This study systematically investigates the role of lattice–matrix stiffness contrast in governing confinement and mechanical performance of cementitious composites reinforced by 3D-printed auxetic (negative Poisson's ratio) lattices. Through combined compression testing, numerical simulations, and representative volume element (RVE) analysis, the mechanistic link between stiffness ratio and macroscopic response is established. The results demonstrate that sufficient stiffness contrast is a prerequisite for activating auxetic-induced confinement, enabling the translation of lattice lateral contraction into effective confinement on the cementitious matrix. Auxetic cementitious composites with 3D-printed steel lattice achieved a compressive strength exceeding 80 MPa (nearly 300% higher than plain mortar and polymer lattice reinforced composites). The specific energy absorption was 90% greater than the theoretical sum of the steel lattice and matrix, owing to the strong confinement and synergy enabled by the stiffness contrast. In contrast, polymer lattice reinforced composites, despite possessing the same geometry and similar negative Poisson's ratios, exhibited limited confinement efficiency as the low stiffness suppressed the transfer of auxetic deformation to matrix. RVE analyses revealed that the stiffness contrast between the lattice and matrix governs the mesoscale confinement behavior, which in turn influences the macroscopic strength, ductility, and energy dissipation capacity of auxetic cementitious composites. These findings establish stiffness contrast as the governing design parameter for auxetic cementitious composites and provide a basis for tailoring architected cementitious composites.

The use of Additive Manufacturing (AM) to create reinforcements for cementitious composites has become a popular research topic in recent years. One illustrative example is the integration of 3D-printed auxetic reinforcements into cementitious matrices, which exhibit superior energy absorption due to their negative Poisson's ratio. This presents the opportunity to tailor the Poisson's ratio of reinforcements to align with local stress distributions and enhance structural efficiency. In this study, Tailored Poisson's Ratio-reinforcements (TPR) were proposed, characterized by a linear gradient of Poisson's ratios along the height of the reinforcement to accommodate varying stress profiles within beams. Specifically, the top chords of TPR exhibit negative Poisson's ratios (auxetic), undergoing lateral contraction under compression and providing confinement to the surrounded matrix. Conversely, the bottom chords possess positive Poisson's ratios, contributing to lateral contraction under tension. These lateral deformations cause a shift in the principal stress state of the confined matrix, extending the loading path in stress space and actively delaying failure. Three novel Tailored Poisson's Ratio-reinforced Cementitious Composite (TPRCC) designs are developed and tested under four-point bending in this study. Experimental recordings indicate increases in load capacity and toughness of up to 191% and 6900% with respect to plain mortar, respectively.

Lattice reinforcement (LR) demonstrates great potential in enhancing cementitious matrices due to its ability to be strategically designed and additively manufactured to optimize composite properties. To fully exploit the synergy between LR and cementitious matrix, a deep understanding of the reinforcing mechanisms is essential. In this study, five lattice designs with various configurations and sizes were examined through uniaxial tensile tests on dog-bone specimens. It was observed that geometric characteristics, including auxetic behavior, significantly influenced the mechanical properties of lattice structures. At the composite level, the flexural performance of lattice-reinforced cementitious composites (LRCC) was investigated through four-point bending tests. It was found that up to 23-fold enhancements in energy absorption capacity can be achieved with a low reinforcing ratio of 3.5 %. Acoustic emission tests and CT scanning provided valuable insights into the distinct reinforcing mechanisms between auxetic and non-auxetic lattice designs. Furthermore, Finite Element Method (FEM) simulations confirmed that auxetic LR effectively mitigated interfacial debonding.

