Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

The surge in machine learning research and recent advancements in 3D printing technologies have significantly enriched materials science and engineering, particularly in the domain of mechanical metamaterials, which commonly consist of periodic truss materials. Despite the extensive exploration of their tailorable properties, truss-based metamaterial design has predominantly adhered to cubic and orthotropic unit cells, a limitation arising from the conventional design method, where the type of symmetry related to the designed truss-based material is determined after the design process is done. To overcome this issue, this work introduces a groundbreaking 3D truss material designing framework that departs from this constraint by employing six distinctive material symmetries (cubic, hexagonal, tetragonal, orthotropic, trigonal, and monoclinic) within the design process. This innovative approach represents a versatile paradigm shift compared to previous design approaches. Furthermore, we are able to integrate anisotropy into the design framework, thus enhancing the property space exploration capability of the proposed design framework. Probing the property space of unit cells using our design framework demonstrates its capacity to achieve a diverse range of mechanical properties. The analysis of the generated samples shows that they can surpass the most extensive datasets available in the literature in regions where directional elastic properties are not linked by structural symmetry. The proposed method facilitates the generation of a truss dataset, which can be represented in a trainable format suitable for machine learning and data-driven approaches. This advancement paves the way for the development of robust inverse design tools for truss materials, marking a significant contribution to the mechanical metamaterial community.

References

1.
Lumpe
,
T. S.
, and
Stankovic
,
T.
,
2021
, “
Exploring the Property Space of Periodic Cellular Structures Based on Crystal Networks
,”
Proc. Natl. Acad. Sci. USA
,
118
(
7
), p.
e2003504118
.
2.
Panetta
,
J.
,
Zhou
,
Q.
,
Malomo
,
L.
,
Pietroni
,
N.
,
Cignoni
,
P.
, and
Zorin
,
D.
,
2015
, “
Elastic Textures for Additive Fabrication
,”
ACM Trans. Graph.
,
34
(
4
).
3.
Sunada
,
T.
,
2012
, “
Lecture on Topological Crystallography
,”
Japanese J. Math.
,
7
(
1
), pp.
1
39
.
4.
O'Keeffe
,
M
, and
Hyde
,
B.G.
,
2020
,
Crystal Structures
,
Courier Dover Publications
,
Mineola, NY
.
5.
Greaves
,
G. N.
,
Greer
,
A. L.
,
Lakes
,
R. S.
, and
Rouxel
,
T.
,
2011
, “
Poisson’s Ratio and Modern Materials
,”
Nat. Mater.
,
10
(
11
), pp.
823
837
.
6.
Wagner
,
M. A.
,
Lumpe
,
T. S.
,
Chen
,
T.
, and
Shea
,
K.
,
2019
, “
Programmable, Active Lattice Structures: Unifying Stretch-Dominated and Bending-Dominated Topologies
,”
Extreme Mech. Lett.
,
29
, p.
100461
.
7.
Meza
,
L. R.
,
Phlipot
,
G. P.
,
Portela
,
C. M.
,
Maggi
,
A.
,
Montemayor
,
L. C.
,
Comella
,
A.
,
Kochmann
,
D. M.
, and
Greer
,
J. R.
,
2017
, “
Reexamining the Mechanical Property Space of Three-Dimensional Lattice Architectures
,”
Acta. Mater.
,
140
, pp.
424
432
.
8.
Portela
,
C. M.
,
Greer
,
J. R.
, and
Kochmann
,
D. M.
,
2018
, “
Impact of Node Geometry on the Effective Stiffness of Non-Slender Three-Dimensional Truss Lattice Architectures
,”
Extreme Mech. Lett.
,
22
, pp.
138
148
.
9.
Paulose
,
J.
,
Meeussen
,
A. S.
, and
Vitelli
,
V.
,
2015
, “
Selective Buckling Via States of Self-Stress in Topological Metamaterials
,”
Proc. Natl. Acad. Sci. USA
,
112
(
25
), pp.
7639
7644
.
10.
Abu-Mualla
,
M.
,
Jiron
,
V.
, and
Huang
,
J.
,
2023
, “
Inverse Design of Two-Dimensional Shape-Morphing Structures
,”
ASME J. Mech. Des.
,
145
(
12
), p.
121703
.
11.
Qu
,
J.
,
Gerber
,
A.
,
Mayer
,
F.
,
Kadic
,
M.
, and
Wegener
,
M.
