The mechanical response of a fiber jamming rod under bending is governed by the interaction between its constituent fibers, mediated by inter-fiber friction. Three distinct mechanical states are identified, as shown schematically in Fig. 1.

The jamming state describes the high-stiffness stage. Under sufficiently small external loads, the inter-fiber shear stress does not exceed the maximum static frictional stress. Consequently, no relative sliding occurs between adjacent fibers, compelling the entire bundle to deform as a monolithic solid. In this state, the structure exhibits its highest bending stiffness, and any induced deformation is fully recoverable upon unloading, as illustrated in Fig. 1a.

For the transition state, as the applied load increases, the internal shear stress at specific locations reaches the maximum static frictional resistance. Slip initiates at these critical interfaces, leading to a gradual decrease in overall structural stiffness. This intermediate state is depicted in Fig. 1b.

The slipping state describes the low-stiffness stage. When the applied load becomes sufficiently large, sliding occurs at all inter-fiber interfaces. In this regime, individual fibers are primarily free to bend about their own neutral axes, resulting in a significantly lower collective bending stiffness for the rod, as shown in Fig. 1c.

The transition between states is determined by comparing the internal shear stress distribution with the inter-fiber frictional resistance. According to the Euler–Bernoulli beam theory, the shear stress τ distribution across the section of the rod is parabolic. By the theorem of conjugate shear stresses, this longitudinal shear stress is equal to the inter-fiber frictional stress. Slip initiates at the location of maximum shear stress when its magnitude equals the maximum static frictional stress μp, where μ is the inter-fiber static friction coefficient and p is the jamming pressure (the hydrostatic pressure applied to maintain the jamming state). Therefore, the condition for the onset of slip, marking the transition from the jamming state, is given by 1τmax⁡Q=μp,

where Q is the transverse shear force on the cross-section and τmax⁡(Q) is the maximum shear stress as a function of Q, determined by the cross-sectional geometry. Solving Eq. (1) yields the upper-bound shear force for the jamming state, denoted as QJ. This force can be expressed in a generalized form as 2QJ=kμp. Here, k is a geometry-dependent coefficient with dimensions of area, determined by the section shape and the elasticity law.

When the applied load is large enough for the rod to enter the full-slipping state, the frictional stress is uniformly equal to μp at all interfaces. Consequently, the lower-bound shear force for the slipping state QS is simply the integral of this constant stress over the total cross-sectional area A: 3QS=Aμp. For fiber jamming, A is the sum of the cross-sectional areas of all fibers.

The bending stiffness of a beam is directly proportional to its area moment of inertia. To describe the variable bending stiffness of the fiber jamming rod, an equivalent area moment of inertia Ieq is defined, which transitions between the values corresponding to the jamming and slipping states.

In the jamming state, the absence of relative sliding forces causes all fibers to bend about the global neutral axis of the composite rod. The equivalent moment of inertia IJ is therefore calculated using the standard formula for a solid beam, integrating over the entire cross-sectional domain D of the fiber bundle: 4IJ=∫DydA, where y is the distance from the area element dA to the neutral axis.

In the slipping state, fibers bend primarily about their individual centroids. However, inter-fiber friction provides an additional resistive moment that contributes to the overall bending stiffness. To derive the equivalent moment of inertia IS, a pure bending scenario under an applied moment M is considered for a bundle of N fibers, each of length l and with an individual area moment of inertia Ifib about its own centroidal axis. According to Euler–Bernoulli theory, the neutral axis of the bundle forms a circular arc with a radius of curvature ρ and a subtended angle θ, as illustrated in Fig. 2. Using the equivalent inertia IS, these geometric parameters are defined as θ=Ml/(EIS) and ρ=EIS/M, where E denotes the effective fiber modulus used in the present structure-level model.

The work done by the applied moment is 5W=12Mθ=M2l2EIS. This work is divided into two components: the elastic strain energy stored in the bent fibers and the energy dissipated by frictional sliding between fibers. The elastic strain energy in a single fiber is 6wie=12mθ=m2l2EIfib, where m is the moment borne by the corresponding fiber; assuming a uniform moment distribution among identical fibers, m=M/N.

