# Biomechanics in skin/clothing interactions

## Abstract:

Skin/clothing interactions or abrasions lead to discomfort or blistering. These irritations may turn out to be critical in athletic competitions or military missions. However, despite the theoretical and practical importance of the problem, no research has been published investigating the connections between skin abnormalities and the physical properties of the fabric (elastic modulus, thickness, mass density, and friction coefficients), or between the initial gap and relative interaction intensity between skin and fabric. This chapter therefore seeks to fill this gap by describing two models of skin/fabric interactions and how these interactions may lead to skin injuries.

## 20.1 Introduction

Skin abrasion leads to hot spots [1]; even mild abnormality in garment/skin regulatory interaction could result in discomfort, with consequences such as itching, rashes and blistering. These irritations can prove to be critical in athletic competition or military operations, when reduced performance or mobility [2–5] has adverse, or even fatal, consequences [6]. This alone necessitates a thorough investigation and understanding of interactions between garment and skin under various conditions. There has been a long string of research papers devoted to this subject. A recent review article [7] focuses on methods of studying and assessing the skin’s response to fabrics in static contact, in terms of changes in capillary blood flow and skin hydration. More thorough investigations on skin blisters due to friction under controlled conditions have been reported [8], followed by laboratory studies on the treatment of such blisters [9]. Another report examined the pathophysiology, prevention and treatment of blisters caused by friction [10]. Other studies investigated the influence of skin friction on the perception of fabric texture and pleasantness under a series of environmental conditions from neutral to hot-dry and hot-humid, and one conclusion is that moisture (not liquid sweat) on the skin surface increases significantly the skin friction [11]. Others analyzed the friction effects of skin in contact with different types of materials and found that friction coefficients varied from 0.37 (skin/nylon), 0.61 (skin/silicone) [12] to 0.9 (skin/rubber hoses) [13]. Still others applied numerical methods to simulate the friction contact effects of soft tissues such as pigskin, and reported that specimens subjected to specimens/platen friction may experience 50% greater stress than those that experienced frictionless contact between specimens [14–16]. A finite element (FE) model was developed by Hendriks *et al.* to characterize the non-linear mechanical responses of human skin to suctions at various pressure levels [17–19].

Skin friction blisters, a frequent dermatological injury associated with intensive abrasion of skin against other surfaces, can inactivate an otherwise healthy individual, and be of significant consequence for such intensive events as sport and military operations: for infantry soldiers carrying heavy equipment and supplies over long distances, blisters can account for 48% of the total injuries [20].

From a mechanical approach, abrasion will lead to ‘sore spots’, portions of the skin suffering excessive stress and strain, and will eventually result in blistering [21]. The blisters are caused by frictional forces which mechanically separate the surface epidermal cells from the stratum spinosum [2]. Hydrostatic pressure then causes the area of separation to fill with a fluid similar in composition to plasma but with a lower protein level [22].

In the late 1950s and early 1970s [2,6,23–25], friction blisters became one of the main focuses of skin research and a special apparatus was designed for creating friction blisters. The instrument consists of a rubbing head to which various materials (including textiles) may be attached. The head can be moved over the surface of any chosen skin site at a selected stroking rate under a given compressive load. The effect of skin moisture was also studied: a dry or nearly dry skin reduced the friction, intermediate degrees of moisture increased friction, and highly moist or completely wet skin decreased the friction again.

The geometry of the rubbing head, its weight and the material attached to it all affect the friction coefficient measurements [26]. Sivamani *et al.* [27,28] utilized the UMT Series Micro-Tribometer, a tribology instrument that permits real-time monitoring and calculation of the important parameters in friction studies, to conduct tests on abdominal skin samples of four healthy volunteers. They concluded that skin friction appears to be dependent on additional factors, such as age, anatomical site and skin hydration; the choice of the probe and the test apparatus also influence the measurement [27,28] and Amonton’s law does not provide an accurate description of the skin surface [29].

Emollients and antiperspirants alleviated blistering. For instance, Darrigrand *et al.* and Reynolds *et al.* [30,31] showed that antiperspirants reduced sweat rates and tended to decrease blisters, in spite of their side effect of introducing irritant dermatitis. However, antiperspirants used with emollients abated irritant dermatitis but did not reduce total foot-sweat accumulation, occurrence of hot spots, or appearance and severity of blisters as the emollients may have altered the antiperspirant’s chemical properties. In addition, the emollients may have acted as moisturizing agents, thus increasing the friction [32], and macerating the stratum corneum [33].

The effects of clothing on blistering have also been documented. Herring and Richie [34] conducted a double-blind study to determine the effect of sock fiber composition on the frequency and size of blistering events in long-distance runners. The two socks were identical except in their fiber content: one was100% acrylic, while the other was 100% natural cotton. The acrylic fiber socks were associated with fewer blisters and smaller blister size compared to cotton socks.