,
2017
, “
Experiments on Metamaterials with Negative Effective Static Compressibility
,”
Phys. Rev. X
,
7
(
4
), pp.
041060
041066
.
12.
Bückmann
,
T.
,
Thiel
,
M.
,
Kadic
,
M.
,
Schittny
,
R.
, and
Wegener
,
M.
,
2014
, “
An Elasto-Mechanical Unfeelability Cloak Made of Pentamode Metamaterials
,”
Nat. Commun.
,
5
(
1
), p.
4130
.
13.
Kumar
,
S.
,
Ubaid
,
J.
,
Abishera
,
R.
,
Schiffer
,
A.
, and
Deshpande
,
V.
,
2019
, “
Tunable Energy Absorption Characteristics of Architected Honeycombs Enabled Via Additive Manufacturing
,”
ACS Appl. Mater. Interfaces
,
11
(
45
), pp.
42549
42560
.
14.
Guell Izard
,
A.
,
Bauer
,
J.
,
Crook
,
C.
,
Turlo
,
V.
, and
Valdevit
,
L.
,
2019
, “
Ultrahigh Energy Absorption Multifunctional Spinodal Nanoarchitectures
,”
Small
,
15
(
45
), p.
1903834
.
15.
Chen
,
Y.
,
Li
,
T.
,
Scarpa
,
F.
, and
Wang
,
L.
,
2017
, “
Lattice Metamaterials With Mechanically Tunable Poisson’s Ratio for Vibration Control
,”
Phys. Rev. Appl.
,
7
(
2
), p.
024012
.
16.
Li
,
Y.
,
Baker
,
E.
,
Reissman
,
T.
,
Sun
,
C.
, and
Liu
,
W. K.
,
2017
, “
Design of Mechanical Metamaterials for Simultaneous Vibration Isolation and Energy Harvesting
,”
Appl. Phys. Lett.
,
111
(
25
), p.
251903
.
17.
Watts
,
S.
,
Arrighi
,
W.
,
Kudo
,
J.
,
Tortorelli
,
D. A.
, and
White
,
D. A.
,
2019
, “
Simple, Accurate Surrogate Models of the Elastic Response of Three-Dimensional Open Truss Micro-architectures With Applications to Multiscale Topology Design
,”
Struct. Multidiscipl. Optim.
,
60
(
5
), pp.
1887
1920
.
18.
Xu
,
S.
,
Shen
,
J.
,
Zhou
,
S.
,
Huang
,
X.
, and
Xie
,
Y. M.
,
2016
, “
Design of Lattice Structures With Controlled Anisotropy
,”
Mater. Des.
,
93
, pp.
443
447
.
19.
Chougrani
,
L.
,
Pernot
,
J.-P.
,
Véron
,
P.
, and
Abed
,
S.
,
2019
, “
Parts Internal Structure Definition Using Non-Uniform Patterned Lattice Optimization for Mass Reduction in Additive Manufacturing
,”
Eng. Comput.
,
35
(
1
), pp.
277
289
.
20.
Azizi
,
M.
,
Aickelin
,
U.
,
Khorshidi
,
H. A.
, and
Shishehgarkhaneh
,
M. B.
,
2022
, “
Shape and Size Optimization of Truss Structures by Chaos Game Optimization Considering Frequency Constraints
,”
J. Adv. Res.
,
41
, pp.
89
100
.
21.
Sigmund
,
O.
,
2000
, “
A New Class of Extremal Composites
,”
J. Mech. Phys. Solids.
,
48
(
2
), pp.
397
428
.
22.
Chen
,
D.
,
Skouras
,
M.
,
Zhu
,
B.
, and
Matusik
,
W.
,
2018
, “
Computational Discovery of Extremal Microstructure Families
,”
Sci. Adv.
,
4
(
1
), p.
eaao7005
.
23.
Bastek
,
J.-H.
,
Kumar
,
S.
,
Telgen
,
B.
,
Glaesener
,
R. N.
, and
Kochmann
,
D. M.
,
2022
, “
Inverting the Structure-Property Map of Truss Metamaterials by Deep Learning
,”
Proc. Natl. Acad. Sci. USA
,
119
(
1
), p.
e2111505119
.
24.
Maurizi
,
M.
,
Gao
,
C.
, and
Berto
,
F.
,
2022
, “
Inverse Design of Truss Lattice Materials With Superior Buckling Resistance
,”
npj Comput. Mater.
,
8
(
1
), p.
247
.
25.