To compute the frictional dissipation, the relative slip distance between fibers must be determined. Under pure bending, the elongation deformation of an individual fiber contributes negligibly to the overall structural deformation compared to the inter-fiber slip; therefore, fiber elongation is neglected. For a fiber located at a distance yi from the bundle's neutral axis, the relative arc length difference si between this fiber and the neutral axis over length l can be obtained based on the geometric relationship, as shown in Fig. 2: si=ρ+yiθ-l=EISM+yiMlEIS-l. Substituting the expressions for θ and ρ leads to 7si=MlEISyi. The energy dissipated by friction due to this slip is 8wif=siμpcl, where c is the perimeter length of a single fiber's cross-section involved in frictional contact, making cl the total contact area per fiber subject to sliding.

Invoking the work–energy balance for the system, and noting that the frictional dissipation for a single interface should be accounted for only once (that is, it should be shared equally by the two adjacent fibers), the relationship is 9W=∑iNwie+12wif. Substituting Eqs. (5) to (8) into Eq. (9) yields M2l2EIS=∑iNm2l2EIfib+12MlEISyiμpcl. Simplifying this expression, and introducing the geometric parameter yC=(1/N)∑iN|yi|, which is analogous to the first moment of area about the neutral axis, we obtain the equivalent moment of inertia for the slipping state: 10IS=NIfib+NEμpclρyC. This formulation captures the combined effect of the intrinsic bending stiffness of individual fibers and the significant stiffening from inter-fiber friction.

The equivalent moment of inertia Ieq is modeled as a function of the applied shear force Q, transitioning between IJ and IS. For shear forces below the jamming state limit Q < QJ, the rod remains jammed, and Ieq=IJ. For shear forces exceeding the slip-state threshold Q > QS, the rod is in the slipping state, and Ieq=IS. In the transition region QJ≤Q≤QS, the mechanical behavior is governed by the progressive propagation of inter-fiber slip. In the absence of a rigorous derivation of the slipped area evolution law, we introduce a simple assumption to obtain a closed-form model for the transition regime. Specifically, the slipped area ratio is assumed to vary quadratically with Q between QJ and QS. This choice is made primarily as a low-parameter interpolation that satisfies the two boundary conditions of zero slip at Q=QJ and full slip at Q=QS, while ensuring continuity of Ieq at both ends of the transition interval: 11Ieq=IJ,Q<QJIJ-ISQ-Qs2QJ-QS2+IS,QJ≤Q≤QS.IS,QS<Q This phenomenological model compactly represents the smooth degradation of bending stiffness from the high-stiffness jammed state to the low-stiffness slipped state as the applied shear force increases. It provides an engineering approximation for the transition regime without claiming a rigorous derivation of the slipped area evolution law. The quadratic interpolation is therefore adopted for model completeness, not as a result strictly derived from fiber-bundle micromechanics.

The VSOC consists of a series of sequentially connected, identical chain links. Each link is designed to fulfill two primary functions: facilitating omnidirectional bending in the slipping state in the low-stiffness stage and enabling effective fiber compaction to achieve the jamming state in the high-stiffness stage.

Omnidirectional bending is achieved through a specialized joint mechanism between adjacent links. A shaft is inserted into opposing double-conical holes machined into the mating surfaces of neighboring link bodies. This configuration provides a ball-joint-like connection, enabling multi-axis rotation while preserving structural integrity and load transfer. The conical geometry intrinsically limits the range of motion in directions orthogonal to the primary bending axis.

To house the fiber bundle, each link body is constructed as a rigid shell with a continuous internal cavity. The cavity comprises a semi-cylindrical channel of radius R, integrated with a rectangular section of width 2R and height a, which together provide a rigid constraint along the entire length of the bundle. A key innovation of the design is the integration of a positive-pressure actuation system. A soft airtight inflatable bladder, placed along the flat base of the channel, serves as the actuating element. Upon pressurization, the bladder expands radially, compacting the fiber bundle uniformly against the curved cavity wall. In the present model, the bladder is treated as a compliant pressure-transmission medium, and its bending stiffness as well as membrane-induced non-uniform deformation are neglected in the local pressure distribution. Accordingly, the bladder pressure is taken as the effective jamming pressure p acting on the fiber bundle. This simplification is supported by the present prototype configuration, in which the bladder is only 0.1 mm thick and made of soft polyethylene, serving primarily to transmit pressure and compact the fibers. The resulting contact pressure p acts as the confining hydrostatic pressure essential for fiber jamming, as described in Sect. 2, effectively inducing and maintaining the bundles' jamming state.

