Introducing the hierarchy into cellular materials has attracted increasing attention in the effort to pursue improved absorbed-energy abilities and impact resistance. In this paper, the dynamic crushing properties and energy absorption capacities of joint-based hierarchical honeycombs with different topologies were explored by means of explicit dynamic finite element (FE) analysis using ANSYS/LS-DYNA. Four types of joint-based hierarchical honeycombs with uniform cell-wall thickness were firstly constructed by substituting each vertex of regular honeycombs with a smaller self-similar cell (hexagon or square). The respective influences of hierarchical parameters and impact velocities on in-plane dynamic deformation modes, mechanical characteristic and energy absorption of joint-based hierarchical honeycombs were discussed. Research results showed that the hierarchy had a far greater influence on the in-plane deformation modes of honeycombs. Compared with regular honeycombs, the dynamic plateau stress and specific energy absorption of joint-based hierarchical honeycombs can be improved if the proper hierarchical parameters were chosen. Adding the joint-based hierarchy into regular honeycombs can enhance the crushing stress efficiency (CSE) of the specimens. In addition, by introducing a non-dimensional dynamic sensitivity index, the dynamic shock enhancement of hierarchical honeycombs was also investigated. These researches are useful for the multi-objective dynamic optimization design and controllable properties of cellular materials.
GibsonLJAshbyMF.Cellular solids: structure and properties.
Cambridge:
Cambridge University Press, 1997.
2.
SunYLLiQM.Dynamic compressive behaviour of cellular materials: a review of phenomenon, mechanism and modeling. Int J Impact Eng2018;
112: 74–115.
3.
ZhuFWangZHZhaoLM, et al.
Analytical investigation and optimal design of sandwich panels subjected to shock loading. Mater Des2009;
30: 91–100.
4.
ChenLMDuBZhangJ, et al.
Numerical study on the projectile impact resistance of multi-layer sandwich panels with cellular cores. Lat Am J Solids Struct2016;
13: 2576–2595.
5.
PattofattoSElnasriIZhaoH, et al.
Shock enhancement of cellular structures under impact loading: part II analysis. J Mech Phys Solids2007;
55: 2672–2686.
6.
QiuXMZhangJYuTX.Collapse of periodic planar lattices under uniaxial compression. Part II: dynamic crushing based on finite element simulation. Int J Impact Eng2009;
36: 1231–1241.
7.
HuLLYuTX.Dynamic crushing strength of hexagonal honeycombs. Int J Impact Eng2010;
37: 467–474.
8.
MukhopadhyayTAdhikariS.Effective in-plane elastic moduli of quasi-random spatially irregular hexagonal lattices. Int J Eng Sci2017;
119: 142–179.
9.
MukhopadhyayTAdhikariS.Equivalent in-plane elastic properties of irregular honeycombs: an analytical approach. Int J Solids Struct2016;
91: 169–184.
10.
RuanDLuGWangB, et al.
In-plane dynamic crushing of honeycombs – a finite element study. Int J Impact Eng2003;
28: 161–182.
11.
LiuYZhangXC.The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs. Int J Impact Eng2009;
36: 98–109.
12.
ZhangXCAnLQDingHM, et al.
Influence of cell micro-structure on the in-plane dynamic crushing of honeycombs with negative Poisson’s ratio. J Sandwich Struct Mater2015;
17: 26–55.
13.
ZhangXCAnLQDingHM.Dynamic crushing behavior and energy absorption of honeycombs with density gradient. J Sandwich Struct Mater2014;
16: 125–147.
14.
HuLLHeXLWuGP, et al.
Dynamic crushing of the circular-celled honeycombs under out-of-plane impact. Int J Impact Eng2015;
75: 150–161.
15.
XuSBeynonJHRuanD, et al.
Strength enhancement of aluminium honeycombs caused by entrapped air under dynamic out-of-plane compression. Int J Impact Eng2012;
47: 1–13.
16.
XuSBeynonJHRuanD, et al.
Experimental study of the out-of-plane dynamic compression of hexagonal honeycombs. Compos Struct2012;
94: 2326–2336.
17.
WangZGTianHQLuZJ, et al.
High-speed axial impact of aluminum honeycomb–experiments and simulations. Compos Part B Eng2014;
56: 1–8.
