A paradigm in nature is to architect composites with excellent material properties compared to its constituents, which themselves often have contrasting mechanical behavior. Most engineering materials sacrifice strength for toughness, whereas natural materials do not face this tradeoff. However, biology's designs, adapted for organism survival, may have features not needed for some engineering applications. Here, we postulate that mimicking nature's elegant use of multimaterial phases can lead to better optimization of engineered materials. We employ an optimization algorithm to explore and design composites using soft and stiff building blocks to study the underlying mechanisms of nature's tough materials. For different applications, optimization parameters may vary. Validation of the algorithm is carried out using a test suite of cases without cracks to optimize for stiffness and compliance individually. A test case with a crack is also performed to optimize for toughness. The validation shows excellent agreement between geometries obtained from the optimization algorithm and the brute force method. This study uses different objective functions to optimize toughness, stiffness and toughness, and compliance and toughness. The algorithm presented here can provide researchers a way to tune material properties for a vast number of engineering problems by adjusting the distribution of soft and stiff materials.

References

References
1.
Sih
,
G.
,
1973
, “
Some Basic Problems in Fracture Mechanics and New Concepts
,”
Eng. Fract. Mech.
,
5
(
2
), pp.
365
377
.
2.
Gao
,
H.
,
Ji
,
B.
,
Jäger
,
I. L.
,
Arzt
,
E.
, and
Fratzl
,
P.
,
2003
, “
Materials Become Insensitive to Flaws at Nanoscale: Lessons From Nature
,”
Proc. Natl. Acad. Sci.
,
100
(
10
), pp.
5597
5600
.
3.
Bonderer
,
L. J.
,
Studart
,
A. R.
, and
Gauckler
,
L. J.
,
2008
, “
Bioinspired Design and Assembly of Platelet Reinforced Polymer Films
,”
Science
,
319
(
5866
), pp.
1069
1073
.
4.
Sen
,
D.
, and
Buehler
,
M. J.
,
2011
, “
Structural Hierarchies Define Toughness and Defect-Tolerance Despite Simple and Mechanically Inferior Brittle Building Blocks
,”
Sci. Rep.
,
1
, p.
35
.
5.
Meyers
,
M. A.
,
Chen
,
P.-Y.
,
Lin
,
A. Y.-M.
, and
Seki
,
Y.
,
2008
, “
Biological Materials: Structure and Mechanical Properties
,”
Prog. Mater. Sci.
,
53
(
1
), pp.
1
206
.
6.
Yang
,
W.
,
Sherman
,
V. R.
,
Gludovatz
,
B.
,
Mackey
,
M.
,
Zimmermann
,
E. A.
,
Chang
,
E. H.
,
Schaible
,
E.
,
Qin
,
Z.
,
Buehler
,
M. J.
, and
Ritchie
,
R. O.
,
2014
, “
Protective Role of Arapaima Gigas Fish Scales: Structure and Mechanical Behavior
,”
Acta Biomater.
,
10
(
8
), pp.
3599
3614
.
7.
Launey
,
M. E.
,
Buehler
,
M. J.
, and
Ritchie
,
R. O.
,
2010
, “
On the Mechanistic Origins of Toughness in Bone
,”
Annu. Rev. Mater. Res.
,
40
(
1
), pp.
25
53
.
8.
Dunlop
,
J. W.
, and
Fratzl
,
P.
,
2010
, “
Biological Composites
,”
Annu. Rev. Mater. Res.
,
40
(
1
), pp.
1
24
.
9.
Mayer
,
G.
,
2005
, “
Rigid Biological Systems as Models for Synthetic Composites
,”
Science
,
310
(
5751
), pp.
1144
1147
.
10.
Fratzl
,
P.
,
2007
, “
Biomimetic Materials Research: What Can We Really Learn From Nature's Structural Materials?
J. R. Soc. Interface
,
4
(
15
), pp.
637
642
.
11.
Wegst
,
U.
, and
Ashby
,
M.
,
2004
, “
The Mechanical Efficiency of Natural Materials
,”
Philos. Mag.
,
84
(
21
), pp.
2167
2186
.
12.
Sanchez
,
C.
,
Arribart
,
H.
, and
Guille
,
M. M. G.
,
2005
, “
Biomimetism and Bioinspiration as Tools for the Design of Innovative Materials and Systems
,”
Nat. Mater.
,
4
(
4
), pp.
277
288
.
13.
Almeida
,
F. S.
, and
Awruch
,
A. M.
,
2009
, “
Design Optimization of Composite Laminated Structures Using Genetic Algorithms and Finite Element Analysis
,”
Compos. Struct.
,
88
(
3
), pp.
443
454
.
14.
Naik
,
G. N.
,
Gopalakrishnan
,
S.
, and
Ganguli
,
R.
,
2008
, “
Design Optimization of Composites Using Genetic Algorithms and Failure Mechanism Based Failure Criterion
,”
Compos. Struct.
,
83
(
4
), pp.
354
367
.
15.
Paluch
,
B.
,
Grediac
,
M.
, and
Faye
,
A.
,
2008
, “
Combining a Finite Element Programme and a Genetic Algorithm to Optimize Composite Structures With Variable Thickness
,”
Compos. Struct.
,
83
(
3
), pp.
284
294
.
16.
Muc
,
A.
, and
Gurba
,
W.
,
2001
, “
Genetic Algorithms and Finite Element Analysis in Optimization of Composite Structures
,”
Compos. Struct.
,
54
(
2–3
), pp.
275
281
.
17.
Sigmund
,
O.
, and
Torquato
,
S.
,
1997
, “
Design of Materials With Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method
,”
J. Mech. Phys. Solids
,
45
(
6
), pp.
