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Proprietà meccaniche dei
materiali bioispirati
Federico Bosia
Dipartimento di Fisica / Nanostructured Interfaces and Surfaces Centre,
Università di Torino
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Outline
Optimization of Strength and Toughness: from
Spider Silk to Nanocomposites
Motivation
Optimization of Adhesion: Gecko
Metamaterials
Tesi
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Bioinspiration
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Damping /shock absorption Strength/low density
Metamaterials
Adhesion
Bioinspiration
Complex constitutive behaviour emerges from simple components (e.g. Hierarchy)
Structure Function
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Adhesion due to van der Waals and capillary forces;
Adhesion strength of about 1 MPa, i.e. 10 times its body weight
Optimization of Adhesion
The most adhesive: the Tokay Gecko
3 requirements:
- Strong adhesion
- Easy detachment
- Self-cleaning mechanisms
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Optimization of Adhesion
Design of “Spiderman suit”:
Nano-fibres
Hierarchical design
“Tapered” spatulae
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Optimization of Adhesion
HIERARCHICAL NANO-ARCHITECTURES E.Lepore, F.Pugno, N.M. Pugno (2011):
The Journal of Adhesion, 88:10, 820-830
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Optimization of Adhesion
SPATULAE: TERMINAL CONTACT UNITS
Similar tape-like geometries (thus the detachment is due to “peeling”),
but of different sizes (3 billions of contacts in geckos)
M.Varenberg, N.M.Pugno, S.N.Gorb
Soft Matter, 2010,6, 3269-3272
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Principle of contact splitting
1) Super-adhesion by nanocontacts: (b total peeling line)
2) Easy detachment by controlling the peeling angle:
3) Self-cleaning “Lotus effect” (Hierarchical architectures)
3 “ingredients”:
cos11 F
bF
Optimization of Adhesion
cos1
RbF
R surface energy
b total peeling line
peeling angle
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Optimization of Adhesion
THEORY OF MULTIPLE PEELING, TO DESIGN GECKO-INSPIRED ADHESIVES
Optimal angle for maximal adhesion
N.M.Pugno, International Journal
of Fracture (2011), 171(2), 185-193
Experimental results
HIERARCHICAL ANCHORAGES?
2/
C
C
F
Ff
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11
Imposed displacement
Initial structure
Deformed structure
Delaminated structure
Tape delamination modelling
Energetic formulation between deformed & delaminated
states:
Delamination takes place when:
K. Kendall, J. Phys, (1975), 8
Surface energy + Work variation + Elastic energy variation = 0
Optimization of Adhesion
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Multiple peeling simulation and spider web anchorages
N. Pugno, Int. J. Fract. (2011), 171:185-193
Optimization of Adhesion
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Asymmetric peeling
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Finite Element simulations
1 2 3
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Multiple peeling simulation and spider web anchorages
I. Grawe, J. R. Soc. Interface (2014) 98 20140477
Optimization of Adhesion
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Optimization of Strength and Toughness
SPIDER WEB DISTRIBUTED LOAD
DISTRIBUTED LOAD, E.G. WIND LOAD: THE WEAKEST LINK IS
THE ANCHORAGE RATHER THAN THE WEB ITSELF.
S.W.Cranford, A.Tarakanova, N.M.Pugno, and M.J.