An ulcer formation hypothesis [35] can also be applied to the formation of blisters from a mechanical perspective. The plantar foot experiences a distributed shear and compressive stresses due to joint tangential and vertical forces. As a result, affected skin may slip (i) toward, (ii) away from or (iii) parallel to (i.e. a region in which no slip occurs) each other. The friction coefficient is defined as the ratio of the tangential/vertical forces, and blister formation is inhibited if the frictional coefficient is below a critical minimum (*μ*_{Rmin}).

Despite extensive friction blister studies, the prevalence or severity of friction blisters remains difficult to predict and prevent. The reasons may lie in the variations of skin condition (surface roughness, hydration, adhesion between skin layers, etc.) among individuals as well as among different anatomical locations on the same individual [36]. These variations may have pronounced effects on the dynamic contact of skin against outer-materials, and may ultimately dictate the occurrence and severity of blisters.

However, no studies investigating the connections between skin abnormalities and the physical properties of the fabric (elastic modulus, thickness, mass density and friction coefficients), or between the initial gap and relative interaction intensity between skin and fabric, have been reported, in spite of the theoretical and practical importance of the problem. This chapter, therefore, will describe two models of skin/fabric interactions and will discuss how these interactions may lead to skin injuries. Specifically, the first model focuses on the dynamic interactions between a fabric sleeve and a rotating arm model, accounting for the above factors, by developing an explicit finite element (EFE) model to simulate the problem. To facilitate a comparison of the numerical results, all the Von-Mises stresses are normalized into relative values. The second model is a blistering model again using the EFE method. For given shear and normal forces, this model is able to account for the influences of the friction coefficient, stiffness of the abrasion material, non-linear dynamic contact between skin and the material, and even the blistering geometry. The static and dynamic responses of the blister are obtained through mode frequency, sweeping frequency harmonic analysis, and highly non-linear contact dynamics. The stresses on the hot spots are also compared to account for the effects of friction coefficients and material stiffness.

## 20.2 An explicit finite element model of skin/sleeve interactions during arm rotation

### 20.2.1 Method

#### System description/analytical model

A part of the forearm (Fig. 20.1(a) and (b)) with an idealized cylindrical shape is taken as the base for simulation. For a problem like this, a two-dimensional model would be unable to effectively account for the interaction of fabric with skin. In a 2-D model, the beam or line element must be used to represent the fabric. It is difficult to calculate the line element dynamic contact where the cross-sectional area of the line element is required, as it calls for 3-D model. The current model adopted, therefore, is 3-D, consisting of the fabric sleeve, and skin, muscle and bone forming the forearm, so as to be closer to the actual structure [37]. The sleeve is cylindrical in shape and larger than the forearm; the gap between the two means that gravity causes the sleeve to drop onto the forearm, providing the initial impact.

20.1 (a) Schematics of the FE model for the skin–fabric–arm system under an arm rotation. (b) A local view of the skin and fabric contact in the model.

Also, if the model only includes the skin and fabric components and ignores the muscle and bone, defining the boundary conditions of the inner side of the skin, which interacts with the muscle, is somewhat problematic. If the normal displacement of the inner skin is constrained, then the reaction force will be greater than the actual value at large angular displacement due to the unrealistic boundary constraint. The skin layer is very sensitive to these constraints, since it is extremely thin. Furthermore, normal constraints may cause the fabric to interact with skin to induce a radial displacement. If no normal constraint is assigned, however, continued simulation of the dynamic interaction will become difficult.

The initial configuration of the model is as follows:

(a) The arm is inside the sleeve coaxially so that there is an initial gap between the sleeve and skin.

(b) Upon rotation of the arm at a given initial angular speed, the sleeve first drops freely under gravity.

(c) The falling sleeve then strikes the skin on the still rotating arm.

One of the key issues in our simulation is how to deal with the contact between skin and fabric. The uncertain and more or less oscillating nature of the contact and the soft, flexible and hyperelastic behavior of the skin present significant difficulties in simulation. We employed the augmented Lagrange algorithm (ALA), instead of the Lagrange multipliers or the penalty algorithm, to overcome this problem.

So the total potential energy variation of the system during the whole dynamic interaction process can be expressed as [38,39],

Here λ_{N} and λ_{T} are the Lagrange multipliers, ε_{N} and ε_{T} are the associated penalty parameters, and *δg*_{N} and *δg*_{T} are the virtual displacements. The subscripts N and T denote the normal and tangent directions, respectively, λ_{T} *δg*_{T} reflects the tangential sticking; the gap *g*_{N} ≥ 0 assures no penetration of fabric into the skin; and λ_{N} ≤ 0 indicates a compressive normal stress (fabric pressure on the arm). *g*_{N} λ_{N} = 0 is required so that if the gap is nonzero g_{N} > 0, then λ_{N} = 0, no contact taking place. And if the gap is zero, the contact normal force ≠ 0.