The unique double-conical joint design leads to two distinct bending modes for the VSOC, as depicted in Fig. 3, each characterized by distinct kinematic constraints and neutral axis orientations.

The shaft bending is defined as rotation purely about the axis of the connecting shafts, as shown in Fig. 3b. The section rotates around the x axis in Fig. 3b. This mode represents the chains' dominant least-constrained deformation path. The lateral bending is defined as rotation about an axis orthogonal to the shaft axis, as shown in Fig. 3c. The section rotates around the x axis in Fig. 3c. This motion is constrained by the interaction between the shaft and the walls of the double-conical holes, resulting in a substantially smaller allowable range of motion compared to the shaft bending mode.

The pressurized compaction of the fiber bundle critically alters its effective cross-sectional geometry for mechanical analysis, as shown in Fig. 3b. In the unpressurized state, the fibers loosely fill the entire semi-circular area. Under pressure, the expanding bladder compacts the fibers upward, creating a densely packed region. The compaction is characterized by a height χ, measured from the cavity base to the lower boundary of the compacted fiber mass. Consequently, the effective cross-sectional domain D for calculating the jammed-state moment of inertia Eq. (4) is not the full semi-circle but a truncated circular segment. Accounting for this compaction effect is essential for accurate stiffness modeling.

The equivalent moments of inertia in the jamming state differ for the two bending modes because their neutral axes are oriented differently relative to the compacted fiber cross-section. For shaft bending, the neutral axis is parallel to the shaft axis and located at distance h from the bottom of the semi-circle. The moment of inertia IJsh is derived by integrating the second moment of area about this neutral axis over the compacted region D (y from χ to R): 12IJsh=∫χR2y+h2R2-y2dy. Here, y+h is the distance from the area element to the shaft bending neutral axis, and the term 2R2-y2 is the horizontal width of the cross-section at height y. Evaluating this integral yields 13IJsh=π8R4-14R4asinχR-χ4R2-χ22χ2-R2. For lateral bending, the neutral axis is orthogonal to the shaft axis and lies along the centroidal axis of the compacted cross-section. The corresponding moment of inertia IJla is calculated by integrating about this axis: 14IJla=2∫0R2-χ2y2R2-y2-χdy, where the term R2-y2-χ represents the vertical height of the compacted fiber area at a given lateral position y for χ≤y.

The geometric difference between the bending modes also influences the critical shear force QJ for the transition from the jamming state, as defined in Eq. (2). The calculation of QJ requires knowledge of the maximum shear stress τmax⁡(Q) for the specific cross-sectional shape under a shear force Q. To obtain tractable analytical expressions, we approximate the shear stress distribution with that of a rectangular section of comparable dimensions, a common simplification in mechanics for complex geometries.

For lateral bending, the compacted cross-section is approximately symmetric. Using the parabolic shear stress formula for a rectangle of area A and height 2R, the distribution of τ can be expressed as 15τlay,Q=32QA1-y2R2. Obviously, the maximum occurs at y = 0, giving τmax⁡la=(2/3)(Q/A). Setting this equal to μp as presented in Eq. (1) and solving for Q gives the critical force for this mode: QJla=23μpA. For shaft bending, the cross-section is asymmetric about its neutral axis. The approximate shear stress distribution for an equivalent rectangle is modified to τshy,Q=32QR+h2-y2AR2R+3h. The maximum stress occurs at y=h, yielding τmax⁡sh=[3Q(R+2h)]/[A(2R+3h)]. Applying the slip initiation condition τmax⁡sh=μp leads to the critical shear force for shaft bending: QJsh=2(R+a)+3h3(R+a)+6hμpA. Conversely, the slipping state shear force limit QS (Eq. 3) and the slipping state moment of inertia IS (Eq. 8) are independent of the bending mode. QS=μpA depends solely on the total fiber cross-sectional area A and the friction-pressure product. IS, derived from energy considerations involving individual fiber bending and aggregate frictional dissipation, depends on the material properties, fiber geometry, and total pressure but not on the specific orientation of the global neutral axis during bending.

