shown in [7] for 3D printed concrete), the compressive stress developed at its extreme lateral sides/tips increases under uniaxial loading. This localized, concentrated compressive stress reduces as a void becomes more pro-late; hence the difference between the (relatively constant) tensile stress developed at poles and the compressive stress developed at sides reduces. Following hereon, it can be deduced that the magnitude of strain experienced in a porous material is influenced by its void topology, where predominantly oblate or prolate voids could lead to orthotropy. Due to the current lack of information on the Poisson ratio for 3D printed concrete, several studies conducted on finite element modelling of printed concrete have adopted typical isotropic Poisson values of conventionally cast concrete, i.e., 0.2 [17; 18; 19; 20; 21; 22] and 0.21 [23]. Thus, no account was made for possible anisotropy in this regard. Similar to fresh state buildability modelling, comprising plastic yielding and elastic buckling failure mechanisms [24], the Poisson value for fresh printable concrete was assumed to be 0.3 [25; 26; 27], mainly adopted from the early experimental work conducted by [PERSON], [PERSON] and [PERSON] [28; 29]. In another study by [PERSON] et al. [30], the fresh state Poisson value was assumed to be 0.5, which, as mentioned earlier, is considered incompressible. The saturation state of fresh concrete, i.e., the amount of free water available to fill pores, influences the Poisson ratio; therefore, fresh concrete can possess Poisson values ranging up to that of water, namely 0.5 [31].