Equation [20.1] can be considered as a generalization of the Lagrange multiplier method where an additional term involving the contact tractions is added to the variation equation. The ALA method will alleviate the ill-conditions (difficulties in convergence) in the penalty and Lagrange methods.

In addition to the ALA, an automatic surface to surface contact method is used with suitable penalty parameters and stiffness factors so as to prevent the fabric from penetrating into itself at large deformation and maintaining the stability of the fabric/skin contact algorithm. The skin is considered to be the master/target and the fabric to be the slave/contact objects in the contact algorithm. In the case of fabric self-contact, however, fabric is treated as both. To ascertain the status of skin/fabric contact at every stage, much finer skin and fabric elements are adopted and the elements in the normal contact direction are treated with special care. All contacts in the normal direction are assumed as plane contact; otherwise the contact stresses (both tangent and normal) will approach a singular state.

Thus the global dynamic equation is

Here [*K*] is the structural stiffness matrix, [*K*_{c}] is contact stiffness matrix, [*M*] is mass matrix and {*f*_{e}} is external force matrix (gravity); {*u*} is displacement matrix and {*ü*} is acceleration matrix. The second term in the left-hand side accounts for the inertial force.

The boundary conditions are as follows:

for the bone: *U*_{x}, *U*_{y}, *U _{z}* = 0, and

*R*

_{x},

*R*

_{y}= 0 (

*R*: rotation degree of freedom)

The initial condition is as follows:

An initial angular velocity *ω*_{Z} is given for bone, muscle and skin at *t* = 0.

In this EFE model, the arm is represented by solid elements with skin thickness 2 mm measured by 20 MHz ultrasound [40], whereas the fabric sleeve is represented by shell elements with a thickness 0.5 mm. The bending stiffness of fabric is

where *E* is the elastic modulus, *h* is the fabric thickness, and *v* is Poisson’s ratio [41].

The skin’s stress–strain curve exhibits a pseudoelasticity, and hence the corresponding strain-energy [42]. In our model, a time-independent, isotropic and hyperelastic constitutive model is used for skin according to [41,43], and the Mooney-Rivlin two-parameter constitutive equation [18,44] is employed with two-parameter *C*_{10} and *C*_{11} to represent the hyperelastic properties of the skin. The bone is considered to be a rigid body, since the elastic modulus of the bone is much larger than that of the muscle or skin. Since our focus is on the interaction between skin and fabric in a very short time, the *muscle* under the skin is presumed to be elastic.

#### Numerical resolution/software

Four numerical simulations, *a, b, c* and *d,* under different conditions, are performed to investigate the interactions between skin and fabric as the forearm is turning by a certain number of degrees in one direction or in alternating directions over a given period of time. Each simulation examines the influence of one parameter at four different levels as detailed in Table 20.1. During calculation, the skin surface nodes experiencing maximum Von-Mises shear stress are located and recorded based on the hypothesis that a higher maximum stress is more likely to cause greater skin irritation. So that different simulation results can be easily compared, normalization is then performed by dividing all other stress values with the corresponding maximum stress in each run, and the normalized relative stresses are plotted against time to illustrate the interactions between the skin and the fabric sleeve during the process. The EFE analyses are performed using commercial FE software (preprocessor: ANSYS V.6.1, Explicit solver: DYNA3D, post-processor: PostGL).

#### Model parameters

Ranges of the parameters for each simulation are listed in Table 20.1.

It is noted that for Simulations *a* and *b,* the arm rotation around axis Z (arm central rotation axis as shown in Fig. 20.1 (a)) is in alternating directions; from 0 to 0.1 s, the arm rotates in one direction for an angular displacement of π/2, i.e. at a constant angular velocity of 15.7 rad/s; then from 0.1 to 0.2 s, the arm reverses in the opposite direction from π/2 to π/2. In other words, the angular speed doubled to 31.4 rad/s upon reversing the rotation direction. This is different from Simulations *c* and *d,* where the arm turns from 0 to π/2 in 0.12 s in one direction only.

The two hyperelastic material properties of the skin are taken from [18] as *C*_{10} = KPa and C_{11} = 100 KPa, input into the card of DYNA3D. For muscle, the normal modulus *E*_{n} is 1 MPa and tangential modulus *E*_{t} 5 KPa adopted from [45]. Thus, computational time is drastically reduced without too much compromise in accuracy. In addition, the contact relationship between parts is classified as perfect bonding (bone/muscle, muscle/skin), and dynamic sliding with friction (skin/fabric), respectively.