Test specimens were fabricated according to the design in Sect. 3. Each chain link was assembled by bolting together two 3D-printed resin shells to form a cavity with R = 6 mm, h = 4 mm, and a = 3 mm. This cavity housed a bundle of 700 nylon fibers, each measuring 0.4 mm in diameter. Adjacent links, with a center-to-center distance of 12 mm, were connected via stainless-steel shafts seated in opposing double-conical holes machined into the mating interfaces. The distance from the flat base of the semi-circular cavity to the axis of the connecting shaft was 5 mm. The key parameters of the link structure are shown in Fig. 4a. A polyethylene inflatable bladder (selected because of its flexibility and for being airtight), with a width of 10 mm and a thickness of 0.1 mm, was integrated along the base of the cavity to apply positive jamming pressure to the fiber bundle.

The three-point bending setup is illustrated in Fig. 4b. A multi-link chain segment was mounted on a custom support frame with a fixed span length L=100 mm. The support frame was fabricated from 3D-printed ABS (acrylonitrile butadiene styrene). Each support end consisted of a 5 mm diameter cylindrical head. A 1 mm depth groove was formed in the middle of the cylindrical head to suppress off-axis sway during bending while still allowing approximate rotational freedom at the supports. The contact between the specimen and the supports was dry friction, and the overall boundary condition was therefore treated as approximately simply supported for the present stiffness analysis. A universal testing machine equipped with a load cell was used to apply a central deflection using a flat indenter with a contact width of 10 mm at a constant rate of 20 mm min⁻¹, while simultaneously recording the applied force F and the corresponding displacement δ. This loading condition can be seen as quasi-static.

To investigate variable stiffness behavior under different confinement levels, the jamming pressure in the inflatable bladder was systematically controlled, ranging from 0 to 300 kPa in increments of 50 kPa. The bladder pressure was supplied by an independent air pump, measured by a dedicated pressure gauge and regulated by a pressure-control valve. Before each test, the specimen was first placed in a straightening fixture to maintain an initially straight configuration. The bladder was then pressurized to the target value by adjusting the control valve, after which the specimen was transferred to the support frame for deformation measurement. For each pressure level, tests were conducted separately for the two primary bending modes: shaft bending and lateral bending. Each combination of pressure and bending mode was repeated five times to ensure statistical reliability, yielding a complete set of load-deflection (F-δ) curves for analysis.

The raw experimental data F-δ for both shaft and lateral bending modes are plotted as gray dots in Fig. 5a and b. To extract statistically representative mechanical responses and to evaluate experimental variability, a systematic data processing procedure was implemented.

To facilitate direct comparison across repeated tests, the raw F-δ curves from the five repetitions for each experimental condition (jamming pressure and bending mode) were spatially aligned onto a unified displacement coordinate system. This was achieved by defining a common displacement grid with 1000 uniformly spaced points spanning from 0 to 10 mm. For each individual raw curve, the corresponding load values were mapped onto this common grid using piecewise linear interpolation, ensuring all datasets shared an identical abscissa. Subsequently, for each unique combination of pressure and bending mode, the average load at each displacement point was calculated from the five aligned curves, yielding a representative average F-δ curve. Concurrently, the standard deviation of the load was computed at each point to quantify data dispersion. A standard deviation band, defined as the average curve ±1 standard deviation, was then constructed to visually display the data dispersion and experimental repeatability.

The analysis of the standard deviation bands reveals a clear trend of increasing data dispersion with higher jamming pressure. The maximum standard deviation for lateral bending increased from 0.0354 N at 0 kPa to 5.4215 N at 300 kPa, while for shaft bending, it rose from 0.0681 to 1.9934 N over the same pressure range. This heightened dispersion under elevated pressure is likely attributable to less-uniform stick-slip-like slipping between fibers, which introduces greater stochasticity into the macroscopic load-deflection response.

To objectively quantify the key mechanical parameters – specifically, the critical loads at stiffness transitions (FJ, FS) and the corresponding stiffness values in the high- and low-stiffness stages (KH, KL) – an adaptive piecewise linear regression algorithm was developed. This data-driven approach was applied to each individual processed F-δ curve to autonomously locate the transition points between distinct linear-response phases, thereby eliminating subjective bias.

The algorithm operates in two sequential stages to identify the linear regimes corresponding to the jamming (high-stiffness) and slipping (low-stiffness) states.

