Investigations On Buckling And Yielding Behaviors Of Some Bending-dominant Lattice Metamaterials

In recent years,with the development of additive manufacturing technology,lat-tice metamaterials have been attracting more and more attentions from both industry and academia.Two kinds of bending-dominant periodic lattice metamaterials,named as BDPL（A）and BDPL（B）,which are composed of curved struts,have been studied in this paper.The buckling and yielding behaviors of BDPL（A）,as well as the energy absorption of two kinds of BDPL under quasi-static and dynamic loading are studied by numerical simulation and experimental analysis.The unconventional mechanical properties of BDPL are revealed,and the relation between these novel macroscopic properties and the microstructural parameters of the material is discussed.This study can provide a useful guidance for optimal designs of mechanical metamaterials.This work includes the following points:（1）The in-plane and out-of-plane buckling behaviors of BDPL are studied.Through numerical simulations and experimental observations,it is found that when BDPL（A）is subjected to uniaxial compression,two kinds of elastic instability behav-iors may occur:in-plane buckling and/or out-of-plane buckling.Furthermore,the buck-ling behaviors are affected by several microstructural parameters.The occurrence dia-gram of in-plane/out-of-plane buckling is given by parameterization research,which provides useful guidance for the design optimization of this kind of materials.The re-sults show that the critical buckling load can be reduced by increasing the curvature of the struts.When the slenderness ratio（S.R.）and relative density(ρ_rel)are large,out-of-plane buckling occurs first.（2）A theoretical method for analyzing the initial yield of BDPL is established.Based on the principle of strain energy equivalence,the macroscopic effective stiff-nesses of lattice are calculated.The relation between the displacements of lattice joints and the macroscopic uniform strain prescribed can be obtained by combining a method of particular displacement fields and finite element analyses.Furthermore,by analyzing the relation between deformation and stress of a single periodic unit cell,forces on both ends of each curved strut can be expressed as a linear function of the macroscopic stresses.An empirical formula for calculating effective stress is employed to consider the contributions of both axial force and bending moment.Finally,the initial yield sur-face of BDPL can be figured out by comparing the effective stress of each curved strut to the yield strength of the matrix material.The above method is applicable to the curved strut lattice and it is an important improvement to the well-known method for lattices comprising axial-tension bars in the literature.（3）Some other characteristics of the two lattices under dynamic and static loads are numerically analyzed.Responses of BDPL（A）and BDPL（B）under quasi-static and dynamic loading conditions are simulated based on finite element method.We have studied influences of microstructural parameters on the out-of-plane flexural stiffness of BDPL（A）.The mechanical response of BDPL（A）under uniaxial compression is in-vestigated to reveal the effect of strut curvature on the crushing performance.The en-ergy absorption characteristics of hyperelastic and elastoplastic BDPL（B）under dy-namic and quasi-static loads are investigated.The results show that when BDPL（B）is under quasi-static compression,an obvious shear deformation occurs along the direc-tion perpendicular to the compression.While under high speed impact-like compres-sion,BDPL（B）made of hyperelastic TPU possesses a longitudinal wave along the im-pact direction,and a transverse shear wave perpendicular to the impact direction,among which the latter can not happen in traditional materials.