Material properties of biological system tissues usually vary greatly from experimental conditions and samples; thus, in order to test the significance of the results and to evaluate their dependence on the model parameter, we take a second set of skin parameter ** C_{10}** = 7.1 KPa and

*C*

_{11}= 34 KPa [18] to simulate the effects of elastic modulus and frictional coefficients on fabric. The results are shown in Tables 20.2 and 20.3.

### 20.2.2 Results

In order to evaluate the shear stress or friction force, the maxima Von-Mises stress (effective shear stress) is used to characterize the skin/fabric interactions in these numerical simulations. The Von-Mises stress is defined as a function of deviated principal stress:

where σ_{i} is the *i*^{th} principal stress, σ* _{j}* are the normal stresses at

*j = x,y,z*axes, and σ

_{xy},

_{zy,xy}are the corresponding shear stresses, respectively.

With the hypothesis that the largest stresses contribute most significantly to skin discomfort, in our simulations we focus on the contact points suffering maximum stresses during arm rotation. In other words, in the following plots, we only provide the time when, not where, the maximum stress occurs on the skin at different levels of the related parameters.

Figure 20.2 shows the results for Simulation *a,* where the normalized maximum effective shear stress at the skin/fabric contact interface is plotted as a function of time at four different fabric elastic modulus levels (A: 200 MPa, B: 400 MPa, C: 600 MPa, D: 800 MPa). It is clear that in this case, all the fabric sleeves strike the arm at the same time as indicated by the peaks at around *t* = 0.04 s, and the second group of peaks occur at the time the rotation direction reverses. Fabric elastic modulus exerts significant influence on the shear response of the skin, and the doubling of the rotation speed at the second period clearly impacted the shear stresses.

20.2 Normalized effective shear stress as a function of time at four different fabric modulus levels for Simulation a: (A) 200 MPa; (B) 400 MPa; (C) 600 MPa; and (D) 800 MPa.

To examine the effects of the fabric/skin friction coefficients on the results, four different fabric/skin friction coefficients are used for Simulation *b*. and the normalized effective shear stresses are plotted against time in Fig. 20.3. Once again, the differences between the two periods of different angular speeds are apparent.

20.3 Normalized effective stresses at different friction coefficients as a function of time for Simulation *b*: (A) 0.3; (B) 0; (C) 0.2; (D) 0.5.

For Fig. 20.3, some curves are shown in more zigzag formats: this is a result of the different sampling frequencies employed during the simulation, which were changed depending on the complexities of each case. However, we used the same number of data points in each graph so as to facilitate comparison among the curves. In other words, some curves are smoother because fewer points were used.

Results in Fig. 20.3 show that the fabric friction coefficients have a significant impact on the skin/fabric interactions. The maximum shear stress corresponds to the value of the friction coefficients, except the anomalous peak *C* with friction coefficient 0.2 at near 0.025 s, a more specific explanation of which is provided in the discussion section.

Effects of initial gap between the fabric and skin are depicted in Fig. 20.4 at four initial gaps: 0.8 (A), 3 (B), 6 (C), and 8 mm (D). The four first-strike peaks take place according to their corresponding initial gaps, yet with samples C and D the sequence was reversed. This shows that the maximum Von-Mises shear stresses are significantly greater with initial gaps of 0.8 and 8 mm than with a gap of 3 and 6 mm, respectively.

20.4 Predicted effective shear stresses at different initial gap between fabric and skin as a function of the rotating time for Simulation *c*: (A) 0.8 mm; (B) 3 mm; (C) 6 mm; and (D) 8 mm.

Note that curve A with initial gaps of 0.8 mm in Fig. 20.4 shows more peaks than other curves. This is not a result of numerical instability. For explicit computation, when the lost energy is smaller than 5% of the initial energy, the result is considered stable. In our simulation, the ratio of final energy to initial energy is close to 1.0. In fact, if we observe that the initial gap in this case is the smallest, 0.8 mm, this tighter arrangement between the skin and sleeve likely leads to more frequent interactions, and thus more peaks.

The effect of fabric density is calculated as seen in Fig. 20.5, where, when the arm is given a constant angular velocity of 13.1 rad/s, the stress magnitude in general increases with an increasing fabric density. The first-strike peaks should occur at the same time the peaks for samples A and B, however, occurred earlier or later.

20.5 Predicated normalized stress response with different fabric density as a function of rotation time for Simulation *d*: (A) 2 × 10^{− 4} g/mm^{3}, (B) 4 × 10^{− 4} g/mm^{3}, (C) 6 × 10^{− 4} g/mm^{3}, and (D) 8 × 10^{− 4} g/mm^{3}.

