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Additively manufactured auxetics (structures exhibiting a negative Poisson’s ratio) offer a unique combination of enhanced mechanical strength and energy absorption. These properties can be further improved through strategic material placement and architectural design. This study investigates the feasibility of fabricating bi-material rotating-square auxetic structures composed of flexible and rigid constituents in their squares and hinges. Rotating-square auxetic structures are manufactured via material extrusion using rigid polylactic acid (PLA) and flexible thermoplastic polyurethane (TPU) to explore the effects of material distribution on mechanical performance and failure characteristics at the macro (i.e., component) and meso (i.e., cell) scales. Baseline tests are conducted to quantify single- and bi-material interfacial strength and failure modes under normal, shear, and combined loading conditions. Upon validation of interface integrity, single- and bi-material auxetic structures are fabricated and tested in uniaxial compression. Relative to the TPU single-material structure, the PLA square-TPU hinge structure provides a 33% increase in structural stiffness, increases energy absorption, delays the global densification strain by 10%, yields a structural Poisson’s ratio at least 0.3 lower than its single-material counterpart through global axial strains of 20%, and demonstrates partial shape recovery. Multiscale experimental analyses supplemented by a kinematic model reveal the rotation-dependent stiffening mechanisms of these structures, highlighting the benefits of flexible hinge materials. Bi-material structures with flexible hinges are shown to have bilinear trends in structural stiffness and energy absorption, not intrinsic to their single-material counterparts. These findings highlight the potential of bi-material design strategies in advancing the functionality and tunability of auxetic structures for the next generation of mechanical metamaterials. 

Auxetic (negative Poisson’s ratio) structures made from rotating squares have attracted considerable attention due to their tunable shape control, strength, and strain energy absorption capacity. The present study aims to explore the interrelations between mesoscale kinematics and the macroscopic mechanical behavior of additively manufactured rotating-square auxetics under compressive loads. Specifically, correlations between the rotational degree of freedom of the squares, mechanical deformation of the cell hinges, and the macroscopic nonlinear mechanical and Poisson’s behaviors are investigated using experimental measurements supplemented by mathematical models. Structures with variable cell hinge thicknesses are fabricated by stereolithography additive manufacturing technique and then subjected to compressive loads applied at quasi-static and dynamic conditions with several orders of magnitude difference in strain rate. Multiscale mechanical deformation of the structure in each case is analyzed using digital image correlation (DIC). Experimental characterizations indicate strongly nonlinear and rate-sensitive auxetic behaviors in the examined structures. The role of cell hinge thickness is discussed in terms of the mechanical constraint that these components impose on the rotational degree of freedom of the solid squares in the structure, concurrently causing a nonlinear strain hardening behavior. 

This study provides an in-depth analysis of the mechanical behavior of rotating-square auxetic structures under various strain rates. The structures are fabricated using stereolithography additive manufacturing with a flexible resin. Mechanical tests performed on structures include quasi-static, intermediate, and high strain rate compression tests, supplemented by high-speed optical imaging and two-dimensional digital image correlation analyses. In quasi-static conditions (5 × 10–3 s-1), multiscale measurements reveal the correlation between local and global strains. It is shown that cell hinges play a significant role in structural deformation and load-bearing capacity. In drop tower impact conditions (intermediate strain rate of ca. 200 s-1), the auxetic structures display significant strain rate hardening compared to loading at quasi-static rates. The thin-hinge structures maintain a Poisson's ratio of approximately -0.8, showing higher auxeticity than slow-rate compression tests. High strain rate conditions (ca. 2000s-1) activate additional deformation mechanisms, including a delayed state of equilibrium exemplified by a heterogeneous distribution of lateral strains, possibly due to stress wave interactions and inertial stresses. The study further reveals nonlinear correlations between Poisson's ratio, strain, and strain rate, indicating reduced auxeticity at higher strain rates. These observations are discussed in terms of complex wave interactions and the strain rate hardening characteristics of the base polymer.