The origin of remarkable resilience of human tooth enamelXiaoli Zhao, Simona O'Brien, Jeremy Shaw, Paul Abbott, Paul Munroe, Daryoush Habibi, and Zonghan Xie

Citation: Applied Physics Letters 103, 241901 (2013); doi: 10.1063/1.4842015 View online: http://dx.doi.org/10.1063/1.4842015 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/103/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in In vitro thermal diffusivity measurements as aging process study in human tooth hard tissues J. Appl. Phys. 114, 194705 (2013); 10.1063/1.4832481 Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel Biomicrofluidics 7, 054110 (2013); 10.1063/1.4820414 Atomic force microscopic observation of surface-supported human erythrocytes Appl. Phys. Lett. 91, 023901 (2007); 10.1063/1.2755874 Contact induced deformation of enamel Appl. Phys. Lett. 90, 171916 (2007); 10.1063/1.2450649 Biomolecular origin of the rate-dependent deformation of prismatic enamel Appl. Phys. Lett. 89, 051904 (2006); 10.1063/1.2245439

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The origin of remarkable resilience of human tooth enamel

Xiaoli Zhao,1,a) Simona O’Brien,1,2 Jeremy Shaw,3 Paul Abbott,4 Paul Munroe,5

Daryoush Habibi,1 and Zonghan Xie1,6,7,b)

1School of Engineering, Edith Cowan University, Perth, WA 6027, Australia2Perth Institute of Business and Technology, Joondalup, WA 6027, Australia3Centre for Microscopy, Characterisation and Analysis, The University of Western Australia, Perth,WA 6009, Australia4School of Dentistry, The University of Western Australia, Perth, WA 6009, Australia5School of Materials Science and Engineering, University of New South Wales Sydney, Kensington,NSW 2052, Australia6School of Mechanical Engineering, University of Adelaide, Adelaide, SA 5065, Australia7School of Materials Science and Engineering, Tianjin Polytechnic University, Tianjin 300387, PR China

(Received 14 August 2013; accepted 21 November 2013; published online 9 December 2013)

The mechanical properties of human tooth enamel depend not only on test locations but also on the

indentation depth. However, it remains uncertain what roles the depth-dependant properties play in

mechanical performance of enamel. Here we reveal that a change in the mechanical properties of

enamel, in particular its strength, with increasing indentation depth promotes inelastic deformation

in material. In doing so, the severity and extent of stress concentration is reduced. Furthermore, we

observed that following unloading, self-recovery occurs in enamel. These findings improve our

understanding of the underlying mechanisms responsible for the remarkable resilience of enamel.VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4842015]

Tooth enamel is a highly mineralized, non-regenerative

tissue.1 It consists primarily of hydroxyapatite (HAP) crys-

tallites embedded in a proteinaceous matrix.2,3 The structural

and physical properties of enamel constituents4,5 and their

spatial arrangement6,7 are determinants of enamel mechani-

cal properties. Moreover, both the hardness and modulus of

enamel change with the depth from the outer surface towards

the enamel-dentin junction.8 Numerical simulations have

shown that the property gradients can enhance resistance to

penetration and mitigate stress concentration in enamel.8,9 In

addition, non-uniform arrangement of HAP crystallites in

prisms was found to promote energy dissipation while main-

taining sufficient stiffness.10 Recent studies have shown that

the mechanical properties of enamel vary with contact

depth,11–13 resulting presumably from combined effects of

its hierarchical structure,14 and the tilting and shear sliding

of the HAP crystallites under loading.15,16 An interesting

question arises: what functional benefits would dental

enamel gain from its adaptive response to mechanical load-

ing? Interestingly, some of biological materials and struc-

tures such as spider silk and mother-of-pearl can adapt to

change in load, and in so doing, remarkable damage toler-

ance results.17,18 Given that enamel has evolved to perform

cutting and grinding tasks, it is thus natural to hypothesize

that the load-adaptive behavior of enamel is programmed to

help maintain its structural integrity and mechanical function

for a lifetime.