Figure 20.6 shows that the fabric B which has a lower elastic modulus and consequently is in closer contact with the rotating arm, exhibits a larger displacement due to its more pliable shape conformity.

20.6 Displacements of the sleeves away from the arm contacting point as a function of time at different levels of fabric elastic modulus: (A) elastic modulus: 800 MPa and (B) elastic modulus: 200 MPa.

In order to further validate the results of the simulation, we adopt the second set of skin mechanical parameters *C*_{10} = 7.1 KPa and *C*_{11} = 34 KPa [18] to confirm the effects of both fabric elastic modulus and friction coefficients on the peak Von-Mises stress, and the predictions are tabulated in Tables 20.2 and 20.3. We once again found pronounced peak stresses around the time *t* = 0.1 s, the point when the turning direction of the arm is reversing and thus generating excessive angular acceleration. This result bears close similarities to what was observed in the predictions using the first set of skin parameters above.

### 20.2.3 Discussion and conclusions

As mentioned above, during each simulation, we first scanned all the nodes of the fabric/skin contacts to identify the maximum stress to plot against time. Therefore, we only examined *when* and *how much*, but not *where,* a maximum stress takes place.

Next, the rotation of the arm is a circular motion. For the fabric sleeve to follow this circular motion, we have included a centripetal force distributed over the fabric in the model, pushing it toward the center of the circular path. The magnitude of the centripetal force is equal to the mass *m* of the fabric times its velocity squared V^{2} divided by the radius *r* of its path: *F* = *m*V^{2}/*r*. Obviously this force plays an important role during the fabric/skin interactions.

The effects of fabric tensile modulus studied in Simulation *a* are plotted in Fig. 20.2, which is shown to have exerted a significant influence on the shear (frictional) response of the skin.

There are two major peak locations. The first is located at *t ≈* 0.04 s, which is most likely the point where the fabrics first strike the skin. Obviously, a stiffer fabric would generate a greater impact stress. However, the exact first-strike time cannot be readily estimated by Newton’s Law alone, i.e. by considering fabric free falling from the height of a given initial gap, as the deformation of fabrics and fabric self-interaction may affect the first-strike time.

Nonetheless, this fabric/skin first-strike time is clearly important and will be discussed again in other simulations below.

After the first strike, from *t* = 0.05 to 0.1 s, it is the least stiff fabric A that generates the highest shear stress, as for a given centripetal force, a less stiff fabric in general maintains a better or tighter contact with the skin during a stable circular motion, hence the greater frictional force.

Another interesting point is at *t* ≥ 0.1 s, when reversed arm rotation starts, the higher acceleration and greater centripetal force intensify the fabric/skin impact and the peak frictional forces for all the four samples as mentioned before. It reveals that fabric/skin interactions are often highly dynamic or bumpy in nature as illustrated in Fig. 20.2 (B), rather than just being cases of smooth or static friction.

These characteristics are also indicated in Fig. 20.3, where different friction coefficients are adopted. Generally speaking, when the friction coefficient is smaller, the corresponding shear stress will be lower. However, the higher acceleration and greater centripetal force in the reverse period again causes greater skin/fabric interactions for all the samples in Fig. 20.3 (A)–(D). There are reasons to consider the unusually high peak C with friction coefficient 0.2 at 0.025 s as anomalous; the potential fabric local folding and wrinkling at the fabric/skin interface is likely to result in penalty force and singular stress effect at fabric element edge.

In Simulations *c* and *d*, a constant angular speed *ω* = 13.1 rad/s is chosen. The effects of the initial gap between fabric and skin are studied in Simulation *c* as shown in Fig. 20.4. It is shown that samples A, B and C strike the skin at different times according to their respective gaps; namely, the smaller the gap, the earlier the first strike. The deviation of sample D, however, again highlights the complexity of the whole process. In terms of the magnitude of impact, although a fabric with larger initial gap, and thus higher impact speed, will generate larger effective stress on the skin, the question of why the very close initial gap (0.8 mm) also leads to a significant peak of effective stress on the contact surface has yet to be resolved. This may suggest that when a garment is excessively tight or loose, greater shear stresses could be generated at the skin/fabric contact interface. Further evidence is still required to verify this hypothesis. If the peaks corresponding to different initial gaps in the first time period (0–0.6 s) are excluded, the rest of the four curves are quite similar to each other, as a consequence of the same fabrics moving at the constant angular speed 13.1 rad/s. Another possible reason may be the low impact speed on the skin: the fabric would then have a tighter contact on the skin, and a greater static friction might have contributed to an increased skin surface stress. However, once fabrics settle down, they all show quite smooth interactions with the skin, in contrast with Simulations *a* and *b* where reversed arm rotation does indeed complicate the situation.

