Cellular Auxetic Structures for Mechanical Metamaterials: A Review

Abstract

Recent advances in lithography technology and the spread of 3D printers allow us a facile fabrication of special materials with complicated microstructures. The materials are called “designed materials” or “architectured materials” and provide new opportunities for material development. These materials, which owing to their rationally designed architectures exhibit unusual properties at the micro- and nano-scales, are being widely exploited in the development of modern materials with customized and improved performance. Meta-materials are found to possess superior and unusual properties as regards static modulus (axial stress divided by axial strain), density, energy absorption, smart functionality, and negative Poisson’s ratio (NPR). However, in spite of recent developments, it has only been feasible to fabricate a few such meta-materials and to implement them in practical applications. Against such a backdrop, a broad review of the wide range of cellular auxetic structures for mechanical metamaterials available at our disposal and their potential application areas is important. Classified according to their geometrical configuration, this paper provides a review of cellular auxetic structures. The structures are presented with a view to tap into their potential abilities and leverage multidimensional fabrication advances to facilitate their application in industry. In this review, there is a special emphasis on state-of-the-art applications of these structures in important domains such as sensors and actuators, the medical industry, and defense while touching upon ways to accelerate the material development process.

Elasticity Approach to Predict Shape Transformation of Functionally Graded Mechanical Metamaterial under Tension

“…where u 0 , v 0 , and w are arbitrary constants of integration that indicate the translation and rotation of the plate. Since the structure is symmetrical, regardless of the rotation and rigid displacements, the displacement of the plate is expressed using Equations ( 12) and (13).…”

“…This means a relatively low number of design parameters are necessary to design re-entrant lattices. That is probably one reason why these particular unit cell designs have received a great deal of attention with respect to other types of unit cell designs (e.g., chiral, rigid rotational structures, and crumpled and perforated sheet models [13]). For example, only by changing the angle of re-entrant unit cells, one can achieve a wide range of elastic properties (i.e., elastic stiffness and positive or negative values of Poisson's ratio) [14].…”

An Overview of Additive Manufacturing of Polymers and Associated Composites

“…These auxetic metamaterials are not limited to polymers only, they can also be made with metal AM processes. Some of the practical applications of auxetic structure range from stents for angioplasty [ 193 ], shape memory alloy cellular antenna [ 194 ], footwear sole [ 195 ], and auxetic polyethylene in textile industries [ 196 ].…”

An Auxetic System Based on Interconnected Y-Elements Inspired by Islamic Geometric Patterns

“…With the advent of 3D printing and other precision materials processing techniques, auxetic metamaterials have been developed [7,8]; these materials derive their properties from the designed microarchitectures rather than from properties of the base materials. The literature on auxetic systems is too voluminous to be fairly cited, and so the reader is referred only to the lists of exhaustive references collated in generic review papers on auxetic materials and structures [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and review papers on specific areas, such as auxetic textiles or fabrics [26][27][28][29], auxetic nanomaterials [30,31], chiral-based auxetics [32], applications of auxetic materials [33,34], and metamaterials with auxetic and negative stiffness inclusions [35], as well as monographs [36][37][38], across the field of auxetics. It suffices to mention that while the Poisson's ratio of anisotropic materials has no bounds, i.e., −∞ < v < ∞ [39,40], in the case of isotropic materials the bounds of Poisson's ratio are −1 ≤ v ≤ 1 for two-dimensional systems and −1 ≤ v ≤ 1/2 for three-dimensional systems, i.e.,…”