First stage. Jamming state identification: for each deflection point across the entire displacement range, a proportional (zero-intercept) linear fit of the form F=KHδ is performed on all data points up to that deflection. The coefficient of determination R2 is computed for this fit to quantify the linearity of the jamming state response. The deflection that yields the maximum R2 is selected as the optimal boundary between the high-stiffness stage and the subsequent transition stage. The corresponding load is recorded as the first critical load FJ, and the slope of the proportional fit defines the high-stiffness stage stiffness KH.

Second stage. Slipping state identification: the algorithm scans the data to locate the onset of the stable low-stiffness stage. For each deflection point, a standard linear (intercept-included) fit F=KLδ+b is performed on all data points from that deflection to the end of the displacement range. The R2 value is again computed, and the deflection maximizing R2 after FJ is taken as the optimal start of the slipping state. The load at this location is recorded as the second critical load FS, and the slope of the linear fit to the subsequent data segment defines the slip-state stiffness KL.

This automated procedure was applied uniformly across the entire dataset, except for the 0 kPa condition. Since no jamming pressure is applied under this condition, the fiber bundle remains in a fully slipping state, and its load-deflection response does not exhibit the distinct three-stage characteristics – the jamming, transition, and slipping states – required for the piecewise linear algorithm. Therefore, the dataset subjected to parameter extraction comprised 60 individual curves (6 pressure levels × 2 bending modes × 5 repeats). For each tested condition, the extracted parameters from all five repeats were aggregated, and their mean values along with standard deviations were calculated. This provides a statistically reliable foundation for analyzing the relationship between mechanical behavior and jamming pressure.

Figure 5c and d exemplify the parameter identification process for shaft bending and lateral bending, respectively, under a jamming pressure of 100 kPa. Each subfigure presents the five individual F-δ curves. The overlaid blue and green lines trace the R2 values for the high-stiffness and low-stiffness linear fits, respectively, as the algorithm scans the displacement axis. The algorithmically determined FJ and FS values for each repeat are marked by blue and green dots on the corresponding curves. The mean and standard deviation of these identified critical loads are annotated on the plots, illustrating the consistency and outcome of the extraction method.

In the present study, the fiber modulus E was not obtained from an independent material test. Instead, an effective modulus suitable for the structure-level model was identified from the bending response under zero jamming pressure (p = 0 kPa), where inter-fiber friction is absent. At p = 0, the inter-fiber friction contribution in Eq. (7) vanishes, and the slipping state equivalent moment of inertia reduces to IS=NIfib. For a three-point bending test, the stiffness KL is related to the equivalent bending rigidity by KL=48EIS/L3. The value of KL at p = 0 kPa was obtained via linear regression (R2=0.785) of the corresponding load-deflection data. Combining this with the known structural geometry yielded an effective fiber modulus E = 4.85 GPa, with a 95 % confidence interval of [4.765, 4.925] GPa.

The model response is sensitive to this parameter. According to Eq. (10), the friction-related contribution to IS scales with 1/E; thus, a larger E reduces the friction-derived component of the slipping state equivalent moment of inertia predicted by the model. In addition, because IJ is back-calculated from the measured jamming state stiffness through IJ=KHL3/(48E), a larger assumed E leads to a proportionally smaller identified IJ for the same experimental stiffness KH. Consequently, variations in E affect both the identified equivalent moments of inertia and the agreement between theoretical predictions and experimentally inferred parameters.

The established theoretical model, specifically Eq. (3), QS=μpA, provides the direct way to identify the effective static friction coefficient μ between fibers, where the total cross-sectional area is A=Nπd2/4, with N = 700 (number of fibers) and d = 0.4 mm (fiber diameter). Linear regression was performed on the experimentally identified full-slipping load FS versus jamming pressure p data for both shaft and lateral bending modes. In the three-point bending configuration, the shear force Q is related to the applied load F by Q=F/2. Consequently, the slope dFS/dp from the regression relates to the friction coefficient via μ=(dFS/dp)/(2A).

The regression for the combined dataset, shown in Fig. 6b, demonstrates a strong linear correlation with a high coefficient of determination (R2 = 0.817). This statistically significant relationship robustly validates the fundamental assumption of a pressure-dependent Coulomb friction interface. The identified effective inter-fiber static friction coefficient is μ = 0.3665, with a 95 % confidence interval of [0.3433, 0.3897]. The narrow confidence interval indicates a precise estimate, and the value itself falls within a plausible range for interfacing polymer surfaces under confinement, lending credibility to the model.