Abu-Mualla
,
M.
, and
Huang
,
J.
,
2023
, “
Inverse Design of 3d Cellular Materials With Physics-Guided Machine Learning
,”
Mater. Des.
,
232
, p.
112103
.
26.
Zheng
,
L.
,
Karapiperis
,
K.
,
Kumar
,
S.
, and
Kochmann
,
D. M.
,
2023
, “
Unifying the Design Space and Optimizing Linear and Nonlinear Truss Metamaterials by Generative Modeling
,”
Nat. Commun.
,
14
(
1
), p.
7563
.
27.
Leuenberger
,
A.
,
Birner
,
E.
,
Lumpe
,
T. S.
, and
Stanković
,
T.
,
2024
, “
Computational Design of 2D Lattice Structures Based on Crystallographic Symmetries
,”
ASME J. Mech. Des.
,
146
(
7
), p.
071703
.
28.
Mao
,
H.
,
Rumpler
,
R.
, and
Göransson
,
P.
,
2020
, “
An Inverse Method for Characterisation of the Static Elastic Hooke’s Tensors of Solid Frame of Anisotropic Open-Cell Materials
,”
Inter. J. Eng. Sci.
,
147
, p.
103198
.
29.
Mao
,
H.
,
Rumpler
,
R.
,
Gaborit
,
M.
,
Göransson
,
P.
,
Kennedy
,
J.
,
O’Connor
,
D.
,
Trimble
,
D.
, and
Rice
,
H.
,
2020
, “
Twist, Tilt and Stretch: From Isometric Kelvin Cells to Anisotropic Cellular Materials
,”
Mater. Des.
,
193
, p.
108855
.
30.
Al Sabouni-Zawadzka
,
A.
,
2020
, “
Extreme Mechanical Properties of Regular Tensegrity Unit Cells in 3d Lattice Metamaterials
,”
Materials
,
13
(
21
).
31.
Li
,
Z.
,
Gao
,
W.
,
Yu Wang
,
M.
,
Wang
,
C. H.
, and
Luo
,
Z.
,
2023
, “
Three-Dimensional Metamaterials Exhibiting Extreme Isotropy and Negative Poisson’s Ratio
,”
Int. J. Mech. Sci.
,
259
, p.
108617
.
32.
Chen
,
X.
,
Moughames
,
J.
,
Ji
,
Q.
,
Martnez
,
J. A. I.
,
Tan
,
H.
,
Adrar
,
S.
,
Laforge
,
N.
,
Cote
,
J.-M.
,
Euphrasie
,
S.
,
Ulliac
,
G.
,
Kadic
,
M.
, and
Laude
,
V.
,
2020
, “
Optimal Isotropic, Reusable Truss Lattice Material With Near-Zero Poisson’s Ratio
,”
Extreme Mech. Lett.
,
41
, p.
101048
.
33.
Sigmund
,
O.
,
1995
, “
Tailoring Materials With Prescribed Elastic Properties
,”
Mech. Mater.
,
20
(
4
), pp.
351
368
.
34.
Ha
,
C. S.
,
Yao
,
D.
,
Xu
,
Z.
,
Liu
,
C.
,
Liu
,
H.
,
Elkins
,
D.
,
Kile
,
M.
,
Deshpande
,
V.
,
Kong
,
Z.
,
Bauchy
,
M.
,
2023
, “
Rapid Inverse Design of Metamaterials Based on Prescribed Mechanical Behavior Through Machine Learning
,”
Nat. Commun.
,
14
(
1
), p.
5765
.
35.
Letov
,
N.
, and
Fiona Zhao
,
Y.
,
2023
, “
Beam-Based Lattice Topology Transition With Function Representation
,”
ASME J. Mech. Des.
,
145
(
1
), p.
011704
.
36.
Makatura
,
L.
,
Wang
,
B.
,
Chen
,
Y.-L.
,
Deng
,
B.
,
Wojtan
,
C.
,
Bickel
,
B.
, and
Matusik
,
W.
,
2023
, “
Procedural Metamaterials: A Unified Procedural Graph for Metamaterial Design
,”
ACM Trans. Graph.
,
42
(
5
).
37.
Liu
,
Y.
,
Zhuo
,
S.
,
Xiao
,
Y.
,
Zheng
,
G.
,
Dong
,
G.
, and
Zhao
,
Y. F.
,
2020
, “
Rapid Modeling and Design Optimization of Multi-Topology Lattice Structure Based on Unit-Cell Library
,”
ASME J. Mech. Des.