To test this hypothesis, we prepared enamel specimens

under hydrated conditions to ascertain the relationship of the

mechanical properties of enamel with contact load/depth.

Then, using finite element analysis, we clarified how the

depth-dependant properties regulate the mechanical

performance of enamel. Finally, supported by the creep tests,

we have revealed the critical roles of self-recovery in render-

ing enamel remarkably resilient.

Nine human teeth were extracted, cleaned, and stored

at 4 �C in Hanks’ Balanced Salt Solution (HBSS) with the

addition of 0.02% thymol crystals to prevent demineraliza-

tion19 and suppress bacterial growth.20 The tooth specimen

was sectioned using a precision saw in a direction parallel

to mesial-distal plane at a distance of �5 mm to the edge.

HBSS was used as a coolant during cutting. The cut surface

was then ground and polished in wet to a mirror finish. The

polished specimen was then clamped onto the bottom of a

specially built stainless steel holder using a slide-screw as-

sembly. HBSS was poured into the holder to submerge the

specimen to ensure the specimen was tested in wet

conditions.

The mechanical properties of enamel were evaluated

using a Berkovich tip. For each specimen, five rows of

indentations were performed near the occlusal surface

wherein the enamel prisms are more parallel without decus-

sation. Each row contained five indents with an interval of

50 lm. The spacing between rows was also 50 lm. The tests

were run in closed-loop under load control. A maximum

load of 400 mN was applied in eight increments, with each

increment followed by ten decrements. The Young’s modu-

lus and hardness were determined at each increment with the

load applied roughly perpendicular to the prism direction21

and then plotted as a function of indentation depth (and

load). Recent nanoindentation studies have shown that prism

orientation has little impact on the hardness and modulus of

enamel.22,23 A typical load-displacement curve obtained

from the indentation experiment is shown in Fig. 1(a). Both

the Young’s modulus and hardness of enamel were found to

decrease with increasing load or contact depth (Fig. 1(b)).

For example, when the indentation depth increases from 0.5

a)x.zhao@ecu.edu.au. Tel.: þ61 8 6304 5782.b)zonghan.xie@adelaide.edu.au. Tel.: þ61 8 8313 3980.

0003-6951/2013/103(24)/241901/5/$30.00 VC 2013 AIP Publishing LLC103, 241901-1

APPLIED PHYSICS LETTERS 103, 241901 (2013)

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to 2.0 lm, there is a �15% decrease in the modulus, and a

�21% decrease in the hardness.

These data were then used to construct 2D axisymmetric

finite element models using COMSOL software, in order to clar-

ify how the load-dependant properties regulate stress and

strain distributions within enamel. A conical indenter having

a tip angle of 70.3� was used to simulate a Berkovich indenter

during loading.24,25 The deformation of the tip is negligible,

due to a large difference in the Young’s modulus between the

diamond indenter and enamel. A tip curvature of 20 nm ra-

dius was used to avoid unrealistically high stress being gener-

ated around the sharp tip. Meshes around the indenter were

refined for higher accuracy. The load was simulated by apply-

ing a distributed pressure along the top face, in such a manner

that the resultant surface displacement follows the same

deformation as that of enamel observed in the real experi-

ment.26 This method avoided non-convergence problem with-

out compromising the physical validity and accuracy of the

model. Boundary conditions are similar to those used in the

previous work27 and described briefly below. The left-hand

side of the simulation block coincides with the axisymmetric

axis. The bottom and the right-hand side are fixed along the

vertical and horizontal directions, respectively, but are free to

move in the other directions. The overall dimensions of the

simulation block are considerably larger than the contact

size; thus, the edge effect due to boundary constraints is neg-

ligible. For each indentation depth, the indentation load,

depth, and corresponding elastic modulus were used as input

data. The yield strength of the enamel was then estimated by

fitting the experimental data using a finite element method, as

shown in Fig. 1(c) and Table I. It is interesting to note that

the yield strength obtained here agrees well with those

derived from the equation ry¼H/3 (Ref. 24) except at low

indentation depths.

