فراماده مکانیکی دو بعدی جدید با نسبت پواسون منفی
Abstract
1- Introduction
2- Modelling and deformation mechanism
3- Characterization of mechanical properties
4- Conclusions
References
Abstract
Artificial auxetic materials with negative Poisson’s ratio enable distinctive elastic response in the direction orthogonal to the loaded direction, i.e. shrinking when compressed and expanding when stretched, compared to conventional materials. Such distinctive mechanical characteristic makes auxetic materials unique in practice. Current studies in this aspect focus mainly on the realization of beam-dominated microstructures such as re-entrant and chiral lattices and of cellular microstructures with orthogonal elliptical hole pattern. In this study, a novel two-dimensional auxetic microstructure is designed by introducing peanut-shaped holes in solid bulk matrix. Compared to the microstructure with elliptical hole pattern, the present design can produce slightly larger negative Poisson’s ratio and achieve significantly lower stress level. The samples consisting of a number of centimeter-scale unit cells with the peanut-shaped holes are fabricated efficiently via additive manufacturing technique. Experiment and finite element simulation of tensile test are carried out on the specific sample to demonstrate the auxetic effect of the present design and simultaneously verify the computational model. Finally, effects of some parameters on Poisson’s ratio, which may control the auxetic behavior of the present microstructure, are discussed for better understanding deformation mechanism of the proposed auxetic material.
Introduction
The concept of metamaterials with specially designed artificial microstructure made by additive manufacturing technology has recently received more and more attention because of its unconventional physical properties that are previously inaccessible in conventional materials [1–4]. With these man-made metamaterials, engineering materials with various properties have been developed including negative Poisson’s ratio (auxetic properties) [5–11], zero/negative thermal expansion materials [12,13], cloaking materials [14,15], phononic materials [16–19], twistable materials [20,21], and materials with vibration absorption [22,23]. Among these examples, mechanical consistence between longitudinal and orthogonal transverse elastic deformations has been achieved in two-dimensional (2D) and three-dimensional (3D) cellular metamaterials with well-designed cellular topologies [24], i.e. re-entrant shape (Fig. 1a), chiral shape (Fig. 1b) and elliptical hole shape (Fig. 1c) [5–11]. In the static case, such mechanical consistence is conflicted to the fact that a conventional elastic solid cannot expand or shrink laterally when stretched or compressed longitudinally (Fig. 1d) [6,25,26]. It has been revealed that the auxetic behavior of a material can be regarded as a consequence of rotation of elastic cell when it is subjected to a compressive or tensile load [5]. Therefore, auxetic structures with negative Poisson’s ratio are beneficial to enhancing shear rigidity, indentation resistance, toughness, energy dissipation ability and acoustic absorption ability in various applications [27–31]. However, the current re-entrant and chiral metamaterials [9,10] with negative Poisson’s ratio are generally designed to have beamdominated microstructures with bending dominated topologies. As a result, they are known to have low macroscopic stiffness, high flexibility, and high porosity. More seriously, joints with sharp corners in the re-entrant and chiral auxetic structures could lead to high stress concentration [32]. As an alternative to the beam-dominated auxetic microstructures, the orthogonal elliptical hole pattern in solid material was revealed to be beneficial in achieving controllable auxetic response. However, the elliptical hole usually leads to high stress level too. In order to achieve the balance of stiffness and flexibility, and meanwhile possess smoothed boundary and controllable porosity, in this study, a new two-dimensional elastic cellular metamaterial with a negative Poisson’s ratio is designed, fabricated, and characterized.