One particularly interesting class of mechanical metamaterials are those having a negative Poisson's ratio, which are referred to as ‘auxetics’. Because of their geometrical complexity, auxetic designs cannot always be easily created. However, Additive Manufacturing (AM) methods like material extrusion in 3D printing present the opportunity to construct auxetic structures. Nevertheless, extruded 3D printed material can be highly anisotropic. Before 3D printed auxetics manufactured through material extrusion can be used in engineering applications, it is important to generate powerful simulation tools that can reliably reproduce and foretell their mechanical characteristics irrespective of their form and intricacy. In view of this, the current work proposes printing path-dependent models based on an experimentally validated multi-scale modelling scheme using the Lattice Beam Model (LBM). This is done by first representing idealized microstructures of extruded 3D printed polymers through geometric models and simulating these on the material scale. The aim is to explicitly model the inter-layer and intra-layer bonds that exist in material extruded 3D printed parts by assigning experimentally obtained interface properties that significantly differ from the bulk material. On the auxetic structure scale, two planar auxetic designs are modelled using the determined material scale relationships as input: Re-Entrant (RE) and Rotating Square (RS). In terms of mechanical response, the experimentally and numerically obtained force displacement curves agree reasonably well: the stiffness of the modelled auxetic designs fit well with the experimentally measured ones while the LBM simulations generally provide a good estimation in strength. Finally, it has been shown on both the material and auxetic structure scales that incorporation of the interfacial bond strengths in simulations of extruded 3D printed polymers is important, because neglecting these results in significant overestimation of the strength.

A novel highly compressible auxetic cementitious composite (ACC) is developed in this work. Contrary to conventional cementitious materials, such as plain concrete and fiber reinforced concrete, the ACC shows strain-hardening behavior under uniaxial compression: the stress continuously increases with strain up to approximately 40 % strain. On one hand, in the early compression stage, the ACC exhibit highly recoverable deformability of 10 % strain under cyclic loading (20 times higher than the constituent cementitious material). In addition, the ACC shows fatigue damage until the stiffness/strength and energy dissipation plateau values are reached after 500 cycles. At 2.5 % strain amplitude, the plateau stiffness/strength is approximately 120 MPa/3 MPa, while these values are only 25 MPa/1.2 MPa at 5 % strain amplitude. In contrast, the energy dissipation plateau of the ACC is independent from the amplitude and remains at 0.05 J/cm3. On the other hand, due to the strain-hardening behavior, the ACC exhibits significantly improved energy dissipation capacity compared to both the conventional cementitious materials and the auxetic frame. This behavior is achieved by a tailored composite action: integrating cementitious mortar with 3D printed thermoplastic polyurethane (TPU) auxetic frame. A rotating-square auxetic mechanism was designed for the TPU frame for the ACC to achieve the tailored cracking behavior. The horizontal ACC cells enable large deformability by enlarging the crack width under the confinement of the auxetic frame, while the vertical cells work as stiffening phase to ensure load resistance. Owing to the outstanding mechanical properties, the ACC shows great potential to be applied in engineering practice where high compressive deformability is required, for instance yielding elements for squeezing tunnel linings.

This study investigates the mechanical properties of cementitious composites with 3D-printed auxetic lattices, featuring negative Poisson's ratios (auxetic behavior) in multiple directions. These lattices were fabricated using vat photopolymerization 3D printing, and three base materials with varying stiffness and deformation capacities were analyzed to determine their impact on the composites’ mechanical behavior. To unravel the reinforcing mechanisms of multidirectional auxetic lattices, which exhibit auxetic behavior in both planar and out-of-plane directions, X-ray computed tomography (X-ray CT) was utilized to analyze composite damage evolutions under different strain levels. The micro-CT characterization reveals that auxetic lattices more effectively constrain crack growth and dissipate energy by distributing stress evenly within the cement matrix. In contrast, due to lack of lateral confinement, the non-auxetic lattice reinforced composites primarily dissipate energy through extensive crack propagation and interfacial damage, leading to lower peak strength. When strain exceeding 5%, although the confinement from the auxetic behavior diminished with crack propagation, the lattice can still maintain the composite's structural integrity, resulting in 1.7 times higher densification energy than conventional cement-based materials. These findings provide valuable insights for designing auxetic lattice-reinforced cementitious composites with enhanced load-bearing capacity and improved dissipation capabilities.