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Tribology International 43 (2010) 2308–2316
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Tribology International
0301-67
doi:10.1
n Corr
E-m
(T.H. C
(B. Hen
journal homepage: www.elsevier.com/locate/triboint
Finite element simulations of static and sliding contact between a humanfingertip and textured surfaces
Fei Shao a,n, Tom H.C. Childs b, Catherine J. Barnes b, Brian Henson b
a VEC, School of Engineering VEC, University of Liverpool, Liverpool L69 3BX, UKb School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK
a r t i c l e i n f o
Article history:
Received 30 March 2010
Received in revised form
13 August 2010
Accepted 16 August 2010Available online 27 August 2010
Keywords:
Elastic contact mechanics
Human fingertip model
Finite element method
9X/$ - see front matter & 2010 Elsevier Ltd. A
016/j.triboint.2010.08.003
esponding author. Tel.: +44 1925864848; fax
ail addresses: [email protected] (F. Shao
hilds), [email protected] (C.J. Barnes), B.H
son).
a b s t r a c t
This paper presents a mechanics study of the variations with position and time of stresses within the
dermis and epidermis of a human fingertip when it is loaded and slid over textured surfaces. Its purpose
is to examine how fingerprints interact with surface texture to cause stress variations in tune with the
sensitivities of Meissner and Pacinian corpuscles through which humans in part interpret tactile
sensations. A two-dimensional multilayer elastic finite element model of a fingertip has been created
for this purpose. Results show that fingertip’s epidermal ridges have little effect on stress distribution
within the fingertip in static loading but significantly increase stress oscillations during sliding over a
textured surface. Oscillation frequencies from the sliding simulations are in ranges that should
stimulate a fingertip’s Meissner and Pacinian corpuscle nerve endings.
& 2010 Elsevier Ltd. All rights reserved.
1. Introduction
In a previous work [1] on the psychophysics and kansei/affective engineering of how people interpret surfaces bytouching them in sliding contact, which also reviews other relatedwork, it was demonstrated that people’s subjective assessmentsof a surface’s roughness depend on both the surface’s physicalroughness and sliding friction resistance. But simple measuresof these such as Ra and the average friction coefficient wereinsufficient to characterise them. It was proposed, as has alsobeen proposed by others (see [1] and later in this introduction),that wavelength spectral measures of roughness and dynamicaspects of friction influence people’s responses. Sliding a fingertipover surfaces with different wavelength and dynamic frictionproperties would stimulate in characteristically different waysthose nerve endings (mechanoreceptors) in fingertips thatrespond selectively to different frequencies. In this paper, two-dimensional (2D) finite element (FE) models and simulations ofthe loading and sliding of a human fingertip against texturedsurfaces are described. Variations of stress and strain withposition and time beneath the fingertip’s surface are reportedand considered in terms of their possible influence on themechanoreceptors’ stimulation. There is a previous literature onFE modeling of fingertips on which this paper builds. There is alsoa literature on the response characteristics of the fingertips’
ll rights reserved.
: +44 1133432150.
mechanoreceptors, including their limits of spatial and temporalresolution. The following paragraphs summarise these, firstly themechanoreceptor, then the mechanical modeling, literature.
A fingertip is composed of skin layers (an outer epidermis andinner dermis), subcutaneous tissue, bone and nail. There are fourtypes of mechanoreceptor in the skin layers: Merkel discs,Meissner and Pacinian corpuscles and Ruffini endings. It isthrough stimulation of these and the consequent transmissionof electrical impulses to the brain that touch perception is built up[2]. Merkel discs and Meissner corpuscles lie at the epidermis/dermis interface. Their density and connectivity to nerves in thefingertip give both of them an ability to resolve features above0.6–1 mm apart, as determined for example by two-pointdiscrimination, dot array and grating tests (reviewed in [2] withoriginal research in [3,4]) but they respond in different ways.Merkel discs are activated by static contact (i.e. frequencieso5–15 Hz). They fire at a rate that increases with the contactpressure above them. Thus the information that they send to thebrain is the overall area and shape of a contact, and the intensityof load within the contact [2,5]. Meissner corpuscles are activatedby dynamic contact, most sensitively around 20–50 Hz. Theyenable feature edges to be detected during sliding contact [2,6].By contrast, Pacinian corpuscles and Ruffini endings lie within thedermis, i.e. further from the surface than Merkel discs/Meissnercorpuscles. Pacinian corpuscles have a very poor spatial resolutionability but they are highly sensitive to vibration frequenciesaround 200–250 Hz [2,7]. There is a view that features that cannotbe resolved by Merkel discs and Meissner corpuscles arerecognized from their sliding vibration spectra that stimulatethe Pacinian corpuscles [8]. Ruffini endings are the stretchreceptors that detect tangential forces generated in the skin
0.6mm
R = 0.2mm
D
0.2 mm
R = 0.05mm
D = 0.2mm
Fig. 1. Textured surfaces: (a) coarse, D¼0.6–1.8 mm and (b) fine.