Fabric density also exhibits considerable influences on the results as examined in Simulation *d* with Fig. 20.5. Since the skin surface node with maximum effective stress is our focus in the simulation, variations of the first peak time for samples A and B are reasonable because the initial location for this node may be different for each test. Magnitudes of initial impact on the skin are exactly proportional to their mass as predicted by Newton’s Law. The rest of the process is a relatively smooth ride for all samples.

With the hypothesis that the largest stresses contribute most significantly to skin discomfort, in our simulations we focus on the contact points suffering maximum stresses during the rotation of the arm and the changing of direction. It is clear from the results that an increase in fabric elastic modulus, friction coefficient, initial gap and fabric density will all increase the skin stress. Our results should provide guidance for analyzing the skin discomfort caused by fabrics. However, the complexity and random nature of the skin/fabric interactions also generate deviations from the trends predicted above in terms of the time of the first stress peak, the fluctuation of stresses during the arm rotating, and the singular stress state at the boundary.

In fact, a simple analysis below can explain some of the apparent anomalies. For simplicity, the skin/fabric contact model is reduced to 2-D as shown in Fig. 20.7. It is also assumed that the initial local contact area is very small and contact only happens very briefly. Thus the rotation angular displacement of the skin could be neglected. Applying Coulomb’s friction law, shear traction can be determined from [46]:

Expanding equation [20.5] at zero respective to (*x/a*)^{2} leads to

where *T*_{x} is the tangent force along the local contact area, *μ* the friction coefficient, *F*_{normal} the local normal force of contact, *a* the approximate length of contact area, and *x* the distance from the center to the edge of the contact area, and *–a* < *x* < *a.*

Our simulation results also indicate that at initial contact stage the curvature radius of the fabric with a smaller elastic modulus is lower than that of the fabric with a larger elastic modulus, so that the initial contact length *a* with smaller modulus will be longer than that with larger modulus, and the tangent force gives the relationship *T*_{xlargestif} *≥ T*_{xsmallstif}, as has been shown in the simulation results in Figs 20.2 and 20.6.

Finally, we have employed a second set of skin properties to check the influences of both fabric elastic modulus and frictional coefficients. The results shown in Tables 20.2 and 20.3 are consistent with those corresponding to the first set of skin parameters.

The simulations carried out for this study focus on the rotation of the arm, a movement frequently performed in daily life. Analysis of the model has for the first time revealed how variations of such related factors as the elastic modulus, friction coefficients, density of the fabric, and initial gap between skin and fabric contribute to the frictional stresses and presumably to the levels of discomfort caused by the friction between skin and cloth during movement.

Obviously, this report only represents an initial attempt at tackling an extremely complex phenomenon. Our model simulated only a 0.2 s transient process. Time consumption was one consideration (each calculation takes about 15 h on a computer with dual CPUs and 2 GB memory). Also, it is widely believed that transient process is critical in studying human sensations. We assume that a simulation carried out over a longer period and with an integral parameter besides instantaneous values would provide additional information.

Furthermore, different models have been proposed to describe the behavior of skin, including isotropic viscoelastic and hyperelastic theories [41,43], as well as the more realistic porelastic model proposed by Wu *et al*. [15,16].

Finally, we will conduct some experiments in order to validate and improve the numerical model, selecting more appropriate material properties and constitutive equations. We will also deal with the fabric edge singular stress and the problem of fabric contact penetration. Our ultimate aim is to work with interested companies to simulate the dynamic interactions between sports garments and the entire human body [47,48].

## 20.3 Skin friction blistering: computer model

### 20.3.1 Model and material properties

#### Blister geometry model

As shown in Fig. 20.8, the blister in the model consists of three parts: (i) roofed skin, (ii) blister fluid and (iii) basal cell layer. The roofed layer is composed of stratum granulosum, stratum corneum and a small segment of amorphous cellular debris [2]. The blister is considered as an ellipsoid shape with a circular base, whose radius is viewed as the longer axis and set as 3 mm. The height of the blister is the shorter axis. We simulated the dynamics of the blister model using the ANSYS system (v.10.0, ANSYS Inc., Canonsburg, PA, USA, 2005) [49].

The thickness of roofed skin is 55 μm taking into account the thickness of the stratum corneum of the sole [50]. The basal skin layer is 1.6 mm thick as measured by ultrasound (20 MHz) [40]. The blister fluid is contained in the cavity between roofed skin and the basal skin layer. During the computation, the lateral surface (3-D) or sides (2-D) of the basal skin layer are given displacement constraints.

