Design And Analysis Of Mechanical Metamaterials Simultaneously Integrating Programmable Poisson’s Ratio And Thermal Expansion

Metamaterials can achieve supernormal or abnormal physical properties that traditional materials do not have through special microstructural design,which has a wide range of application values.The shapes and sizes of the metamaterials with programmed Poisson’s ratio and the metamaterials with programmed thermal expansion can be controlled in the load field and temperature field respectively,which has aroused extensive research.It is an important development direction of metamaterials with multi-function integration to realize integrated control of the Poisson’s ratio and thermal expansion.However,the current metamaterials based on bi-material curved beams do not consider the difference in thermal expansion coefficient between the layers of bi-material curved beams that the theory is not accurate,and most of them are articulated,which adds difficulties to engineering manufacturing.The design of metamaterials for the integrated program of Poisson’s ratio and thermal expansion is very limited and cannot provide sufficient reference and selection for engineering applications.Therefore,this paper first optimizes the analytical solution of bi-material curved beams and then designs a series of multi-directional programmable thermal expansion metamaterials with fixed connections based on bi-material curved beams.Furthermore,two kinds of bi-material curved beam re-entrant triangular metamaterial and bi-material curved beam re-entrant honeycomb metamaterials with the integrated program of thermal expansion Poisson’s ratio are designed.The main achievements are as follows:（1）In this paper,theoretical analysis proves that the thermal expansion coefficient difference between the lower and middle layers of the bi-material curved beams can reach 10ppm/℃,which cannot be ignored.Three kinds of programmable thermal expansion metamaterials with fixed connections are designed based on bi-material curved beams.Theoretical analysis and simulation show that the three metamaterials can program the thermal expansion coefficient from positive to negative.Then the coupling between relative density and thermal expansion coefficient and the specific thermal expansion of the three metamaterials are analyzed.The results show that in the case of negative thermal expansion,the coefficients of thermal expansion and the relative density are competitive with the increase ofθ,synergistic with the change of ₁L,and competitive first and then synergistic with the change of m.The absolute values of negative thermal expansion coefficients of TS,QS,and HS of metamaterials increase in turn with the same lightweight level.（2）In this paper,a bi-material curved beam re-entrant triangular metamaterial ES with the integrated program of Poisson’s ratio and thermal expansion is designed.According to the deformation characteristics of metamaterial in load field and temperature field,the other two kinds of bi-material curved beam re-entrant triangular metamaterial are designed.Then Poisson’s ratio of metamaterials is analyzed by theory and numerical simulation.The thermal expansion of metamaterials is simulated.The results show that the metamaterials can program the Poisson’s ratio and thermal expansion before and after optimization.The program range of Poisson’s ratios for the optimized metamaterials CE and CX increases.The program range of thermal expansion for the optimized metamaterial CE is also increased.（3）In this paper,a bi-material curved beam re-entrant honeycomb metamaterial with integrated control of Poisson’s ratio and thermal expansion is designed.The structural dimensions are constrained to prevent overlapping inside and outside cells.Poisson’s ratio and thermal expansion of metamaterials are analyzed theoretically and verified by simulation.The results show that the Poisson’s ratio and the thermal expansion coefficient in X and Y directions can be programmed by changing the structural parameters.In this paper,through design optimization,theoretical analysis,and finite element analysis,the programmable Poisson’s ratio and thermal expansion coefficient performance of the designed metamaterials are completely analyzed and studied,which provides an important theoretical basis for engineering application.