F. Shao et al. / Tribology International 43 (2010) 2308–2316 2309
during tasks like grasping objects [9]. Their function is notconsidered further in this paper, rather the interest is toinvestigate stress fields and oscillations (both with position andtime) in the stress fields caused by static and sliding contacts, thatmight be detected by Merkel discs and Meissner and Paciniancorpuscles.
Early work on fingertip mechanical modeling, both analytical(considering the tip as an elastic continuum [10] or as a waterbed,i.e. a fluid contained by a skin [11]) and numerical [12], was notsuccessful at accurately simulating both the contact deformationof a fingertip and the sub-surface stresses at the positions ofmechanoreceptors. It was concluded [11] that it would benecessary to model the epidermis/dermis/subcutaneous tissue/bone layering of a tip. Subsequently, two areas of research havedeveloped. In one, there has been a concentration on whatmaterial properties to assign to the layers. Both linear elastic [13]and more complicated hyperelastic, linear viscoelastic skin over afluid/hyperelastic biphasic subcutaneous tissue [14–17] proper-ties have been chosen, for both 2D [14–16] and 3D [17] models. Inthe other, while describing the material layers by linear elasticity,model geometry has been made more realistic by including bothepidermal ridges (fingerprints) and the matching undulatinginterface between the epidermis and dermis (papillae) [18–20]as part of the fingertip. The conclusions carried forward to thepresent paper are that linear elasticity is sufficient for its purposeand that modeling fingertip ridges is important.
The previous FE modeling just summarised is focused on staticloading of a fingertip against plane surfaces or simple indenterssuch as gratings, wedge or line contacts or single or two pins,although [18] does consider fingertips sliding over flat surfaces.Its conclusions on resolution limits of Merkel disc receptors are inagreement with the physiological ones. None of these previousstudies extend to the treatment of fingertips sliding over texturedsurfaces. This paper’s contribution is to add sliding motion to theloading of a 2D FE fingertip model, with fingerprints, againstsimply textured surfaces, to generate data on the spatial and timevariation of sub-surface stresses and strains relevant to the stimu-lation of Meissner and Pacinian corpuscles. However, it considersonly such variations caused by texture. In this first paper,adhesive friction effects are not considered. Also the modeling isa static elastic one, i.e. ignoring inertia and viscous effects. Futurework will certainly need to be more realistic in these respects. Thesimulations to be presented show that even with these simpli-fications the sliding interactions between fingerprints and modelrough counterfaces can produce stress and strain oscillations offrequencies that would stimulate both Meissner and Paciniancorpuscles.
2. Methods
2D FE models have been constructed of both textured surfacesand of fingertips with and without fingertip ridges. Simulationshave been carried out in static loading and sliding conditions. Thestatic loading results are reported for model validation reasonsand to provide a base line against which the sliding results can becompared.
2.1. The models
Profiles of the textured surfaces are shown in Fig. 1. In all casesthe raised portions (plateaux) are rectangular with roundedcorners. In Fig. 1a their width and height of 0.6 and 0.2 mm werechosen to match features of a plastic moulded surface of interestto the researchers. A range of different surfaces were created byvarying plateaux spacing D from 0.6 to 1.8 mm, chosen to cover
the range of just resolvable by a fingertip to easily resolvable asdescribed in Section 1 [3,4]. Fig. 1b shows a finer textured surface,chosen to investigate contact at roughnesses below that resolu-tion limit.
