A comparison between rotating squares and anti-tetrachiral systems: Influence of ligaments on the multi-axial mechanical response

Mizzi, Luke; Sorrentino, Andrea; Spaggiari, Andrea; Castagnetti, Davide

doi:10.1177/09544062211043145

Cited by 18 publications

(9 citation statements)

References 60 publications

(75 reference statements)

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“…It has been shown for systems with cubic symmetry and deformation mechanisms with limited degrees of freedom, such as rotating squares, that while PR varies very little with changes of loading direction, the changes in the Young's modulus and, particularly, the shear modulus can be considerable. [76] This effect of average PR appearing as isotropic has been observed and discussed earlier. [65] In Figure 7, it is worth to note that diminishing auxetic properties also occur for the decreasing σ 0 =σ values (especially apparent for the C2 system).…”

Section: Resultssupporting

confidence: 65%

Poisson's Ratio of f.c.c. Hard‐Sphere Crystals with Cubic Supercells Containing Four Nanochannels Filled by Hard Spheres of Another Diameter

Narojczyk

Tretiakov

Wojciechowski

2022

Physica Status Solidi (b)

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It is known that a face centered cubic (f.c.c.) crystal of identical hard spheres containing a periodic array of nanochannels, oriented along one of the principal crystallographic directions and filled by hard spheres of another diameter, shows a significant decrease of its Poisson's ratio with respect to pristine crystal. This indicates an essential enhancement of auxetic properties by such nanoinclusions. The present work describes studies of the f.c.c. hard‐sphere crystal containing four nanochannel arrays, oriented along the [ 111 ] direction and its images with respect to cubic symmetry group transformations and selected in such a way as to not affect the symmetry of the crystal. The elastic properties of the current model are analyzed under different thermodynamic conditions and for different sizes of inclusions. These studies reveal that the auxetic properties of the system vanish when the diameters of inclusion spheres are greater than the ones forming the matrix f.c.c. crystal and, in the case of the widest nanochannels, also when these diameters are smaller. The studies are performed by Monte Carlo computer simulations in the isothermal–isobaric (NpT) ensemble, using the Parrinello–Rahman approach.

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Section: Resultssupporting

confidence: 65%

Poisson's Ratio of f.c.c. Hard‐Sphere Crystals with Cubic Supercells Containing Four Nanochannels Filled by Hard Spheres of Another Diameter

Narojczyk

Tretiakov

Wojciechowski

2022

Physica Status Solidi (b)

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“…On the other hand, as illustrated in Figure 5.A, the Type II design manifested a strongly different deformation behavior respect to its idealized model, showing a large reduction in auxeticity, with an excellent qualitative agreement between the FE model and the experimental tests. This is probably the result of the relative higher length of ligaments, since this modification in the auxeticity is typically observed for rotating unit models with chiral characteristics subject to off-axis loading regimes [26], [34]. As we expected, the peak of stresses in the metamaterials are primarily located at the joint's regions of the systems, see Figure 5.B, where Type I architecture exhibits the highest level of stress intensity, particularly, along the vertical ligaments between the rotating units.…”

Section: Discussionmentioning

confidence: 89%

Three-Dimensional Auxetic Mechanical Metamaterials Based on Triangular Prism Architecture

Sorrentino,

Castagnetti

2023

10th ECCOMAS Thematic Conference on Smart Structures and Materials

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Auxetic mechanical metamaterials are a class of architected materials that exhibit the exotic characteristic of a negative Poisson's ratio (NPR). This work aimed to evaluated the NPR potential of differently-oriented architected structures consisted of hinged triangular prisms connected by their corners. By implementing kinematic models of the systems, we assessed the deformation mechanism of the idealized structure: the models allow to investigate some geometrical variants of the rotating polyhedrons with different orientation schemes, which are at 45° to each other. The computational results showed that the Poisson's ratio (PR) of the system varies from -0.3 up to -1.3, depending both on geometrical parameters of the polyhedral elements and on the orientation of the unit cells. To further investigate the deformation behavior of the metamaterial, we designed prismatic architectures with chiral connections between the rotating units, which were validated using finite element (FE) method. The numerical simulations reveal a remarkably different auxetic properties between these designs, with a PR ranging between -0.08 and -0.70. Hence, physical models were additively manufactured in Onyx material and experimentally tested under uniaxial compression, showing an excellent agreement with the numerical predictions. Our results demonstrate the highly tunable NPR ability of such mechanical metamaterials, with a possible application in the biomedical field.

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“…Typical example of 2D motif is the rotating squares mechanism which possesses a Poisson's ratio equal to −1 [31]. Rigid unit motifs are not restricted to regular squares: also rectangles, triangles, rhombi, parallelogram cells, irregular shape units [32][33][34] and rotating cells with chiral ligaments [35,36] can be retrieved from the literature. By analogy, 3D rotating structures can be designed using the structural motif of a 2D rotating unit structure, resulting in 3D polyhedral metamaterials able to generate auxetic effect.…”

Section: Introductionmentioning

confidence: 99%

Novel polyhedral mechanical metamaterial exhibiting negative Poisson’s ratio

Sorrentino

Castagnetti

2023

Smart Mater. Struct.

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The work presents a novel polyhedral mechanical metamaterial based on rotating triangular prisms connected by their corners, which possesses the ability to attain large values of negative Poisson’s ratio (NPR). Through a kinematic model of the proposed rotating structure, we evaluate the auxeticity of the system by varying the geometrical parameters of the polyhedrons composing the elementary cell of the structure. The kinematic results highlight the peculiar NPR of the system, whose values are nearly constant over significant strain ranges. Focusing on the most promising auxetic mechanisms we designed chiral architectures that replace the ideal hinges at the corners with curved-shape ligaments, and validated these configurations through 3D printed specimens. The specimens were tested under uniaxial compression and simulated through finite element analyses. Experimental results exhibited an excellent agreement with computational predictions in terms of elastic modulus and auxeticity, showing a value of Poisson’s ratio up to -1.3 for one of the designs. Our findings demonstrate the highly auxetic property of rotating polyhedral systems, which allow the design of novel architected materials useful, for example, in biomechanical applications.

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A comparison between rotating squares and anti-tetrachiral systems: Influence of ligaments on the multi-axial mechanical response

Cited by 18 publications

References 60 publications

Poisson's Ratio of f.c.c. Hard‐Sphere Crystals with Cubic Supercells Containing Four Nanochannels Filled by Hard Spheres of Another Diameter

Poisson's Ratio of f.c.c. Hard‐Sphere Crystals with Cubic Supercells Containing Four Nanochannels Filled by Hard Spheres of Another Diameter

Three-Dimensional Auxetic Mechanical Metamaterials Based on Triangular Prism Architecture

Novel polyhedral mechanical metamaterial exhibiting negative Poisson’s ratio

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