,
142
(
9
), p.
091705
.
38.
Shubnikov
,
A.V
, and
Koptsik
,
V.A
,
1974
,
Symmetry in Science and Art
, 1 ed.,
Plenum Press
,
New York
.
39.
Cowin
,
S. C.
,
2013
,
Continuum Mechanics of Anisotropic Materials
,
Springer Science & Business Media
,
New York
.
40.
Cowin
,
S. C.
, and
Mehrabadi
,
M. M.
,
1995
, “
Anisotropic Symmetries of Linear Elasticity
,”
Appl. Mech. Rev.
,
48
(
5
), pp.
247
285
.
41.
Latture
,
R. M.
,
Begley
,
M. R.
, and
Zok
,
F. W.
,
2018
, “
Design and Mechanical Properties of Elastically Isotropic Trusses
,”
J. Mater. Res.
,
33
(
3
), pp.
249
263
.
42.
Rastegarzadeh
,
S.
,
Muthusamy
,
S.
, and
Huang
,
J.
,
2023
, “
Mechanical Profile of Smooth Cellular Materials
,”
ASME J. Manuf. Sci. Eng.
,
145
(
2
), p.
021005
.
43.
Chadwick
,
P.
,
Vianello
,
M.
, and
Cowin
,
S. C.
,
2001
, “
A New Proof that the Number of Linear Elastic Symmetries is Eight
,”
J. Mech. Phys. Solids.
,
49
(
11
), pp.
2471
2492
. The Jean-Paul Boehler Memorial Volume
44.
Dong
,
G.
,
Tang
,
Y.
, and
Zhao
,
Y. F.
,
2019
, “
A 149 Line Homogenization Code for Three-Dimensional Cellular Materials Written in Matlab
,”
ASME J. Eng. Mater. Technol.
,
141
(
1
), p.
011005
.
45.
Bensoussan
,
A.
,
Lions
,
J.-L.
, and
Papanicolaou
,
G.
,
2011
,
Asymptotic Analysis for Periodic Structures
, Vol.
374
,
American Mathematical Soc
,
Providence, RI
.
46.
Hill
,
R.
,
1952
, “
The Elastic Behaviour of a Crystalline Aggregate
,”
Proc. Phys. Soc. Section A
,
65
(
5
), p.
349
.
47.
Bi
,
Z.
,
2018
,
Finite Element Analysis Applications: A Systematic and Practical Approach
,
Academic Press
.
48.
Fiedler
,
M.
,
1973
, “
Algebraic Connectivity of Graphs
,”
Czechoslovak Math. J.
,
23
(
2
), pp.
298
305
.
49.
Qi
,
X.
,
2022
,
A Review: Random Walk in Graph Sampling
.
50.
Erdös
,
P.
, and
Rényi
,
A.
,
1959
, “
On Random Graphs I
,”
Publ. Math. Debrecen
,
6
, pp.
290
297
.
51.
Meyers
,
M. A.
, and
Chawla
,
K. K.
,
2008
,
Mechanical Behavior of Materials
,
Cambridge University Press
,
New York
.
52.
Lethbridge
,
Z. A.
,
Walton
,
R. I.
,
Marmier
,
A. S.
,
Smith
,
C. W.
, and
Evans
,
K. E.
,
2010
, “
Elastic Anisotropy and Extreme Poisson’s Ratios in Single Crystals
,”
Acta Mater.
,
58
(
19
), pp.
6444
6451
.
53.
Ting
,
T. C. T.
, and
Chen
,
T.
,
2005
, “
Poisson’s Ratio for Anisotropic Elastic Materials Can Have No Bounds
,”
Q. J. Mech. Appl. Math.
,
58
(
1
), pp.
73
82
.
54.
Vannucci
,
P.
,
2018
,
General Anisotropic Elasticity
, Vol.
85
,
Springer Singapore
,
Singapore
, pp.
19
73
.
55.
Bond
,
W. L.
,
1943
, “
The Mathematics of the Physical Properties of Crystals
,”
Bell Syst. Tech. J.
,
22
(
1
), pp.
1
72
.
56.
Ramirez-Chavez
,
I. E.
,
Anderson
,
D.
,
Sharma
,
R.
,
Lee
,
C.
, and
Bhate
,
D.
,
2022
, “
A Classification of Aperiodic Architected Cellular Materials
,”
Designs
,
6
(
4
).
You do not currently have access to this content.