Fig. 2 shows the general shape of the fingertip model,representative of the index finger of a typical male subject,approximated to an elliptical form of major and minor axes 20and 14 mm [14]. It is composed of epidermis, dermis, subcuta-neous tissue, bone and nail. Fingertip models with and withoutepidermal ridges were analyzed. Papillae (the undulations at theepidermis/dermis interface) were not included. The left of centreof Fig. 2a shows the ‘without ridges’ epidermis shape. Right ofcentre shows ‘with ridge’ form with ridge size taken from [17].Both the thickness of the epidermis and dermis layers wereassumed to be 0.7 mm [21] and 0.8 mm [22], respectively. As aresult there was a slightly greater cross-section of material withinthe ‘without’ than ‘with’ ridges model that contributed to aslightly larger stiffness of the former, as will be seen in Section 3.
Fig. 3 shows the meshing of the fingertip models, created withthe software ABAQUS/CAE v.6.6, used in implicit mode. 4-nodebilinear plane stress quadrilateral elements and 3-node linear planestress triangle elements were used. In total, 29 213 elements wereused in this simulation. Path A is identified at the dermis/epidermisinterface, as well as (in close up) two individual elements. One, atthe centre of Path A, is at the typical position of a Merkel disc orMeissner corpuscle. The other is in the dermis, next to the dermis/subcutaneous tissue interface, taken to represent the position of aPacinian corpuscle. They are considered further in Section 2.2.(Neither plane stress nor plane strain is entirely appropriate for thepresent case in which the full 3D contact is circular. The view wastaken that it would not matter which extreme was chosen as long asthe model’s compliance was calibrated against that of real fingertips,as described next.)
The fingertip model materials were taken to be elastic, andinertia effects were not included in the simulations, as alreadymentioned in Section 1. Material properties are thus completelycharacterized by Young’s modulus E and Poisson’s ratio n.Historically, E and n values for models’ dermis, epidermis andsubcutaneous tissue have been determined and validated in oneof two ways. In one, values have been chosen so that the model’s
14
0.7
3
206 Nail
Bone
Soft tissue
Dermis
Epidermis
7.5
Soft tissue
Dermis
Epidermis
0.8
0.7
0.450.05
Fig. 2. The multi-layer fingertip model (a) overall view and (b) detail of epidermal ridges (all dimensions mm).
Element near Pacinian corpuscle
Element near Meissner corpuscle
Path A
0.7mm
Start point
Fig. 3. Model meshing, with Path A and individual elements from which data were
extracted.
Table 1The mechanical properties of the fingertip model [21].
Calibrated Young’s modulus (kPa) Poisson’s ratio
Bone 17�106 0.3
Soft tissue 24 0.4
Epidermis 80 0.48
Dermis 50 0.48
Nail 17�104 0.3
F. Shao et al. / Tribology International 43 (2010) 2308–23162310
skin surface deflection in response to concentrated loading, forexample a line load [11] or two adjacent line loads [14], matchedexperimentally measured deflections. In the other, the model’scompliance in loading against a flat surface has been matched toexperiment [18]. In the present work, loading against a flatsurface was applied, as has already been published [23]. Table 1records the values obtained, as well as the model’s bone and nailproperties.
0.5862 sec (peak) Finger sliding direction
0.5811 sec (valley) Finger sliding direction
Finger sliding direction 0.5919 sec (peak)
0.5958 sec (valley) Finger sliding direction
Fig. 4. Von Mises stress distribution during (a) the static, (b) sliding with 0.6 mm
surface and (c) sliding with 0.2 mm surface simulations.
F. Shao et al. / Tribology International 43 (2010) 2308–2316 2311
Fig. 3 also shows the textured counterface against which thefingertip was loaded. Two types of models were created. In one,used for the majority of simulations, from which internal stressdistributions were extracted, it was modeled as an elastic solidbody (with mesh as shown) with a Young’s modulus and Poisson’sratio of 2 GPa and 0.3, as for a plastic material. These values are solarge compared to the fingertip moduli that the body is effectivelyrigid. In the other, used only when overall loads and sliding forceswere the outcomes of the simulations (Fig. 7), it was modeled as arigid shell, with the same surface definition as that of the solid,with a reference point from which the forces were taken.
2.2. The simulations
Static loading was performed by displacing the fingertip1.2 mm towards the textured surfaces of Fig. 1a. For the real(three-dimensional contact) fingertips [23] against which themodel was calibrated, this was equivalent to a contact load of0.5 N which is a typical static touch loading. Mises stress, strainenergy density and maximum strain distributions along Path A(Fig. 3) were extracted and displayed. These measures werechosen as they have been selected by other researchers [17,18].The Path A is at the epidermis/dermis interface (0.7 mm beneaththe surface), where Merkel discs and Meissner corpuscles arepositioned.