For comparison, a hypothetical material named

“HM-A” that represents typical solids was introduced by

assigning to it fixed modulus and yield strength values iden-

tical to that of enamel obtained at 0.5 lm indentation depth

(see Table I). Fig. 2 shows that a greater displacement is

induced in enamel by indentation (Fig. 2(a)), compared to

the HM-A. Additionally, the volume of resultant plastic

zone in enamel is more than double that in HM-A

(Fig. 2(b)) under 288 mN (corresponding to 2.0 lm depth).

Moreover, the total strain energy stored in enamel, derived

by the domain integration of the energy density, is nearly

double that in HM-A, meaning that enamel is capable of

dissipating more energy than HM-A, and consequently, the

damage tolerance is enhanced. This agrees well with recent

observations that enamel has exceptional energy dissipation

ability when compared with engineering ceramics which, as

with HM-A, typically have a Young’s modulus and strength

independent of contact load.28

Solids will deform plastically if the von Mises stress

exceeds their yield strength. For enamel, the inelastic defor-

mation is controlled largely by the shear sliding between

HAP crystals.29 Therefore, it is important to gauge both the

von Mises and shear stress level in enamel under mechanical

load. Through numerical simulations, we found that the

stress in enamel is considerably lower than that in HM-A

(Figs. 2(c) and 2(d)). By limiting the stress build-up, the

load-bearing ability of enamel increases. This has significant

implications, given that enamel sometimes experiences

extreme loads, for example, during dental function and at

sporting events.

FIG. 1. Depth-sensing indentation experiments performed near the occlusal

surface of tooth enamel. (a) A load and partial unload curve generated using

a Berkovich indenter. (b) Young’s modulus (E) and hardness (H) as a func-

tion of indentation depth. (c) Yield strength (ry) as a function of indentation

depth, estimated from fitting the experimental data using finite element mod-

elling. The dashed line indicates the values as calculated from ry¼H/3.

TABLE I. The mechanical properties of enamel obtained at three indenta-

tion depths.

Indentation depth (lm)

Physical parameter 0.5 1.0 2.0

Indentation load (mN) 24.6 (65.0) 82.0 (61.4) 288.3 (64.2)

Young’s modulus (GPa) 103.5 (60.3) 98.1 (60.4) 87.4 (60.8)

Hardness (GPa) 4.71 (60.03) 4.30 (60.05) 3.73 (60.04)

Yield strength (GPa) 1.70 (60.07) 1.45 (60.10) 1.24 (60.06)

241901-2 Zhao et al. Appl. Phys. Lett. 103, 241901 (2013)

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Now the question is: between the change in modulus

and strength with contact depth, which parameter plays a

more critical role in alleviating the stress concentration? To

answer this question, two more hypothetical materials—

HM-B and HM-C—are introduced to simulations (Fig. 3):

HM-B has a fixed yield strength, but its modulus changes

with contact depth as that of enamel (see Table I). In con-

trast, HM-C has a fixed modulus, but with changing yield

strength as that of enamel. The simulation results show that

the change of yield strength plays a dominant role in regulat-

ing the stress level in enamel (Fig. 3). Building on the mod-

eling results, the volume fraction of regions governed by

different stress levels was quantified for enamel in compari-

son to hypothetical materials. It reveals that lowering yield

strength is much more effective than reducing modulus in

minimizing the volume percentage of materials populated by

high stress levels (Fig. 4). For example, in the case of HM-C,

the volume populated by the stress level greater than 1.5 GPa

is �60 lm3, similar to that in enamel (79 lm3), but only

about 6% of that for both HM-A and HM-B. When the stress

level approaches 1.7 GPa, i.e., the yield strength of conven-

tional material HM-A, the volume populated by stresses

above this level in HM-C (i.e., enamel) is less than 1% of

that in HM-A and HM-B.

