## 1 Introduction  
Auxetics which possess negative Poisson's ratios show a transverse expansion or contraction effect under uniaxial tension or compression load, respectively. The counter-intuitive properties of tension-expansion deformation lead to enhanced mechanical and other physical performances, such as large plane strain fracture toughness, high shear modulus, low fatigue crack propagation rate, superior specific strength, excellent shock and sound absorption, etc. [1; 2; 3; 4; 5] Since [PERSON] [6] manufactured a novel foam structure with a negative Poisson's ratio (NPR) of \(-0.7\), a variety of cellular structures with auxetic features have been proposed from nano-scale to macro-scale levels [7]. However, the low mechanical performance of auxetic cellular structures largely restricts their applications, especially in load-bearing fields [8].  
By changing the orientation or stacking sequence of laminate layers, laminated structures with auxetic properties can be obtained with excellent mechanical performance. The Poisson's ratio cannot take a negative value according to experimental investigations, however, for laminated composites, the inter-laminar stresses cause overall auxetic behavior which can be controlled by special layup [9]. [PERSON] [10] reported an early work on composite laminates with out-of-plane negative Poisson's ratios and concluded that the Poisson's ratios can be positive or negative, mainly depending on fiber orientation. The out-of-plane NPR can affect the vibration [11], dynamic responses [12] and low velocity impact [13] responses of laminated structures. For in-plane NPR, [PERSON] [14] studied the unique behavior of the Poisson's ratio of laminated composites and observed a minimum value of Poisson's ratio of \(-0.369\) for unbalanced bi-directional laminates. [PERSON] [9] used GA to obtain the minimum negative Poisson's ratio of \(-0.3536\) for a laminated composite plate with the configuration of (15/60/15).  
Buckling is a common failure mode for an aerospace structure under compression. Many researchers have studied the buckling of rectangular composite plates [15; 16], and the buckling behavior of auxetic materials has also received significant attention. [PERSON] [17] indicates that the buckling performance of a rectangular plate under uniaxial compression can be significantly improved by replacing the traditional material, that has a positive Poisson's ratio, with an auxetic material. [PERSON] [18; 19] reported that the post-buckling behaviors of pressure-loaded graphene-reinforced metal-matrix-composite laminated cylindrical shells are affected substantially by the in-plane NPR. [PERSON] studied the analysis and design of composite structural components such as fuselage and wings, and proposed optimization methods [20].  
The aim of this study is to investigate the buckling enhancement of a laminated rectangular plate under uniaxial compression through an auxetic composite layup design. As a brief representation of laminate stiffness, lamination parameters are employed to obtain the NPR envelope and buckling load with negative Poisson's ratio. The structure of this paper is as follows: firstly, the Poisson's ratio of laminated structures and feasible region of lamination parameters are described briefly. Next, a mechanism analysis of the enhanced buckling for the laminated orthotropic auxetic plate is provided in Section 3. Section 4 introduces the results and discussion for various lamination parameters and Poisson's ratios. Finally, Section 5 gives the conclusion.