1037
1067
.
18.
Wang
,
M. Y.
,
Wang
,
X.
, and
Guo
,
D.
,
2003
, “
A Level Set Method for Structural Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
1
), pp.
227
246
.
19.
Rozvany
,
G. I.
,
2009
, “
A Critical Review of Established Methods of Structural Topology Optimization
,”
Struct. Multidiscip. Optim.
,
37
(
3
), pp.
217
237
.
20.
Hassani
,
B.
, and
Hinton
,
E.
,
2012
,
Homogenization and Structural Topology Optimization: Theory, Practice and Software
,
Springer Science & Business Media
,
London
.
21.
Sigmund
,
O.
,
2001
, “
A 99 Line Topology Optimization Code Written in matlab
,”
Struct. Multidiscip. Optim.
,
21
(
2
), pp.
120
127
.
22.
Hajela
,
P.
,
Lee
,
E.
, and
Lin
,
C.-Y.
,
1993
, “
Genetic Algorithms in Structural Topology Optimization
,”
Topology Design of Structures
,
Springer
,
Dordrecht, The Netherlands
, pp.
117
133
.
23.
Sigmund
,
O.
, and
Petersson
,
J.
,
1998
, “
Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboards, Mesh-Dependencies and Local Minima
,”
Struct. Optim.
,
16
(
1
), pp.
68
75
.
24.
Guo
,
X.
, and
Gao
,
H.
,
2006
, “
Bio-Inspired Material Design and Optimization
,”
Proceedings of the IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials
,
Springer
,
Dordrecht, The Netherlands
, pp.
439
453
.
25.
Challis
,
V. J.
,
Roberts
,
A. P.
, and
Wilkins
,
A. H.
,
2008
, “
Fracture Resistance Via Topology Optimization
,”
Struct. Multidiscip. Optim.
,
36
(
3
), pp.
263
271
.
26.
Zhang
,
Z.
,
Schwartz
,
S.
,
Wagner
,
L.
, and
Miller
,
W.
,
2000
, “
A Greedy Algorithm for Aligning DNA Sequences
,”
J. Comput. Biol.
,
7
(
1–2
), pp.
203
214
.
27.
Ruiz
,
R.
, and
Stützle
,
T.
,
2007
, “
A Simple and Effective Iterated Greedy Algorithm for the Permutation Flowshop Scheduling Problem
,”
Eur. J. Oper. Res.
,
177
(
3
), pp.
2033
2049
.
28.
Dunstan
,
F.
, and
Welsh
,
D.
,
1973
, “
A Greedy Algorithm for Solving a Certain Class of Linear Programmes
,”
Math. Program.
,
5
(
1
), pp.
338
353
.
29.
Irwin
,
G. R.
,
1997
, “
Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate
,”
SPIE Milestone Series MS
,
137
, pp.
167
170
.
30.
Lawn
,
B.
,
1993
,
Fracture of Brittle Solids
,
Cambridge University Press
,
Melbourne, Australia
.
31.
Anderson
,
T. L.
, and
Anderson
,
T.
,
2005
,
Fracture Mechanics: Fundamentals and Applications
,
CRC Press
,
Boca Raton, FL
.
32.
Dimas
,
L. S.
,
Bratzel
,
G. H.
,
Eylon
,
I.
, and
Buehler
,
M. J.
,
2013
, “
Tough Composites Inspired by Mineralized Natural Materials: Computation, 3D Printing, and Testing
,”
Adv. Funct. Mater.
,
23
(
36
), pp.
4629
4638
.
33.
Dimas
,
L. S.
, and
Buehler
,
M. J.
,
2014
, “
Modeling and Additive Manufacturing of Bio-Inspired Composites With Tunable Fracture Mechanical Properties
,”
Soft Matter
,
10
(
25
), pp.
4436
4442
.
34.
Finnemore
,
A.
,
Cunha
,
P.
,
Shean
,
T.
,
Vignolini
,
S.
,
Guldin
,
S.
,
Oyen
,
M.
, and
Steiner
,
U.
,
2012
, “
Biomimetic Layer-by-Layer Assembly of Artificial Nacre
,”
Nat. Commun.
,
3
, p.
966
.
35.
Tang
,
Z. Y.
,
Kotov
,
N. A.
,
Magonov
,
S.
, and
Ozturk
,
B.
,
2003
, “
Nanostructured Artificial Nacre
,”
Nat. Mater.
,
2
(
6
), pp.
U413
U418
.
36.
Munch
,
E.
,
Launey
,
M. E.
,
Alsem
,
D. H.
,
Saiz
,
E.
,
Tomsia
,
A. P.
, and
Ritchie
,
R. O.
,
2008
, “
Tough, Bio-Inspired Hybrid Materials
,”
Science
,
322
(
5907
), pp.
1516
1520
.
37.
Launey
,
M. E.
,
Munch
,
E.
,
Alsem
,
D. H.
,
Saiz
,
E.
,
Tomsia
,
A. P.
, and
Ritchie
,
R. O.
,
2010
, “
A Novel Biomimetic Approach to the Design of High-Performance Ceramic–Metal Composites
,”
J. R. Soc. Interface
,
7
(
46
), pp.
741
753
.
38.
Gu
,
G. X.
,
Su
,
I.
,
Sharma
,
S.
,
Voros
,
J. L.
,
Qin
,
Z.
, and
Buehler
,
M. J.
,
2016
, “
Three-Dimensional-Printing of Bio-Inspired Composites
,”
ASME J. Biomech. Eng.
,
138
(
2
), p.
021006
.
You do not currently have access to this content.