Bioinspired Structural Materials, Notas de estudo de Engenharia Elétrica

Bioinspired Structural Materials, Notas de estudo de Engenharia Elétrica

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Science Magazine

ing a sequence of moves, each of which is

random but with probabilities that should

optimize expected gains. These elegant the-

oretical results have long been known to

provide poor fits to laboratory data from

real players.

The success of their model is impressive,

but, as they point out, it is only part of the sig-

nificance of their results. The three best-per-

forming models are (i) a model drawn from

the previous literature known as Normalized

Fictitious Play (7), (ii) the simplest Marchiori-

Warglien model, and (iii) a variant of their

model with one free parameter. Although they

vary in how it is incorporated, all three are

regret-driven learning models.

To these results we can add others (8)

showing that a regret-based model can also

account for puzzling empirical patterns

in various forms of auction bidding. As

Marchiori and Warglien recognize, the supe-

rior fit of these regret-based models aligns

very nicely with results from recent neu-

ropsychological work, where studies of brain

activity during decision-making have

pointed increasingly to the crucial role

played by brain areas implicated in feelings

of regret (9). In particular, regret involves

constructing a counterfactual image of what

the actor would have felt if he or she had

acted differently. Psychological subjects

with impaired abilities to construct such felt

counterfactuals—for example, because

of damage to brain areas such as the

orbitofrontal cortex—are observed to behave

quite differently from normal subjects in

choice situations (10).

Although the Marchiori-Warglien model

gives a central role to regret-driven learning

in making its successful predictions, it is

important to recognize that the learning in

their model is an approximation of the learn-

ing dynamics of experimental players, just as

the regret is an approximation of the complex

feelings of success and failure experienced

by the players. The adaptive neural net struc-

ture used in their model converges toward its

stable propensities for long-run play fairly

quickly, generally in fewer iterations than

experimental subjects require. Thus, the data

on play that it fits least well are the cases

where subjects take the longest to stabilize

their patterns of play. Other models, typically

those based on more traditional reinforce-

ment learning, have been found to do better

at tracking the early stages of experimental

play (5). But versions of those reinforcement

models that were included in the present

work did less well overall than any of the

regret-driven models.

The great virtue of the parsimony and

rigor of economic theorizing is exactly that

improvements often accumulate rapidly.

Thus, the Marchiori-Warglien model may not

be the final word in this development of psy-

chologically plausible approximations for

economic game play (11). However, the

authors have made an important contribution

with their psychologically grounded insight

that regret-driven learning provides the best

approximating form to date for some of the

most recalcitrant economic laboratory data

that we have. And their use of a neural network

structure incorporating payoffs has interesting

possibilities for generalization to other classes

of games. They have made a step that both

takes us forward and simultaneously helps to

define the road that lies ahead.

References and Notes

1. D. Marchiori, M. Warglien, Science 319, 1111 (2008).

2. C. Camerer, U. Malmendier, in Economic Institutions and

Behavioral Economics: Proceedings of the Yrjö Jahnsson

Foundation 50th Anniversary Conference, P. Diamond, H.

Vartiainen, Eds. (Princeton Univ. Press, Princeton, NJ,

2007), pp. 235–280.

3. M. D. Cohen, in Economic Institutions and Behavioral

Economics: Proceedings of the Yrjö Jahnsson Foundation

50th Anniversary Conference, P. Diamond, H. Vartiainen,

Eds. (Princeton Univ. Press, Princeton, NJ, 2007), pp.


4. E. Fehr, C. Camerer, Trends Cogn. Sci. 11, 419 (2007).

5. I. Erev, A. E. Roth, R. L. Slonim, G. Barron, Econ. Theory

33, 29 (2007).

6. R. Gibbons, Game Theory for Applied Economists,

(Princeton Univ. Press, Princeton, NJ, 1992).

7. I. Erev, A. E. Roth, Am. Econ. Rev. 88, 848 (1998).

8. R. Engelbrecht-Wiggans, E. Katok, Econ. Theory 33, 81


9. G. Coricelli, R. J. Dolan, A. Sirigu, Trends Cogn. Sci. 11,

258 (2007).

10. A. Bechara, H. Damasio, A. Damasio, Cereb. Cortex 10,

295 (2000).

11. For example, the few cases that the simple model has

trouble predicting are ones in which the optimal behavior

is fairly close to an unmixed, or pure strategy, suggesting

that there are further regularities that may be captured

in a subsequent variation on the model.

