Hybrid Finite Element Model for Predicting the Interface Pressure of Medical Compression Stockings

ABSTRACT

Accurate prediction of interface pressure is essential for optimising product design and ensuring the therapeutic effectiveness of medical compression stockings. Finite‐element (FE) methods are commonly used for this purpose, allowing for the integration of specific mechanical and dimensional properties of both fabric and body. However, existing models rely on homogenisation approaches to model the fabric, neglecting its mesoscale architecture and the individual mechanical contributions of yarn systems. This study presents a hybrid FE model that combines discrete and continuous elements to represent local fabric architecture and yarn behaviour. A mesoscale unit cell couples 1‐D connectors for the inlay yarn with 3‐D shell elements for the loop structure, with mechanical parameters identified from uniaxial tensile tests. Two compression zones (ankle and calf) of a class‐II stocking were modelled with zone‐specific course densities, directly linking local architecture to macroscopic response without homogenisation. Interface pressure was predicted in several in‐use configurations by simulating garment placement over rigid leg cylinders. The model was validated against Laplace's law and PicoPress sensor data. Predicted average pressures differed by 5.1%–20.5% from Laplace estimates, and by ≤ 20% from sensor measurements on 3‐D‐printed legs. Local pressure profiles reproduced the therapeutic gradient (ankle > calf) and remained numerically stable after mesh‐ratio optimisation (8:1). The proposed framework enables precise integration of structural and mechanical parameters and represents a significant improvement over homogenised models for pressure prediction and garment design.

The proposed hybrid finite element model for predicting the interface pressure of medical compression stockings considers local fabric architecture and individual mechanical contributions of yarn systems. FE simulations on ankle and calf zones reproduce the therapeutic pressure gradient and match PicoPress sensor data within 10%–20% of error and Laplace's predictions within 5%–20% of error.

1. Introduction

Compression therapy is widely used in the treatment of venous, arterial and lymphatic disorders [1, 2, 3, 4]. Among therapeutic garments, medical compression stockings are the most common solution for lower limb treatment. These garments are typically manufactured from weft‐knitted fabrics, whose loop structure provides high extensibility in both wale and course directions, allowing the fabric to conform to the shape of the leg [5, 6]. A key structural feature of medical compression fabrics is the integration of an inlay yarn, inserted into each course of the loop structure. This yarn strongly reinforces the fabric in the course direction, leading to a marked anisotropy in its mechanical behaviour [4, 7]. While the ground yarns forming the loop structure are highly extensible, the inlay yarns are significantly stiffer and act as mechanical reinforcements [8, 9]. This hybrid architecture results in high stiffness in the circumferential direction and greater elasticity in the longitudinal direction.

The course density defines the spacing and distribution of inlay yarns along the longitudinal direction of the fabric. A higher course density implies a larger number of inlay yarns per region, which increases the circumferential reinforcement. As a result, when the fabric is stretched to be placed over the limb, higher tensile forces are generated, leading to a higher compression effect [3, 9, 10, 11, 12]. In graduated compression products, the course density is varied along the length of the stocking to achieve a progressive pressure decrease from the ankle to the thigh, which is essential for therapeutic efficacy [3, 10, 13]. In medical compression stockings, these compression zones are typically located at the ankle, calf and thigh regions.

The interface pressure, defined as the pressure exerted between the fabric and the body surface, is the most critical parameter in compression therapy [14, 15, 16, 17]. Traditionally, this pressure is estimated using Laplace's law, which relates the interface pressure ($\mathrm{IP}$) to the fabric tension ($T$), fabric width ($W$) and limb perimeter ($P_{\mathrm{leg}}$), as presented in Equation (1) [15, 18, 19].

$$\mathrm{IP}=\frac{T*2\pi }{W*P_{\mathrm{leg}}}$$ (1)

Although widely used, Laplace's law presents important limitations, as it assumes cylindrical body geometries and homogeneous fabric behaviour, which do not accurately reflect either real anatomy or the complex mechanics of knitted textiles. While this approach enables simplified simulations, it does not model the garment itself and therefore cannot account for the influence of fabric design parameters.

To overcome these limitations, finite element (FE) models have become a key tool for simulating the mechanical interaction between compression stockings and the limbs. This approach allows to predict the interface pressure with great accuracy by considering real body morphologies and fabric properties [20, 21, 22, 23, 24, 25, 26, 27].