Two sliding simulations were carried out. In the first thefingertip was slid against Fig. 1a surface, with D¼0.6 mm. Inthe second, sliding was against the Fig. 1b surface. In both cases,the fingertip was first displaced towards the textured surfacewithout sliding by a distance of 0.6 mm (equivalent to creating aload of 0.1 N, which is typically gentle to medium stroking load)over a time span of 0.5 s. Then the fingertip was slid over thesurface at constant separation, at a speed of 25 mm/s for 1 s, i.e.for a 25 mm sliding distance. Speed of 25 mm/s is a typical touchsliding speed. The adhesive friction coefficient was set to zero, tofocus on stress variations within the fingertip caused purely byfinger and counterface topography. In initial trials no overlap wasallowed between the master (counterface) and the slave (finger-tip) contacting surfaces during sliding. This resulted in computa-tional failures, even with the fine mesh sizes used to define thetopography. Relaxation of this condition to allow 0.01 mm overlapresolved this problem.
In the sliding stage, the simulation was divided into steps eachof 10�4 s. The consequent sampling frequency of 10 kHz is morethan sufficient for the study of stress variations up to 500 Hz, nearthe upper limit of sensitivity of Pacinian corpuscles. Mises stressvariations were recorded along Path A, as in the static loadingsimulations. They were also recorded at the positions of theMeissner and Pacinian corpuscles shown in Fig. 3, as defined inSection 2.1. Fast Fourier Transforms (FFT) analysis was carried outon the stress variations extracted from the Meissner and Paciniancorpuscle sites.
3. Results
Fig. 4 shows a range of views of static and sliding contacts for afingertip with ridges, with their Mises stress distributions. Fig. 4a,for a fingertip loaded statically on to a D¼1.8 mm surface, showsthat even at the normal displacement of 1.2 mm, the fingertip didnot contact the counterface between the 0.2 mm high plateaux. Itcan also be seen that for the plateaux to either side of the centre ofcontact, the peaks of stress from the contact with the fingertipridges are away from the plateaux mid-points. This arises fromthe difference in pitch between the plateaux and the fingertipridges.
Fig. 4b (D¼0.6 mm) and c (D¼0.2 mm) is for the slidingsimulations. In each case, the two images show stresses atdifferent times. These times are ones at which maximum andminimum values of oscillating force and stress levels wereobserved, as considered in more detail in Section 3.2.
A final point may be made, indirectly relating to validation ofthe model. In Fig. 4a the surface texture (D¼1.8 mm) clearlycauses stress variations of the same repeat distance at the depthbelow the surface of the Merkel discs. But in Fig. 4b and c, at thatdepth, there is no periodicity, respectively, of 0.6 or 0.2 mm to beseen. This is consistent with people’s inability to resolve textureas its scale reduces below the range 0.6–1 mm [3,4].
0
0.002
0.004
0.006
0.008
0.01
0.012
0
Distance along the path (mm)
Von
Mis
es s
tres
s (M
Pa)
D = 0.6mmD = 0.6mm No ridgeD = 1.8mmD = 1.8mm No ridge
1 2 3 4 5 6 7 8 9 10
Fig. 6. Differences of Mises stress variation between fingertip models with and
without epidermal ridges.
0.0116
0.0118
0.012
0.0122
0.0124
l for
ce (
N/m
m)
F. Shao et al. / Tribology International 43 (2010) 2308–23162312
3.1. Static loading
The Mises stress, strain energy density and maximum strainalong Path A are shown in Fig. 5a, b and c for the loading of thefingertip model with epidermal ridges against Fig. 1a surfaceswith D¼0.6, 1.0, 1.4 and 1.8 mm. Decrease in the amplitudes ofoscillation are seen with decrease in D. It is also seen that forD¼1.8–1 mm, adjacent stress peaks are D apart, but for D¼0.6mm this is no longer the case. Not only are the peak stressesfurther apart than for D¼1 mm, but their spacing is not constant.There is a transition from the stress variation along Path A beingdominated by the texture to being determined by the epidermalridges.
This is further developed in Fig. 6 in which (for the example ofMises stress) the results from Fig. 5a for D¼0.6 and 1.8 mm arecompared to the equivalent results from the ‘without ridge’fingertip model. For D¼1.8 mm the results are almost the same.For D¼0.6 mm the without ridge fingertip model results in amuch smoother variation of stress with position than the withridge model.
