Abstract
Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts—one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles and . Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle (related to tension-dominated struts) has the highest influence on the sign of Poisson’s ratio and its extent, while angle (related to compression-dominated struts) has the lowest influence on the Poisson’s ratio. Nevertheless, the compression-dominated struts (defined by angle ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson’s ratio for a specific range of and angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.
Highlights
The Poisson’s ratio is defined as the ratio of the negative value of transverse strain to the longitudinal strain of a body subjected to uniaxial stress [1]
To have a better understanding of the main factors influencing the overall performance of the auxetic lattice structure, the effect of each main geometrical parameter of the structure such as relative density, angle θ, and angle φ are studied individually
According to analytical relationships of mechanical properties of the re-entrant unit cell obtained in Section 2.1, elastic modulus, Poisson’s ratio, and yield stress of the structure depend on seven geometrical main parameters, namely, r1, r2, r3, l1, l2 or l3, θ, and φ
Summary
The Poisson’s ratio is defined as the ratio of the negative value of transverse strain to the longitudinal strain of a body subjected to uniaxial stress [1]. There are some materials that reveal the opposite behavior of common materials and present negative Poisson’s ratio, which means that their transverse dimensions increase (or decrease) when they are subjected to axial tensile (or compressive) loads [3]. These materials have been given different names in the literature, including anti-rubber, dilational [4], and auxetic materials [5]. The term “auxetic” is currently the most widely accepted name used for materials with a negative Poisson’s ratio. Auxetic behavior has been observed in a few natural materials such as cristobalite (polymorphic silicones) [6], metals [7], zeolites [8], silicates [9,10], and some biological tissues such as cancellous bone [11], tendons [12], and some animal skins [13,14]
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