18.
FratzlPWeinkamerR.Nature’s hierarchical materials. Prog Mater Sci2007;
52: 1263–1334.
19.
ChenQPugnoN.Bio-mimetic mechanisms of natural hierarchical materials: a review. J Mech Behav Biomed Mater2013;
19: 3–33.
20.
QingHMishnaevskyL.3D hierarchical computational model of wood as a cellular material with fibril reinforced, heterogeneous multiple layers. Mech Mater2009;
41: 1034–1049.
21.
AjdariAJahromiBHPapadopoulosJ, et al.
Hierarchical honeycombs with tailorable properties. Int J Solids Struct2012;
49: 1413–1419.
22.
OftadehRHaghpanahBPapadopoulosJ, et al.
Mechanics of anisotropic hierarchical honeycombs. Int J Mech Sci2014;
81: 126–136.
SunYTChenQPugnoN.Elastic and transport properties of the tailorable multifunctional hierarchical honeycombs. Compos Struct2014;
107: 698–710.
27.
SunYTPugnoN.In plane stiffness of multifunctional hierarchical honeycombs with negative Poisson’s ratio sub-structures. Compos Struct2013;
106: 681–689.
28.
SunYTWangBPugnoN, et al.
In-plane stiffness of the anisotropic multifunctional hierarchical honeycombs. Compos Struct2015;
131: 616–624.
29.
ZhuHXYanLBZhangR, et al.
Size-dependent and tunable elastic properties of hierarchical honeycombs with regular square and equilateral triangular cells. Acta Mater2012;
60: 4927–4939.
ZhuHXZhangHCYouJF, et al.
The elastic and geometrical properties of micro- and nano-structured hierarchical random irregular honeycombs. J Mater Sci2014;
49: 5690–5702.
34.
SeifiHJavanARGhaedizadehA, et al.
Design of hierarchical structures for synchronized deformations. Sci Rep2017;
7: 41183.
35.
SunFFLaiCLFanHL, et al.
Crushing mechanism of hierarchical lattice structure. Mech Mater2016;
97: 164–183.
36.
LiuLLiDDongL.Mechanical properties of 2D hierarchical re-entrant cellular structures with Voronoi sub-structures. EPL2018;
123: 16002.
37.
ZhangYLuMHWangCH, et al.
Out-of-plane crashworthiness of bio-inspired self-similar regular hierarchical honeycombs. Compos Struct2016;
144: 1–13.
38.
QiaoJXChenCQ.In-plane crushing of a hierarchical honeycomb. Int J Solids Struct2016;
85-86: 57–66.
39.
ZhengJJZhaoLFanHL.Energy absorption mechanisms of hierarchical woven lattice composites. Compos Part B Eng2012;
43: 1516–1522.
40.
AnLQZhangXCWuHX, et al.
In-plane dynamic crushing and energy absorption capacity of self-similar hierarchical honeycombs. Adv Mech Eng2017;
9: 1–15.
41.
QiuXMZhangJYuTX.Collapse of periodic planar lattices under uniaxial compression, part I: quasi-static strength predicted by limit analysis. Int J Impact Eng2009;
36: 1223–1330.
42.
HallquistJO.LS-DYNA theory manual.
Livermore, CA:
Livermore Software Technology Corporation, 2006.
43.
ZhangXCDingHMAnLQ, et al.
Numerical investigation on dynamic crushing behavior of auxetic honeycombs with various cell-wall angles. Adv Mech Eng2015;
7: 679678.
44.
LiQMMagkiriadisIHarriganJJ.Compressive strain at the onset of the densification of cellular solids. J Cell Plast2006;
42: 371–392.
45.
LiuYWuHXWangB.Gradient design of metal hollow sphere (MHS) foams with density gradients. Compos Part B Eng2012;
43: 1346–1352.
46.
ZhangJJWangZHZhaoLM.Dynamic response of functionally graded cellular materials based on the voronoi model. Compos Part B Eng2016;
85: 176–187.
47.
KucewiczMBaranowskiPMałachowskiJ, et al.
Modelling, and characterization of 3D printed cellular structures. Mater Des2018;
142: 177–189.
48.
ReidSRPengC.Dynamic uniaxial crushing of wood. Int J Impact Eng1997;
19: 531–570.