It is worth commenting that in both Figs. 5 and 6 the spacingbetween stress peaks is generally not equal to the epidermal ridgespacing of 0.45 mm. Thus the Merkel discs and Meissner cor-puscles, which are positioned discretely at the epidermis/dermis
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0
Distance along the path (mm)
Von
Mis
es s
tres
s (M
Pa) D = 0.6mm
D = 1mm
D = 1.4mmD = 1.8mm
0.00E+001.00E-042.00E-043.00E-044.00E-045.00E-046.00E-047.00E-048.00E-04
0
Distance along the path (mm)
Stra
in e
nerg
y de
nsit
y(N
/mm
2)
D = 0.6mmD = 1.0mmD = 1.4mmD = 1.8mm
0
0.02
0.04
0.06
0.08
0.1
0
Distance along the path (mm)
Max
imum
str
ain
D = 0.6mm
D = 1.0mm
D = 1.4mm
D = 1.8mm
1 2 3 4 5 6 7 8 9 10
2 4 6 8 10
1 2 3 4 5 6 7 8 9 10
Fig. 5. (a) Mises stress, (b) strain energy density and (c) maximum strain along
Path A in static contact, for a fingertip with epidermal ridges.
0.011
0.0112
0.0114
0.5Time (sec)
Nor
ma
With epidermal ridges
No epidermal ridges
-1.0E-04
-5.0E-05
0.0E+00
5.0E-05
1.0E-04
Time (sec)
Fri
ctio
n fo
rce
(N/m
m)
With epidermal ridges
No epidermal ridges
0.52 0.54 0.56 0.58 0.6
0.5 0.52 0.54 0.56 0.58 0.6
Fig. 7. (a) Load and (b) friction variations with time from sliding test, D¼0.6 mm.
interface at this spacing, will systematically sample, from one tothe next, different phases of the cyclic stress variations seen inthese figures. As long as the wavelength of the stress variationexceeds 0.45 mm, the variation will be detectable, even thoughonly being sampled and not being experienced as a continuouswave. Finally, Fig. 5 indicates it does not matter which parameter(energy density, Mises stress or maximum strain) is used to studyvariations of distortion, even though one or another may be morebiologically plausible. In the remainder of this paper, as in Fig. 6,Mises stress will be reported.
3.2. Sliding
Fig. 7a and b (note the false origins) show the load and frictionforce variations over the first 0.1 s sliding time (2.5 mm slidingdistance) of the first sliding simulation, for fingertip models withand without epidermal ridges. A number of comments may bemade. (1) The mean load (Fig. 7a) reduces by E5% and theamplitude of oscillation of the friction forces (Fig. 7b) increasesand approaches a steady state over the sliding time. These are
0.003
0.0032
0.0034
0.0036
0.0038
0.004
0.0042
0.0044
0.5
Time (sec)
Mis
es s
tres
s (M
Pa)
Meissner Corpuscle No RidgePacinican Corpuscle No RidgePacinian Corpuscle With RidgeMeissner Corpuscle with Ridge
0.52 0.54 0.56 0.58 0.6
F. Shao et al. / Tribology International 43 (2010) 2308–2316 2313
artifacts of allowing a small overlap to develop between thesurfaces as sliding commenced, as mentioned in Section 2.2.(2) The load in the without ridge fingertip test is E3% larger thanthat in the with ridge test. This can be accounted for by the extramaterial in the without ridge model’s epidermal layer (Fig. 2), sothat it is stiffer, as already mentioned in Section 2.1. (3) Both theload and friction force (Fig. 7b) oscillate with time, with thefrequency from the with ridge model twice that from the withoutridge model. Both are due to the changing interference with timebetween the fingertips and textured surface. For the without ridgemodel the oscillation periodic time of 0.024 s (frequency 42 Hz)is the time for one plateau of the textured surface to move toits adjacent plateau’s original position (D¼0.6 mm, slidingspeed¼25 mm/s). The oscillations arise from the varying overlapwith time between the fingertip and counterface under theconstant separation imposed between them. For the with ridgemodel, the periodic time of 0.012 s is associated with cyclesof loading and unloading of the fingertip ridges against theplateaux, in this example where there are four fingertip ridges(spacing¼0.45 mm) for every three plateaux. The detail of Fig. 4bshows that at the time 0.5862 s of peak friction force there aremore fingertip ridges loading (coming into contact) than unload-ing. At the time 0.5811 s of minimum friction force there are moreridges unloading. The oscillations of friction force are as expectedfrom a deformation mechanism of friction as considered furthernext. (4) Finally, the amplitudes of oscillation of the friction force(Fig. 7b) are of order 10�3 times the load mean values (Fig. 7a)and the mean values of the friction forces are zero. This isconsistent with the deformation friction forces in these simula-tions arising from loading and unloading elastic deformation(i.e. there is no viscous deformation and therefore no energy lossin the model).