10.1126/science.1155477 SCIENCE VOL 319 22 FEBRUARY 2008 1053


T he huge diversity of structural biologi-

cal materials that exist in nature, even

within a single species, and the com-

plexity, multifunctionality, and multiscale

nature of their structure-property relation-

ships has been studied extensively for decades

(1). Using materials available in the environ-

ment that typically exhibit poor macro-scale

mechanical properties (brittle biological

ceramics and compliant macromolecules),

they can achieve orders-of-magnitude in-

creases in strength and toughness; in many

cases, this “mechanical property amplifica-

tion” occurs in a nonadditive manner that goes

beyond the simple composite rule of mixture

formulations. Synthetic structural materials

that take advantage of the mechanical design

principles found in nature could transform

many fields; e.g., materials science, mechani-

cal and civil engineering, and aeronautics and

astronautics. Here, we highlight a few recent

developments in this area and summarize

unexplored opportunities for the future.

Bonderer et al. [page 1069 of this issue (2)]

have carried out the deliberate microstructural

design of a multilayered alumina platelet-rein-

forced chitosan nanocomposite, inspired by

the inner nacreous layer of many seashells.

The alumina platelets possess higher ultimate

tensile strength than the aragonite platelets

found in nacre; this reflects a general design

concept, whereby the weak constituents found

in nature are replaced with more advanced

synthetic engineered materials, with the goal

of producing structural composite materials

with mechanical properties that exceed both

those of nacre and those of state-of-the-art

synthetic materials.

The thickness of the alumina platelets was

chosen to be similar to that found in nacre (~200

nanometers). At such sub-micrometer thick-

nesses, the strength of brittle materials often

increases compared with the bulk material

because of the decreasing size and probability

of flaws (3). The average platelet aspect ratio

was selected based on a classic composite shear

lag load transfer model (4); this critical length

maximizes the load transferred to the platelet

while averting platelet fracture and instead

favors a failure mechanism of platelet pullout

Materials scientists are seeking to create

synthetic materials based on the mechanical

design principles found in biological materials

such as seashell nacre. Bioinspired Structural Materials Christine Ortiz and Mary C. Boyce


Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. E-mail:

Published by AAAS

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and matrix shear (as observed in nacre). The

authors also achieved excellent alignment and

dispersion of the platelets in the matrix up to

volume fractions of 0.2, using a colloidal-based

technique. Tensile mechanical properties were

amplified in the composite material compared

to the chitosan matrix, and significant plasticity

was retained, suggesting pathways for extensive

deformation of the matrix at these volume frac-

tions before platelet pullout. The authors have

thus created a material that is simultaneously

stiff, strong, and tough by via constituents of

appropriate length scale and geometry, using

mechanical design principles derived from

nature, as well as achieving dispersion of the

reinforcing component in the matrix.

Podsiadlo and colleagues (5) have taken an

alternative approach in the design of a mont-

morillonite clay platelet–poly(vinyl alcohol)

matrix nacre-mimetic artificial nanocompos-

ite by focusing on tailoring the chemistry of

the platelet-matrix interface to enhance load

transfer. Biological composites make use of

local chemistry, compositional gradients,

macromolecular supramolecular structure,

length scale effects, geometry, and other fac-

tors to design robust interfaces and inter-

phases that bond together different material

phases, even in the presence of water (6). In

the material prepared by Podsiadlo et al. (4),

the platelets and matrix exhibit extensive epi-

taxial hydrogen bonding, as well as cyclic

cross-linking. Gluteraldehyde treatment cre-

ated additional covalent acetal bridges be-

tween the matrix and platelets, and dramatic

increases in stiffness and strength were

achieved compared to the matrix material.

Another example of nacre-mimetic interfacial

design between structural elements in a nano-

composite has been reported by Tang et al. (7).

Here, an ionically bonded polyelectrolyte matrix

was used to mimic the high toughness exten-

sional “sawtooth” macromolecular elasticity

profile due to sacrificial noncovalent bonding

observed experimentally in the organic com-

ponent of nacre (8) and modeled theoretically

by Qi et al. (9). This unique inter-

facial property governs the adhe-

sive matrix behavior, thus con-

trolling and mitigating shear lag

load transfer to the aragonite

tablets, averting failure of both

the tablets and the organic adhe-

sive layers, and increasing ductil-

ity and energy dissipation.

Even in the limited context of

nacre, many design principles

remain to be explored. The abil-

ity to access a wide range of vol-

ume fractions of the reinforcing

component will enable addi-

tional design optimization in

terms of tailoring stiffness,

strength, and toughness. Recent

theoretical models (10) and elec-

tron microscopy studies (11) of

nacre have shown that additional

microstructural features— platelet

layer offset, platelet surface

waviness, the Voronoi arrange-

ment of platelets in each plane,

and screw dislocations leading

to large, interconnected layer-to-

layer spiral structures (see the

figure, panel C) and a tessellated

zigzag morphology—may all

play a role in the biomechani-

cal functionality.

