Auxetic metamaterials with two component exhibit widely potential engineering applications due to their exotic mechanical properties. In this work, a novel straight-arc coupled structure (SACS) is designed by introducing a circular arc structure to a classical re-entrant structure. This work aims to explore the linear and geometrical nonlinear mechanical of SACS at large strains. According to the Castigliano’s second theorem, the in-plane linear theoretical model is established to obtain equivalent Poisson's ratio and elastic modulus. A geometrical nonlinear model is further established based on large deflection theory and chain algorithm. The finite element method is used to verify the prediction of the theoretical solution, and linear and nonlinear mechanical properties of the SACS are studied by numerical simulation. The influence of geometric parameters re-entrant angle and arc radius on the mechanical properties of the SACS is investigated to compare the linear and nonlinear mechanical properties. The linear numerical simulation of straight-arc coupled structure with two transverse ribs (SACS-TR) and classical re-entrant honeycomb structure with two transverse ribs (CRS-TR) with the same dimension is carried out to analyze the in-plane elastic properties. These results demonstrate that considering the geometric nonlinear can predict the actual structural deformation more accurately, which is verified by the quasi-static compression experiment results at large strains. The straight-arc coupled structure design can enhance the auxetic effect and structure Young’s moduli under same dimension.

When the sensor works in a limited environment, its accuracy is easily affected by unnecessary strain loss. The key to improve accuracy is to reduce the transverse strain of the dielectric layer structure. It is an innovative technology to construct zero Poisson's ratio dielectric layer to limit the lateral strain of dielectric layer under normal pressure. The porous metamaterial dielectric layer with zero Poisson's ratio is constructed based on the paper-cutting theory. The equivalent nonlinear mechanical model is established by use of Bernoulli Euler beam theory and energy method. The analytical expressions of equivalent Poisson's ratio and equivalent Young’s modulus are given, and the necessity of considering geometric nonlinear large deformation is revealed. An improved variable step iterative method is proposed in order to solve the problem of equivalent internal force analysis caused by geometric deformation nonlinearity. The key of this method is to determine the displacement at the free end under the premise of considering the nonlinear superposition of the rigid body motion of the curved bar of the metamaterial. Based on the equivalent nonlinear mechanical model, the structural deformation characteristics of the dielectric layer structure in the linear small deformation stage and the nonlinear large deformation stage are analyzed. The results of theoretical, finite element simulation and experimental research reveal the necessity of considering geometric nonlinear factors in the practical application of the structure, which means that the foundation is theoretically and experimentally laid for the design of porous elastic dielectric layer of flexible capacitive pressure sensor.