Fig. 8 shows the variation of stress along Path A at an instant oftime that may be compared with the D¼0.6 mm results of Fig. 6.The overall stress levels are lower because of the smallerdisplacement of the fingertip towards the counterface for thesliding than the static simulation. But a larger fractionaloscillation of stress can be seen for the sliding than the staticridged fingertip model. As points of validation, the area under thecurve (E0.5pasM, with a the half-width and sM the central Misesstress) leads to a load (N/mm) E0.025–0.03. This is of the sameorder as the load of E0.01 N/mm in Fig. 7a, the factor 2–3difference arising from the fact that the Mises stress is not thesame stress measure as the normal stress (syy, Fig. 2) over thecontact. If the same stress distribution acted over the circular areaof a 3D contact, the volume under the surface (E0.67pa2sM)leads to a load (N) E0.13–0.2. This is E twice the intended loadof 0.1 N (see Section 2.2), the same proportionate difference as forthe N/mm comparison with Fig. 7a, again arising from thedifference between the Mises stress measure and syy.
0
0.001
0.002
0.003
0.004
0.005
0Distance along the path (mm)
Von
Mis
es s
tres
s (M
Pa) With epidermic ridges
No epidermic ridges
2 4 6 8 10
Fig. 8. Path A Mises stress distribution, sliding simulation 1.
The oscillations with time of Mises stresses at Meissner andPacinian corpuscle locations are shown for both sliding simula-tion conditions in Fig. 9a and b. In the case of sliding test 1(D¼0.6 mm, Fig. 9a) oscillations in stress occur at twice thefrequency in the with ridge than the no ridge model. This is for thesame reason as friction forces oscillate at twice the frequency (asdescribed around Fig. 7b). In the case of sliding test 2 (D¼0.2 mm,Fig. 9b), oscillations in stress are at the same frequency for boththe with and without ridge models. They arise at the frequency of125 Hz expected from the time for one plateau of the texturedsurface to move to its adjacent plateau’s original position(D¼0.2 mm, sliding speed¼25 mm/s). In this case, the fingertipridge spacing (0.45 mm) is close to twice the plateaux separation(D¼0.2 mm). After 0.1 mm sliding distance (when at the start thefingertip ridge and plateau at the centre of contact are directly ontop of each other) there is least interference between the twosurfaces and least loading. This can be seen in Fig. 4c.
FFT from these data are presented in Figs. 10 (D¼0.6 mm) and11 (D¼0.2 mm), respectively. Fig. 10a and b, for fingertips withepidermal ridges, shows clear peaks at the 84 Hz identified inFig. 7. For the fingertip without ridges, a peak at 42 Hz is seen inthe Pacinian site data (Fig. 10c) again as expected in Fig. 7.However, at the Meissner site (Fig. 10d) there may be a peak at42 Hz but there is certainly one at 84 Hz. Both with and withoutepidermal ridges, the peaks at the Pacinian are clearer than thoseat the Meissner sites. There is a high level of noise that comesfrom the sampling frequency’s minimal value for the purpose ofidentifying spectral characteristics over the Pacinian corpuscles’sensitivity range.
Fig. 11, from the second sliding simulation’s data, shows adifferent noise characteristic. It comes from collecting data over4 s sliding time rather than the 1 s used for Fig. 10. However,peaks at 125 Hz are clear at both Pacinian (Fig. 11a) and Meissner(Fig. 11b) sites, for fingertips with ridges. The peak is stronger atthe Pacinian site. In addition harmonics at 250 and 375 Hz are
0.003
0.0032
0.0034
0.0036
0.0038
0.004
0.0042
Time (sec)
Mis
es s
tres
s (M
Pa)
Pacinian corpuscle no ridgeMeissner corpuscle no ridge
Pacinian corpuscle with ridges
Meissner corpuscle with ridges
0.5 0.52 0.54 0.56 0.58 0.6
Fig. 9. Mises stress oscillations at Meissner and Pacinian corpuscle sites:
(a) D¼0.6 mm and (b) D¼0.2 mm.