While lowering the yield strength of enamel can allevi-

ate the stress concentration, the resultant larger “plastic”

zone in enamel is detrimental to its long-term survival

(Fig. 2(b)). Consequently, the ability to recover when the

load is removed is critical to retaining the structural integrity

of enamel. To test such ability in enamel we performed the

creep tests using a Berkovich tip in the near surface region

of enamel and monitored the change of contact depth at the

peak load (50 mN) and when the load is removed (Fig. 5(a)).

Fig. 5(b) shows that creep occurs when enamel is being held

at 50 mN; a careful examination reveals that the deformation

occurred mainly in the first few seconds, before rapidly slow-

ing down (inset in Fig. 5(b)), indicative of increasing resist-

ance to deformation in the material. A similar creep effect

FIG. 2. Simulations of deformation and stress distribution in both enamel

and HM-A, induced by a Berkovich indenter under a load of 288 mN.

(a) Contours of vertical displacement, (b) size and geometry of plastic defor-

mation zone, (c) von Mises stress field, and (d) shear stress field.

FIG. 3. Distribution of von Mises

stress field generated by indentation

simulations under a load of 288 mN in

(a) HM-A, (b) HM-B, (c) HM-C, (d)

enamel.

FIG. 4. Volume fraction of materials under the influence of different stress

levels, namely, r> 1.28 GPa, r> 1.47 GPa, and r> 1.65 GPa.

241901-3 Zhao et al. Appl. Phys. Lett. 103, 241901 (2013)

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was observed by He et al.8 Further, when the load is

removed, the recovery took place up to �6% within 900 s,

more evidently in the first 100 s (Fig. 5(c)). Such a response

is presumably enabled by refolding of sacrificial bonds in the

protein matrix of the enamel.30–32 New experimental evi-

dence has also been provided by others, suggesting that

enamel can recover from contact damage.33 According to the

above analysis, the survival strategy of enamel under severe

load is to increase deformation by lowering the yield strength

in return for lower stress build-up and higher damage toler-

ance. In doing so, catastrophic failure often seen in brittle

solids under extreme loads is averted. Upon removal of load,

the self-recovery occurs to restore the structural integrity and

mechanical function of enamel.

These findings improve our understanding of enamel

mechanics and are valuable to the design and evaluation of

enamel-mimetic dental materials.34–36 In addition, many

mineralized tissues, such as nacre and bone, exhibit load-

dependant properties, and self-recovery.13,32,37,38 Therefore,

the results obtained from this work also shed light on the ori-

gin of their superior mechanical performance.

In summary, the origin of the remarkable resilience of

enamel is explored in this work by combining depth-sensing

indentation tests with finite element analysis. Experimental

results show that both the Young’s modulus and yield

strength are load (or depth) dependent. The increased plastic-

ity with contact depth lowers the stress build-up and enhan-

ces the energy dissipation of enamel. Finite element analysis

reveals that, compared to solids having fixed strength, much

greater strain energy is dissipated by enamel. Moreover, the

material volume populated by high stress is reduced consid-

erably. Self-recovery of enamel was also observed after

unloading, which plays a vital role in restoring the structural

integrity and mechanical function of enamel. The findings of

this study deepen our understanding of the mechanical

design principles of human tooth enamel and could be signif-

icant for developing more reliable hybrid materials and

exploring new deformation pathways in biological materials

and coatings.

The authors thank Sparkle Dental in Joondalup, Western

Australia, for providing fresh human molars. Z. Xie thanks

Professor Michael Swain of Faculty of Dentistry, the

University of Sydney for his constructive comment. This

work was supported by the Australian Dental Research

Foundation (Grant No. 6/2010) and the start-up grant for Z.

Xie at the University of Adelaide. S. O’Brien acknowledges

an ECU Postgraduate Scholarship for her PhD study. The

authors also acknowledge the facilities, scientific and techni-

cal assistance of the Australian Microscopy & Microanalysis

Research Facility at the Centre for Microscopy,

Characterisation & Analysis of the University of Western

Australia, a facility funded by the University, State and

Commonwealth Governments.

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