Geometric nonlinear analysis of dielectric layer based on concave paper-cut structure with zero Poisson’s ratio

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.