Maximum Stresses in Rectangular Auxetic Membranes

Abstract

Auxetic materials exhibit a negative Poisson's ratio. Herein, the performance of rectangular auxetic membranes, under uniform load, is evaluated in terms of the maximum stress encountered. To facilitate convenient calculation, empirical modeling is conducted on the exact solution to reproduce displacement coefficients that are sufficiently accurate. A dimensionless maximum stress is then introduced to allow the effect from the membrane's Poisson's ratio and aspect ratio to be directly observed. Results reveal that 1) the dimensionless maximum stress reduces monotonically and nonmonotonically for conventional and auxetic membranes, respectively, 2) for the same Poisson's ratio magnitude the stresses in auxetic membranes are lower than those from conventional ones, 3) the optimal Poisson's ratio, on the basis of dimensionless maximum stress minimization, falls within the negative range, and 4) the dimensionless maximum stress minimization is especially effective for square membranes as well as very long and narrow membranes. It is therefore recommended that material auxeticity be taken into account-alongside geometrical and other material properties-in designing membranes and highly compliant very thin plates.

Cancellation of Auxetic Properties in F.C.C. Hard Sphere Crystals by Hybrid Layer-Channel Nanoinclusions Filled by Hard Spheres of Another Diameter

“…Novel fabrics with auxetic properties [28,29,30,31], targeted for personal applications have been developed. Alongside the experimental studies, new theoretical models exhibiting negative Poisson's ratio [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46] have been proposed. The search for the negative Poisson's ratio in known and naturally occurring materials revealed that around 70% of metals with cubic symmetry have such properties [47].…”

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

“…[19,20] In this work, we use the more recent classification [20] which distinguishes between nonauxetics, partial auxetics, and auxetics. Vast potential applications of auxetic materials drive the theoretical and experimental investigations, which branch into auxetic metamaterials, [21][22][23][24][25][26][27][28] models, [16,[29][30][31][32][33][34][35][36][37][38][39][40][41] structures, [42][43][44][45][46][47][48] polymers, [49,50] composites, [51] foams, [52][53][54] and fabrics. [55][56][57][58] Most of the research on auxetics is focused either on developing new materials or searching for auxetic properties in existing ones.…”

Self-rotating 3D chiral mechanical metamaterials

“…Mechanical metamaterials [1][2][3][4] are a class of novel materials that exhibit their effective properties due to their rational design rather than the chemical composition. Based on their structure, these systems can exhibit counterintuitive mechanical properties such as negative Poisson's ratio (auxetic behaviour) [1,2,[5][6][7][8][9][10][11][12][13][14], negative stiffness [15][16][17][18][19][20] or negative compressibility [21][22][23][24][25]. In recent years, a continuous growth of the metamaterials research field led to their implementation in the case of superior biomedical [26,27] and protective devices [28,29].…”