Buehler, Nature 482, 72–76 (2012)
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Optimization of Strength and Toughness
E.Lepore, A.Marchiore, M.Isaia, M.Buehler,
N.M.Pugno, PlOS One (2012)
STRENGTH 1 GPa, STRAIN UP TO 750%
Hierarchical heterogeneous material
A.Nova, S.Keten, N.M.Pugno, A.Redaelli and M.J. Buehler, Nanoletters 10, 2626–2634 (2010)
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Biological structural materials
- Multiphase
- Porous
- Hierarchical structure
- Fibre-based
- Self-healing
Lakes (1993): Nature, 361, 511
Hierarchical structure in human compact bone
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- Microstructure
- Hierarchical geometry
- Fibre-based
- Self-healing
Hierarchical structure in human tendon
Biological structural materials
Zhang et al (2011): Proc. R. Soc. B 278, 519
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Dactyl clubs in Odontodactylus scyllarus
- chitin fibril helicoidal structural motif
-multiphase composite:
oriented crystalline hydroxyapatite
and amorphous calcium phosphate
and carbonate, between thin layers
of chitosan- Multiphase
- Microstructure
- Complex geometry
- fibre-based
Weaver et al. (2013), Science, 336, 1275
Biological structural materials
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- High stiffness and strength/weight ratios
- Tailor-made properties
- Processability ~ 10-5 m
~ 10-3-10-1 m
~ 10-2-10-1 m
~ m
Multiscale modelling
Accurate models
required for the main
structural elements
e.g. Equivalent Single Layer theories
Composite materials
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Composite materials
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NanocompositesCARBON NANOTUBES (CNT)
Theoretical predicted strengths 100 GPa
Measured strengths 60 GPa Role of defects
“STRONGEST MATERIAL EVER MEASURED”
GRAPHENE
“fibres”[Xu et al. Nat. Comm. 2, 571 (2011)]
“nanoribbons”[Kosynkin et al. Nature 458, 872 (2009)]
graphene-based
composites
[Stankovich et al. Nature 442,
282 (2006)]
Intrinsic strength:s = (130 ± 10) GPa [Lee et al. Science 321,
385 (2008)]
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Optimization of Strength and Toughness
Strength and toughness are competing properties in artificial materials
Artificial Natural
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Optimization of Strength and Toughness LOCALIZED LOAD MD simulations by M.J.Buehler’s group, MIT
S.W.Cranford, A.Tarakanova, N.M.Pugno, and M.J.
Buehler, Nature 482, 72–76 (2012)
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NECESSARY “INGREDIENTS”:
Optimization of mechanical properties
Appropriate properties (starting at nanoscale)
Material heterogeneity
Hierarchy
Interaction between structure and constitutive behaviour
Tailor-made geometry/topology, tapering etc
...
+ SELF-HEALING
n
1
l
h
t
(i) Tough, soft matrix
(ii) Strong hard inclusions
(iii) Hierarchy
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Effect of defects, grain boundaries, etc
Effect of “upscaling”
Need for theoretical modeling and simulations using a relatively simple model
which is capable of spanning various orders of magnitude
In composites/nano-composites:
Need to optimize mechanical performance (stiffness, strength, toughness,
adhesion...) as a function of material properties, volume fractions, structure,
topology, hierarchy, etc.
Theory/Numerical simulations
In nano-materials (e.g. Graphene/CNT ):
MULTISCALE NUMERICAL TOOLS ARE ESSENTIAL IN THE EVALUATION
OF THE EFFECT OF THE ADOPTED OPTIMIZATION STRATEGIES
Determine physical mechanisms responsible for observed behaviour
In biomaterials:
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Fibre Bundle Model (FBM)
[S. Pradhan et al., Rev. Modern Phys., 82, 499-555 (2010)]
l
EAk
ij
ij Weibull strength distribution:
𝑷 𝝈𝑭𝒊𝒋 = 𝟏 − 𝒆𝝈𝒊𝒋𝝈𝟎
𝒎
Fracture criterion:
𝝈𝒊𝒋 > 𝝈𝑭𝒊𝒋
))()(()(
ijii
ij
ijktKtK
ktC
Compliance variation after single fracture event
kij 0,
Equal Load Sharing (ELS) hypothesis
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- Weibull-distributed fibre strengths and stiffnesses at level 0
- linear/nonlinear elastic behaviour assigned to fibres
- multiple fibre types possible
- brittle/ductile fracture behaviour possible
- Equal Load Sharing (ELS) : after each fibre break, load is
redistributed equally among surviving fibres
- stiffness/strength/toughness for fibre bundle derived from
repeated simulations (~103)
- fibre characteristics at level (i+1) derived from level i bundle
results
- different hierarchical structures evaluated (load redistribution)
Hierarchical Fibre Bundle Model (HFBM)
Based on a Fibre Bundle Model, applied recursively in a hierarchical scheme
Evaluation of the mechanical behaviour of multiscale defective, heterogeneous
materials under tensile loading
Full-scale properties derived from level 0 characteristics (no additional parameters)
[N. Pugno et al., Small 4, 1044-1052 (2008)]
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CNT-PVA composites
[F.Bosia, N.M.Pugno, M.J. Buehler
Phys.Rev.E 82, 056103 (2010)]
CNT composites
Ductile matrix / brittle reinforcing fibres
RECORD TOUGHNESS: 870 J/g
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Hierarchy
[N.M.Pugno, F.Bosia, T.Abdalrahman,
Phys.Rev.E 85, 011903 (2012)]
Twisted cable yarns (Bombyx mori silkworm yarns )Tendon
[F.Bosia, N.M.Pugno, T.Abdalrahman.