The theoretical model predicts a direct proportionality between the jamming pressure p and the two critical shear forces: QJ for the onset of slip and QS for full slipping. The validity of these relationships was tested against the experimental data using the material constants identified in Sect. 5.1.

For shaft bending, the relationship between QJsh and p is shown in Fig. 6a. Linear regression yields R2 = 0.4311. The 95 % confidence interval for the proportionality coefficient is [6.8795, 10.9578] N kPa⁻¹. This interval perfectly encompasses the theoretical value of 9.9763 N kPa⁻¹, calculated using the identified μ and the geometric factor ksh from Eq. (2). The relative error between the fitted coefficient (9.0591 N kPa⁻¹) and the theoretical value is 8.5 %. Taken together, these results suggest reasonable agreement with theory, but they also indicate that jamming pressure is a dominant factor rather than the sole determinant of the measured critical load.

Similarly, for lateral bending, the QJla vs. p data (Fig.  6a) also support a proportional trend, with a linear fit yielding R2 = 0.4475. The 95 % confidence interval for the fitted coefficient is [8.1129, 12.5543] N kPa⁻¹, which again fully contains the theoretical prediction of 11.3065 N kPa⁻¹. The relative error between the fitted value (10.4563 N kPa⁻¹) and the theoretical value is 7.6 %. The consistency between the experimental confidence intervals and the theoretical predictions for both bending modes confirms the validity of Eq. (2) in describing the jammed-state load capacity.

The relationship for the slipping state QS∝p is inherently validated by the high-quality linear fit used to identify the friction coefficient μ in Sect. 5.1 and Fig. 6b. Since the expression for QS in Eq. (3) is identical for both bending modes, the data from both were pooled for this analysis, resulting in the strong correlation already discussed. By contrast, the more moderate R2 values for the QJ–p regressions suggest that, although the experimental trend is consistent with the theoretical prediction and the theoretical values fall within the fitted confidence intervals, other sources of variability are also influencing the onset of slip. Plausible contributors include stochastic stick-slip behavior between fibers, non-uniform jamming pressure transmission, and local compaction caused by the bladder and the packing state of the bundle. The influence of these factors requires the construction of more refined theories and more detailed experiments for characterization and description.

The equivalent area moment of inertia in the jamming state IJ was calculated from the measured stiffness KH using the relation IJ=KHL3/(48E) and the identified effective fiber modulus E used in the present structure-level model. As theorized in Sect. 3.2 and shown in Fig. 6c, IJ remains largely independent of jamming pressure p. For shaft bending, the mean IJ is 47.02 mm⁴ (95 % CI: [40.89, 53.14]), and for lateral bending, it is 43.22 mm⁴ (95 % CI: [37.00, 49.43]). This pressure independence confirms that, once jammed, the fiber bundle acts as a monolithic beam whose bending stiffness is primarily governed by its compacted geometric shape and the effective fiber modulus used in the present structure-level model, rather than by the pressure level itself. The mean compaction heights χ inferred from these IJ values are 5.51 mm for shaft bending and 3.20 mm for lateral bending, consistent with the compaction shown in Fig. 4.

Conversely, the equivalent moment of inertia in the slipping state IS, derived from the measured stiffness KL, shows a clear linear increase with jamming pressure p (Fig. 6d), as predicted by Eq. (8). For shaft bending, the fitted slope is 8.95 mm⁴ kPa⁻¹ (R2 = 0.651), and for lateral bending, it is 3.41 mm⁴ kPa⁻¹ (R2 = 0.551).

Although only one specimen configuration was tested experimentally, the analytical form of the model makes its parameter dependence explicit. According to Eq. (2), QJ is proportional to the friction coefficient μ, the jamming pressure p, and the geometry-dependent coefficient k, so variations in frictional conditions or section geometry will directly affect the onset of slip. According to Eq. (3), QS is proportional to μpA. Since the total cross-sectional area A depends directly on the number of fibers N and the fiber diameter d, both parameters are expected to directly influence the full-slipping threshold. Likewise, Eq. (10) shows that IS depends on E, N, and Ifib, indicating that both material properties and bundle geometry will modify the slope of the low-stiffness stage. Therefore, the model structure allows extension to parameter variations, but the robustness of these dependencies has not been validated here through inter-specimen experiments using different fiber types, diameters, or fiber counts.