The Negative Poisson’s Ratio Properties Of The Curved Shell And Its 3D Combination Structures

Mechanical metamaterials have attracted the research of domestic and foreign scholars due to their special mechanical properties.As a mechanical metamaterial with excellent mechanical properties,negative Poisson’s ratio materials have been applied in aerospace,vehicle engineering and biomedical applications.The current research on negative Poisson’s ratio structure is mainly focused on the design of new structures,static analysis and impact resistance properties.Not enough attention has been paid to the stress distribution and stress concentration phenomen on in the structure.To reduce the stress concentration phenomenon,maintaining the structure smooth and continuous is an effective method.In this paper,the negative Poisson’s ratio properties of structures such as bi-sinusoidal curved shell were verified and analyzed,and the mechanism of negative Poisson’s ratio in smooth curved shells were expounded.For bi-sinusoidal smooth curved shell,a simplified analytical model of negative Poisson’s ratio was proposed.Mid-surface equations of new curved shells were formulated by additive combination of different periodic functions.Threedimensional curved shell combination structures were designed which can realize the positive and negative Poisson’s ratio.The negative Poisson’s ratio effect and stress concentration effect of the bisinusoidal curved shell are verified and analyzed by means of experimental and numerical analysis.The effect of the arrangement of the convex con igurations in the bi-sinusoidal curved shell on the negative Poisson’s ratio effect was analyzed,and the checkerboard pattern of the convex con igurations was proved to be a necessary condition for the negative Poisson’s ratio.The deformation of the special section of the bi-sinusoidal curved shell under tensile load is obtained.The mechanism of the in-plane negative Poisson’s ratio effect resulting from out-of-plane deformation is described.The effects of structural and material parameters on the mechanical properties of the bi-sinusoidal curved shell were investigated.The results show that relative amplitude and relative thickness of the curved shell are the main structural influencing parameters.Unlike the general negative Poisson’s ratio structures,t he material Poisson’s ratio can also affect the Poisson’s ratio of the bi-sinusoidal curved shell.The stress concentration phenomenon of bi-sinusoidal curved shell is analyzed.The results show that the bi-sinusoidal curved shell has a low stress concentration factor.A simplified analytical model composing interactive orthogonal curved beam array for the negative Poisson’s ratio of bi-sinusoidal curved shell was established.The interaction between the curved beams is introduced to realize the coupling of the deformation in the principal directions.The deformation of two principal directions of the beam array model were calculated.The Poisson’s ratio of the bi-sinusoidal curved shell was predicted.The coupling between the beams was realized by introducing a linear elastic spring,and the influence of the interaction parameters on the Poisson’s ratio was analyzed.The distribution of the Poisson’s ratio with the geometric parameters was obtained for different material Poisson’s ratios.The influence of geometric and material parameters on Poisson’s ratio was analyzed.The method of regulating the structural Poisson’s ratio by changing the relative amplitude,relative thickness and material Poisson’s ratio of the structure was mastered.The negative Poisson’s ratio effect of three periodic curved shells with checkerboard pattern was analyzed,and the results show that the mid-surface equation of the curved shell was a factor to determine whether the structure has the negative Poisson’s ratio property.A method of constructing curved shells by translational sweeping smooth curves is proposed and sinusoidal sweeping curved shells that can realize bi-directional negative Poisson’s ratio effect was obtained.The negative Poisson’s ratio effect of the structures can be enhanced by increasing the degree bending of the generating line.An additive combination of different periodic functions was proposed for the design of the mid-surface equations of the curved shell.The results of the combination of equal weights were analyzed to obtain the influence of different functions on the final curved shell.The selection method of the function for different design requirements was given.The effect of the combined weights on the Poisson’s ratio and stress concentration factor of the curved shell was analyzed.Positive,negative and zero Poisson’s ratios designs of two and three function combinations were achieved.The design method of 3D curved-shell combination structures with different Poisson’s ratio combinations was proposed by embedding curved-shell units or flat units into 3D orthogonal frame structures.Four 3D curved-shell combination structures with different Poisson’s ratio combinations were obtained and fabricated.The negative Poisson’s ratio effect of the 3D curved-shell combination structures was verified by experimental and numerical analysis.The results shows that the Poisson’s ratio of 3D curved-shell combination structures was determined by the nature of the repeating unit in the corresponding plane.The instantaneous Poisson’s ratio was introduced to characterize the negative Poisson’s ratio effect at finite strain,and the variation of the Poisson’s ratio of four structures was investigated.The adjacent repeating units interact with each other so that the flat unit turned into checkerboard pattern under the load.The negative Poisson’s ratio mechanism of the 3D curved-shell combination structures was described.The out-of-plane deformation of the repeating units in the structure caused the corresponding negative Poisson’s ratio of the overall structure.The Poisson’s ratio of the structure is smaller than that of the smooth curved shell due to the restriction of the frame and the adjacent repeating units.3D curvedshell combination structures with different negative Poisson’s ratio character istics can be obtained by selecting load-bearing units with different parameters.