#### Material properties

The elastic modulus of roofed skin is about 13 MPa measured using the *in vivo* dynamic (sonic) method [51], and the skin is assumed to be isotropic. For a simulation of steady or transient time span (a time much shorter than the skin relax time), a linear elastic constitutive behavior can be assumed. The Poisson ratio is taken as 0.4 [50]. The blister fluid is more or less like the plasma derived from blood with bulk modulus: 2150 MPa and apparent viscosity: 1.1 × 10^{− 9} MPa.s [6].

#### Contact algorithm

Materials contact skin with different friction coefficients and the effects on blisters are highly significant [34,52]. Such contact is an extremely nonlinear dynamic problem. The ALA is employed to cope with the challenges through use of the Lagrange multipliers or penalty parameters. So the total potential energy (virtual work) of the system can be expressed as [38,39],

where λ_{N} and λ_{T} are the Lagrange multipliers, ε_{N} and ε_{T} are the associated penalty parameters, and *δg*_{N} and *δg*_{T} are the virtual displacements. The subscripts N and T denote the normal and tangent directions respectively. Equation [20.7] can be considered as a generalization of the Lagrange multiplier method where an additional term involving the contact tractions is added to the variational equation.

### 20.3.2 Results

The model designed in this way is executed as a 3-D model with a radius ratio of 0.5. The mode natural frequencies calculated are shown in Table 20.4, and detailed descriptions of the mode and harmonic analysis are provided in Section 20.3.3. The lowest modal frequency is 28.38 Hz with a modal shape (resonance) shown in Fig. 20.9.

Table 20.4

The modal natural frequencies for the model from 1st to 6th order to account for resonance frequency

The lowest frequency 28.38 Hz is far higher than those occurred in sports competition.

20.9 1st order modal shape with frequency 28.38 Hz. When the loading frequency reaches this value, the blister shape will be excited.

Figure 20.10 (a) and (b) shows the model harmonic analysis with sweeping frequency from 1 to 7 Hz. The loads are 0.1 and 0. 01 N respectively along the normal and tangential directions on the tip of the blister. From the figures, the maximum displacement at 1.6 Hz is 0.031 mm in Fig. 20.10 (a), less than 0.46 mm at 6 Hz in Fig. 20.10 (b).

20.10 Displacement of the blister at different frequencies of excitation: (a) 1.6 Hz and (b) 6 Hz. Blister displacement increased in response to the frequency changing from 1.6 to 6 Hz.

To account for the effects of material properties on blistering in terms of the contacting friction coefficient and stiffness, we simplify the blister into a 2-D FE model with radius ratio 0.5 (Fig. 20.11) for ease of illustration.

20.11 A 2-D FE model of a blister. When force or displacement is loaded on the contacting material, a blister will be formed. Different friction coefficients and contact stiffness could be compared.

In the 2-D model, line elements are used for the roofed skin and contacting material domain, the fluid elements are employed in the blister fluid domain, and the plane elements are in the basal skin layer. To maintain displacement continuity, displacement constrained equations are applied to the interfaces between the roofed skin and blister blood, blister fluid and basal skin layer, respectively.

Two equal compressive forces are applied at both ends of the contacting material in a vertical direction. We assume that the displacement is constrained by the two ends of the basal skin layer. The contact algorithm is used to study the interactions between the contacting material and roofed skin. The contacting materials have an elastic modulus of 100 MPa and a Poisson ratio of 0.3. The two compressive forces are 0.1 N each and a 1 mm horizontal displacement is added to the contacting material in order to generate the friction movement. The blister responses are obtained with frictional coefficient at 0 (frictionless), 0.1, 0.2, 0.3 and 0.4 respectively as shown in Fig. 20.12.

20.12 The displacement and hot spot stress at five friction coefficient levels. In panels (a) to (e), image (i) shows blister displacement and image (ii) shows Von-Mises stress of the hot spot. Friction coefficients are: (a) 0, (b) 0.1, (c) 0.2, (d) 0.3 and (e) to 0.4. The effect of friction coefficient on blister displacement and stress can be compared.

The maximum tangential friction stress τ_{m} and normal pressure *P*_{n} occurred on the top contact point of the blister shown in Table 20.5.

Table 20.5

The maximum tangential friction stress (*r*_{m}) and normal pressure (*P _{n}*) at different friction coefficients

Friction stress (*τ*_{m}) and normal pressure (*P*_{n}) are critical to blister formation. To compare the effect of the friction coefficient, *τ*_{m} and *P*_{n} are calculated.

With the same friction coefficient 0.1 and the same compressive loads, the elastic modulus of the contacting materials changes to 80, 100, and 120 MPa, the respective results of Von-Mises stress in hot spots and displacement of blister show no significant changes; as a result, only data from 120 MPa are provided in Fig. 20.13.

