Proprietà meccaniche dei materiali bioispirati - unito.it file1 Proprietà meccaniche dei materiali...

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Proprietà meccaniche dei

materiali bioispirati

Federico Bosia

Dipartimento di Fisica / Nanostructured Interfaces and Surfaces Centre,

Università di Torino

federico.bosia@unito.it

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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

11

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

1313

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

federico.bosia@unito.it

tel.: 011 670 7889

ufficio: T50 (piano terra istituto vecchio)

http://www.dfs.unito.it/solid/index.html

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