Nanoscale 4, 1200 (2012)]
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Composite fracture modeling
Nodal relations:
2-dimension / 2 dof
Linear / Nonlinear behavior
Yield strain / fracture strain
Base element description:
4 nodes / 8 dof
6 relations
Mesh construction:
Regions defined for different
element properties (Matrix /
reinforcement structure)
2-D modeling
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Composite nanofibers of graphene oxyde and gelatin
S. Panzavolta, Carbon (2014) 78 566-577
Nanocomposites modeling
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Self-healing
Numerical model:
1. “Random healing”: replace
random fibre at a healing rate h
2. “Local healing”: replace last
fractured fibre at healing rate h
(a) Damage event causes crack formation in the matrix;
(b) crack ruptures the microcapsules, releasing liquid
healing agent into crack plane;
(c) healing agent polymerizes upon contact with
embedded catalyst, bonding crack closed
[White et al. Nature 409:794–7 (2001)]
IN ARTIFICIAL MATERIALS
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Self-healing
[F.Bosia, T,Abdalrahman, N.M.Pugno. Langmuir (2014)]
Strength vs. h Dissipated energy vs. h
Considerable improvement in Strength and especially Toughness, as well as lifetime
healing location is critical
NUMERICAL MODELING RESULTS
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LYCURGUS CUP (BRITISH MUSEUM) - 1
Metamaterials
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LYCURGUS CUP (BRITISH MUSEUM) - 2
Metamaterials
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Conventional materials:
properties derives from the
constituents atoms.
Metamaterials: properties derive
from constituent units. These can
be engineered as we please.
Metamaterials
“Meta” = above, superior, beyond
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Normally waves propagate and
interact with different media
according to Snell’s Law.
A metamaterial “manipulates”
waves giving rise to surprising
phenomena such as negative
refraction, cloaking, waves
isolation etc.
Metamaterials
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Types of metamaterials
• Electromagnetic– Control EMWs (visible light waves, microwaves, and infrared
waves).
– Negative electric permittivity and negative magnetic permeability.
• Acoustic– Manipulate waves associated to particle vibrations.
– Rely on a negative bulk modulus and negative mass density.
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• Electromagnetic/acoustic
cloacking
• Acoustic Insulators
• Acoustic Filters
• Military Applications
• Seismic Shielding
• Ultrasonic silent blocks
• Resonators
• Sound lenses
• Wave focusing & waveguiding
Applications
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Tesi di Laurea
1) Simulazioni numeriche su multiple peeling e ancoraggi a geometria
gerarchica
Tesi disponibili:
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Tesi di Laurea
2)Simulazioni numeriche sull’ ottimizzazione della resistenza/tenacità di
strutture gerarchiche “self-healing”
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Tesi di Laurea
3) Simulazioni numeriche FEM sull’ ottimizzazione di metamateriali
gerarchici
a
a
Inclusion
y
x O
a
a
Inclusion
y
x O
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Federico Bosia
Dipartimento di Fisica
tel.: 011 670 7889
ufficio: T50 (piano terra istituto vecchio)
http://www.dfs.unito.it/solid/index.html
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