The Prediction On Mechanical Properties Of Hierarchical Aluminum Honeycombs

Honeycomb materials have been widely used in many industrial fields because of their high specific strength.However,compared with the performance of the corresponding solid material,the traditional honeycombs still havetheir shortcomings.Hierarchical honeycombs can improve the mechanical properties of the material by increasing the number of layers.In addition,the mechanical properties of hierarchical nano-honeycombs are different from those of macroscopic materials due to the surface stress of nano-materials.A user element subroutine was incorporated into the traditional finite element（FE）method for investigating the mechanical behavior of self-similar hierarchical aluminum honeycombs（SSHAHs）,in which the surface stresswas considered.Then based on the proposed FE SSHAHs model,the size-dependent mechanical properties of SSHAHs were especially studied.In addition,molecular dynamics（MD）simulations were used instead of experiments to explore the mechanical properties of self-similar hierarchical aluminum honeycombs（elastic modulus E and compressive strengthσ）.The conclusions are illustrated as follows:（1）A user element subroutine is incorporated into the traditional finite element（FE）method for investigating the mechanical behavior of self-similar hierarchical aluminum honeycombs（SSHAHs）,in which the surface elastic effect is considered.The user subroutine is firstly validated by the classical plate-hole model,showing a good agreement with the theoretical results.Then based on the proposed FE SSHAHs model,the size-dependent mechanical properties of SSHAHs along different directions are especially studied.The numerical results indicate that the influences of surface effect are approximately identical along armchair and zigzag directions.With the increase in the order of the SSHAHs,the strength enhancing efficiency is not noteworthy due to the（111）surface effect,while the softening effect is significantly growing.The proposed approach provides a new method to study the mechanical properties of hierarchical honeycombs.（2）The molecular dynamic（MD）simulations were used to investigate the mechanical behavior（elastic modulus E and compressive strengthσ）of self-similar hierarchical aluminum honeycomb（SSHAH）subjected to in-plane compressive loadings.The influence of relative density,hierarchy order,and length ratio on mechanical properties of SSHAHs were especially investigated.The MD results show that,the in-plane elastic modulus of SSHAHs decrease with the decrease of relative density.Due to the surface stress of nano SSHAHs,the elastic modulus calculated from the Gibson model are underestimated by comparing with those predicted from MD simulations.Moreover,by comparing the deformation mechanism of the SSHAHs with different orders,we found that,their mechanical properties can be optimized in the hierarchical structures by connecting a hexagon at the angular point of the 1^stt honeycomb structure.Compared to the 1^storder honeycombs,more dislocations are generated in the 2ⁿdd and 3^thh honeycomb structures under compression loadings,resulting in greater energy absorption capacity.Our results also indicate that,the 2ⁿdd nano SSHAHs have the best comprehensive mechanical properties.In other words,the mechanical behavior of nano SSHAHs cannot be infinitely enhanced by increasing the number of orders.In the end,the MD results show that,when the length ratios is 0.3,the2^ndSSHAHs have the best in-plane mechanical properties.This study is helpful for the optimal design of SSHAHs with enhanced performance.（3）The molecular dynamic（MD）simulations were used to investigate the mechanical behavior（elastic modulus E and compressive strengthσ）of self-similar hierarchical aluminum honeycomb（SSHAH）subjected to out-of-plane compressive loadings.The influence of relative density,hierarchy order,and length ratio on mechanical properties of SSHAHs were especially investigated.The MD results show that the out-of-plane mechanical properties of self-similar hierarchical aluminum honeycomb are obviously superior to the in-plane.Moreover,out-of-plane mechanical behavior of nano SSHAHs cannot be enhanced by increasing the number of orders,only related to the wall thickness of the honeycomb structure.The MD results also show that the out-of-plane mechanical behavior of SSHAHs enhanced with the increasing of wall thickness.In the end,the MD results show that,when the length ratios is 0.4,the 2ⁿdd SSHAHs have the best out-of-plane mechanical properties,which is different from the optimal in-plane length ratio.