0 50 100 150 200 250 300 350 400 450 5000
1
2
3
4
5
6
x 10-6
Frequency (Hz)
MP
a
0 50 100 150 200 250 300 350 400 450 5000
1
2
3
4
5
6
Frequency (Hz)
MP
a
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10-6
Frequency (Hz)
MP
a
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10-6
Frequency (Hz)
MP
a
x 10-6
Fig. 10. FFT (from data collected over 0.1 s sliding time) of the Mises stresses from Fig. 9a, at (a,c) Pacinian and (b,d) Meissner corpuscle sites, fingertips (a,b) with
epidermal, (c,d) without epidermal ridges.
F. Shao et al. / Tribology International 43 (2010) 2308–23162314
seen at the Pacinian site; they are only just observable abovethe noise at the Meissner site. In the absence of fingertip ridges(Fig. 11c and d) no obvious spectral peak occur at all.
4. Discussion
It is known that different surfaces do provoke different sensoryevaluations from people when they slide their fingers over them,from psychophysical feelings such as rough or smooth toemotional feeling such as exciting or boring [1,24]. It is alsoknown that surfaces’ textures are sensed by fingertip receptorsand interpreted by the brain. Factors such as surface roughness,friction, vibration behaviour cause those feelings [25,26]. In thepresent study, a multi-layered elastic FE model of the fingertiphas been developed to investigate the biomechanics of tactilesensation. Its advantage over waterbed and continuum fingertipmodels is that it can, as can other previous FE models consideredin Section 1, predict the surface deflection of the fingertip and the
stress and strain distribution within the soft tissues. Its originalcontribution is to extend its analysis to sliding over texturedsurfaces.
Guided by previous studies [14,18,19] three parameters wereinitially selected for considering the responses of nerve endings tocontact with a counterface: energy density, Mises stress and maxi-mum strain. All three parameters were extracted in the case ofstatic loading. As is seen in Fig. 5, for variations of these parameterswith position, at the depth of Merkel discs/Meissner corpuscles,they gave similar results. The peak-to-valley variation with posi-tion increased when the repeat distance D between two plateauxincreased. The human psychophysical performance data indicatesthat people begin to discriminate gaps at 0.5 mm with very reliablejudgments at 1.0 mm [3,4]. In this study, the peak-to-valleydifferences were relatively small and unchanging over the rangeof D from 0.6 to 1 mm. However, when D was increased to 1.4 mm,the peak-to-valley difference tripled. The peak-to-valley differencewas five times higher when D increased to 1.8 mm. These resultsare consistent with the earlier psychophysical data.
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Fig. 11. FFT (from data collected over 0.4 s sliding time) of the Mises stresses from Fig. 9b, at (a,c) Pacinian and (b,d) Meissner corpuscle sites, fingertips (a,b) with
epidermal, (c,d) without epidermal ridges.
F. Shao et al. / Tribology International 43 (2010) 2308–2316 2315
The influence of fingerprints on Mises stress variations in staticcontact is explored in Fig. 6. When D¼1.8 mm there is nodifference in stress variation between the fingertip models withand without ridges. Since the resolution limit of a fingertip instatic contact is around 1 mm this finding indicates thatfingerprints are not essential for human static touch feelings(through Merkel discs), nor by implication for simulations ofstatic loading, even though (Fig. 6) fingerprints do enhance stressvariations, relative to contact without fingerprints, when D
reduces to 0.6 mm.A different conclusion comes from the sliding contact simula-
tions. Then the increased variations of stress with position causedby the presence of fingertip ridges, found with small D values instatic contact (Fig. 6) and also in sliding contacts (Fig. 9) translateto oscillations within a fingertip significantly different betweenmodels with and without such ridges. This is consistent with arecent work on the function of fingerprints [27]. Fig. 10, sliding ata speed of 25 mm/s over a surface with D¼0.6 mm showsoscillations over the frequency range up to 100 Hz, from the
model with fingertip ridges, at the sites of both Meissner andPacinian corpuscles. Most likely the Meissner corpuscles wouldreact to these. With D¼0.2 mm (Fig. 11) spectral peaks occur athigher frequencies when fingertip ridges are present. In particularthere is a peak at 250 Hz in this example, in the region of thePacinian corpuscles (Fig. 11a). They would be sensitive to this ashas recently been directly demonstrated in a tribological context[28]. This paper therefore provides numerical evidence to supportthe idea from psychophysical studies [8] that surfaces withroughness wavelength detail below the threshold resolvable instatic contact by Merkel discs and in sliding contacts by Meissnercorpuscles may be recognized by the oscillations that slidingcauses at Pacinian corpuscle sites.