### 20.3.3 Discussion

Friction blisters are a common problem in long-distance running [5] and infantry road marching [20], and as such underline the significance of understanding the dynamic response of the skin under intensive loading. Based on the numerical model, the eigen equation for the system can be established as

where [*K*], [*M*], **[λ],** [*ϕ*], and [0] are, respectively, the stiffness matrix, mass matrix, eigen value matrix, corresponding mode shape matrix, null matrix of the FE assemblage [53].

We first computed the natural frequency of the skin system by finding the eigen frequency from equation [20.8], as this frequency closely relates to the resonance, which has arisen due to the coincidence between the natural and the loading frequencies and leading to much greater deformation and stress, finally resulting in broken blisters.

We assume the gait frequency is from 1 Hz (normal walk) to 7 Hz (fast run). From the mode analysis result, the 1st order natural frequency is > 20 Hz (Table 20.4). It means the loadings with human gait frequency cannot cause resonance, and are consequently unable to lead to the mode shape shown in Fig. 20.9.

Furthermore, to account for the frequency effects on blistering, a normal force 0.1 N and tangential force 0.01 N were loaded on the top point of the blister simultaneously. Then a sweeping frequency harmonic analysis as in equation [20.9] was conducted to investigate the blister deformation at different frequency values.

where the forces are modulated by multiplying with a harmonic term *Sin* (*ωt*) with *ω* as the angular frequency and *t* the time, i.e. *F _{i}* =

*ASin*(

*ωt*) with

*A*as the force amplitude.

The displacement amplitudes of blisters at 1.6 and 6 Hz are extracted and compared as shown in Fig. 20.10. The displacement amplitude at 6 Hz is 15-fold greater that at 1.6 Hz. It suggests that the displacement amplitude of the blister is non-linearly proportional to the loading frequency before the resonance frequency. That is, although the same forces are loaded on the skin, a fast runner is more susceptible to blister formation than a normal walker. Although this is a seemingly simple fact, no experiments or theoretical analyses have been carried out to demonstrate it.

Next, since blistering results from the friction interactions between skin and contact materials, the frictional coefficient contributes to a large degree to the process. Because of the blister symmetry about the related axis, a 2-D FE model was employed here to examine the effects. We consider the deformation and the Von-Mises stress [54] at one hot point at interaction;

where σ_{i;} is the *i*^{th} principal stress, σ* _{j}* are stresses at

*j = x, y, z*axes, respectively, and σ

_{xyzyxz}are the corresponding shear stresses.

The effects of the frictional coefficient are calculated (Fig. 20.12), where five levels of the frictional coefficient from 0.0 to 0.4 are represented by the panels (a) to (e); in each panel, the upper image (i) shows blister displacement while the lower image (ii) represents the Von-Mises stress. Results are summarized in Table 20.5.

From the figures and the table of results, it is clear that the influence of the frictional coefficient *μ* is not monotonic. In Table 20.5, both stress τ_{m} and normal force *P*_{n} reach their corresponding maximum values at *μ* = 0.1. Since the range of *μ* in our study – 0.0 to 0.4 – covers a wide range, our conclusion seems valid in general, except perhaps in the cases where the *μ* value becomes excessive.

The stiffness of the contact materials is also a concern in blister forming and breaking. Some interesting results are obtained from our simulations. When the elastic modulus of contact material increased from 80 to 100 MPa, then to 120 MPa under the same loads and friction coefficient, the tangential friction stress and normal pressure, displacement presented almost no change (as shown in Fig. 20.13). The result is somewhat different from the experiment [34] where different materials show different blistering scenarios. However, from our simulations, the elastic modulus shows no pronounced difference under the calculated range. With the complicated blister forming process, in the above experiments, the different blister events with various contact materials may arise from the difference in the moisture level of the material.

### 20.3.4 Summary

Due to experimental difficulties and variations in skin, we designed a nonlinear dynamic FE model to simulate the deformation of the blister and stress under various loading conditions. From the mode and harmonic analysis, we can concluded that since our gait frequencies (both walking and running) are far below the lowest natural frequency of a blister, human activities are unlikely to lead to blister resonance, presumably with consequences such as broken blisters. Our analysis also indicates that increased frequency will lead to monotonically increasing deformation and stress of the blister. However, increasing the friction coefficient does not necessarily cause greater stress or displacement of blister hot spots. In fact, there is a local maximum friction stress and Von-Mises stress at certain friction coefficient values. Furthermore, the change of elastic modulus in contact material (within 20–30% range) has not generated significant effects on either the deformation or the Von-Mises stress. The model and method provided here have been shown to be robust in evaluating material properties to prevent blistering. As an ongoing project, we will use different fabrics with variable periodic tension forces on skin to investigate the influences and also to further verify our model, avoiding unfounded generalizations regarding the value of the model.

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