The smaller and larger length

scale design principles of sea-

shells have received less attention.

At the smaller length scales,

individual nacre platelets are

complex organic-inorganic com-

posites with a unique sector structure; each sec-

tor possesses nanometer-sized surface domains

or asperities (12, 13). Individual platelets can

exhibit considerable plasticity before fracture

upon penetration by an indenter (12), and the

constituent surface “nanograins” can deform

and rotate under an applied tensile load (13)

(see the figure, panel D). In addition, there is a

complex three-dimensional distribution of

organic matrix components spatially within the

plane parallel to the nacre tablets (14).

At the larger length scale of the shell (see

the figure, panel A), the multilayered struc-

ture, the prismatic calcite outer layer, integrity

of the calcite-nacre interface (see the figure,

panel B), confinement effects between the

layers, structure and property gradation

within and between layers, and anisotropy of

the layers all work collectively to provide

enhanced mechanical performance.

Last, we have yet to fully understand and

take advantage of the inherent specificity of

natural mechanical design principles. For

example, multilayered armored fish scales

serve as protection from predatory penetrat-

ing impacts (15), mussel byssal threads are

hysteretic yet resilient to large strain deforma-

tion in order to maintain adhesion to rocks in

the face of the pounding surf (16), and graded

layer junctions in teeth resist catastrophic frac-

ture during mastication (17). Each of these

systems experiences, and has been designed

to endure, very different loading conditions in

their environment and during their function.

References and Notes 1. S. A. Wainwright, W. D. Biggs, J. D. Currey, J. M. Gosline,

Mechanical Design in Organisms (Princeton Univ. Press, Princeton, NJ, 1976).

2. L. J. Bonderer, A. R. Studart, L. J. Gauckler, Science 319, 1069 (2008).

3. H. Gao, B. Ji, I. L. Jager, E. Arzt, P. Fratzl, Proc. Natl. Acad. Sci. U.S.A. 100, 5597 (2003).

4. A. P. Jackson, J. F. V. Vincent, R. M. Turner, Proc. R. Soc. London Ser. B. 234, 415 (1998).

5. P. Podsiadlo et al., Science 318, 80 (2007). 6. S. Weiner, F. Nudelman, E. Sone, P. Zaslansky, L. Addadi,

Biointerphases 1, 12 (2006). 7. Z. Y. Tang, N. A. Kotov, S. Magonov, B. Ozturk, Nat. Mat.

2, 413 (2003). 8. B. L. Smith et al., Nature 399, 761 (1999). 9. H. J. Qi, B. J. F. Bruet, J. S. Palmer, C. Ortiz, M. C. Boyce, in

Mechanics of Biological Tissues, G. A. Holzapfel, R. W. Ogden, Eds. (Springer, Graz, Austria, 2005), pp. 175–190.

10. F. Barthelat, H. Tang, P. D. Zavattieri, C. M. Li, H. D. Espinosa, J. Mech. Phys. Solids 55, 306 (2007).

11. N. E. Yao, A. Akey, J. Mat. Res. 21, 1939 (2006). 12. B. J. F. Bruet et al., J. Mat. Res. 20, 2400 (2005). 13. X. Li, Z. H. Xu, R. Wang, NanoLetters 6, 2301 (2006). 14. F. Nudelman, B. A. Gotliv, L. Addadi, S. Weiner, J. Struc.

Biol. 153, 176 (2006). 15. J. Daget, M. Gayet, F. J. Meunier, J.-Y. Sire, Fish Fisheries

2, 113 (2001). 16. E. Carrington, J. M. Gosline, Am. Malacological Bull. 18,

135 (2004). 17. V. Imbeni, J. J. Kruzic, G. W. Marshall, R. O. Ritchie, Nat.

Mat. 4, 229 (2005). 18. The authors would like to acknowledge funding from the

U.S. Army (DAAD-19-02-D0002).


Deformed grains Nanograin

Rotating grains

Calcite layer

Cross-section of a red abalone shell





Calcite-nacre junction

Surface of a nacre platelet Nacre platelet under tension

Spiral structure in nacre

Nacreous layer

Growth lines

10 mm

ε ε

100 nm

10 µm10 µm

Multiscale mechanical design principles of seashells. (A) Multi- layered structure of the cross-section of California red abalone shell (10). (B) Artificially colorized scanning electron microscopy (SEM) image of the calcite-nacre junction region in a Trochus niloticus shell (9). (C) Artificially colorized SEM image of a layer-to-layer spiral in T. niloticus nacre. (D) (Left) Atomic force microscopy image of surface nanograins on an individual nacre platelet from California red abalone and (right) schematic of nanograin rotation under tension (13).

Published by AAAS

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