The particular frequencies observed in Figs. 10 and 11 arisefrom the particular way in which this paper’s artificially simple(regular) textured surfaces interact with a fingertip, as describedin Fig. 9 in Section 3. A more naturally rough surface, with aspectrum of wavelengths in its surface structure, would beexpected to generate a more complex variation of stress with
F. Shao et al. / Tribology International 43 (2010) 2308–23162316
time at a Meissner/Pacinian corpuscle site. Furthermore, thispaper’s model is not a dynamic one, i.e. it does not include wavepropagation phenomena. The extracted time variations of stressin Fig. 9, together with their FFT descriptions, Figs. 10 and 11, areto be regarded as the forcing vibrations to which a dynamicfingertip will react. The importance of wave transmission throughthe skin layers has been established for a long time [7]. A nextstage of modeling/simulation must include dynamic effects andextend to more complicated (natural) rough surfaces.
There is a question whether such a next stage should alsoinclude modeling the undulating geometry (papillae) of theepidermis/dermis interface. Maeno et al. [18], for example, hasshown that including papillae increases the stress level at aMerkel disc site, though Meissner corpuscle sites are moreinfluenced by the inclusion of epidermal ridges, and neitherepidermal ridges nor papillae are important for stressing Paciniancorpuscles. These conclusions come from fingertips in contactwith flat surfaces. The present paper has shown oscillations ofstress at Pacinian corpuscle sites (Fig. 9) both with and withoutmodeling epidermal ridges. They come from surface texture.Considering a next stage of modeling, Maeno’s results suggestthat including papillae might be important only if stress levels atMerkel discs are of interest.
Finally, this paper has not included adhesive friction in itsmodeling. Variations of stress have come entirely from surfacetopography. Maeno et al. [18]again has included adhesive frictionin his modeling, with an adhesive sliding friction coefficient of 1.0.He has demonstrated a redistribution of stresses from the leadingto the trailing edge of a contact similar to that expected from theloading of an isotropic cylinder on a plate. Future developments ofthis paper’s modeling must include adhesive friction, not just at asteady level but to include dynamic (stick-slip) friction.
5. Conclusion
2D finite element models have been created of a fingertip bothin static contact with and sliding over a range of simple roughsurfaces. Loads have been typical of human fingertips exploring asurface (i.e. less than strong gripping loads). Sliding has beencarried out at 25 mm/s, again typical of exploratory speeds.
Investigations of how stress at the depth of Merkel discs varieswith position in a static contact have shown that as roughnesswavelength increases above 0.6 mm the stress variations becomeincreasingly large, such that Merkel discs would be expected toresolve them. This conclusion applies whether or not epidermalridges (fingerprints) are included in the FE fingertip model.
In the case of sliding contacts, the existence or not ofepidermal ridges strongly affects the models’ behaviours. Slidingover surfaces with roughness wavelength 0.6 mm has given riseto oscillations in the range 40–100 Hz at both Meissner andPacinian corpuscle sites, much clearer with the presence ofepidermal ridges than without. These would be expected tostimulate the Meissner corpuscles. Sliding on surfaces with awavelength of 0.2 mm has generated oscillations of frequencygreater than 100 Hz that would be detectable by Paciniancorpuscles, but only with the fingertip model including epidermalridges.
This initial study demonstrates that FE modeling is able to giveinsights as to how skin microstructure may aid tactile perceptionbut further work is needed on sliding over more realisticallyrough surfaces, with dynamic FE models with more complete(including viscosity) material models and including adhesive(stick-slip) friction.
Acknowledgments
This work was funded by the UK’s EPSRC (EP/D060079/1) andthe EC (NEST 043157), and supported by MacDermid AutotypeLtd. The views expressed here are the authors’ and not those ofthe EC.
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