Two main modelling strategies can be distinguished in the literature. One common approach is to model only the soft tissue of the leg and apply a boundary condition representing the stocking's effect. In this case, the fabric is not modelled directly; instead, a pressure distribution is imposed on the limb surface, often derived from Laplace's law, presented in Equation (1), or obtained experimentally. For instance, Karakashian et al. and Dubuis et al. computed the pressure using the Laplace formula based on fabric tension and leg radius, and assessed its influence on venous return in 2D and 3D leg geometries [26, 28]. Similarly, Yanmei et al. used Laplace‐based estimations to analyse calf pressure distribution under static and dynamic conditions [29]. In other works, Dubuis et al. imposed pressure profiles obtained experimentally through wearable sensors in patient‐specific simulations [30].

While this method allows for simplified simulations of body–fabric interactions, it overlooks the internal structure of the garment and its dependency on fabric design parameters such as yarn type or course density. Moreover, it assumes uniform and isotropic fabric response, which can lead to inaccurate local predictions.

The other method consists of explicitly modelling the stocking as a continuum layer. In FE models, compression fabrics are often treated as thin structures, with small thickness compared to their other dimensions. This simplification allows the use of membrane or shell elements, which reduce computational cost and are suitable for simulating surface behaviour and contact pressure [17, 27, 31]. The mechanical properties of the fabric are represented by global constitutive laws, typically identified from uniaxial tensile tests of the finished fabric. These models can be linear isotropic, orthotropic, or nonlinear hyperelastic. Wu et al. constructed a simplified isotropic model for seamless compression garments based on average tensile modulus values [22]. However, compression fabrics, especially inlaid weft‐knitted structures, are highly anisotropic; therefore, isotropic models do not accurately reflect the directional stiffness of the fabric, particularly in the circumferential direction, which is key to compression performance.

Orthotropic models offer improved accuracy by distinguishing the mechanical responses in wale and course directions. Ye et al. and Dai et al. developed 3D FE models of compression garments using orthotropic elastic properties derived from biaxial tensile tests [20, 25]. Similarly, Chen et al. performed biaxial tests and identified orthotropic parameters by fitting the model response to the experimental curves [32]. On the other hand, Lu et al. adopted orthotropic material models calibrated from uniaxial tensile tests conducted in both principal directions [13]. These orthotropic approaches enable more realistic simulation of fabric anisotropy compared to isotropic models, but they still rely on full homogenisation of the fabric architecture.

Other models use hyperelastic laws to model large circumferential deformations. For example, Ye et al. developed an isotropic hyperelastic model for a compression stocking, with parameters identified from uniaxial tensile tests along the circumferential direction [31]. The model was used to predict interface pressure, and validation was performed by comparing simulation results with measurements obtained using pressure sensors on 3D‐printed rigid leg models. Although this approach models nonlinear deformation more effectively, it remains based on homogenised fabric behavior.

Overall, most models rely on homogenisation defining the compression fabric with a continuous material law and not differentiating the behaviour of the two yarns. As a result, these models do not account for the separate mechanical contributions of the loop structure (ground yarns) and inlay yarns, nor for structural parameters, such as course density, that strongly influence circumferential stiffness and local compression. Indeed, in these models, the mechanical response of the fabric is not linked to the mesoscale architecture and yarn level mechanics. Consequently, to use these models for predicting the interface pressure, each fabric configuration must be experimentally tested to identify its global material parameters since internal structure and yarn properties cannot be directly modified or controlled within the simulation.

To overcome the limitations of homogenised descriptions, hybrid mesoscopic modelling strategies have been proposed. These models explicitly represent the textile architecture using repeated unit cells composed of different element types. Pita Miguelez et al. developed and validated a hybrid model for predicting the tensile response of inlaid weft‐knitted fabrics used in medical compression stockings [33]. In this approach, the loop structure was modelled using shell elements, while the inlay yarns were represented by axial connectors, with mechanical parameters identified experimentally. The unit cell dimensions were directly linked to the fabric architecture in each compression zone, allowing the natural generation of a graduated compression profile.

Similar mesoscopic models have been proposed recently by Ghorbani et al., You et al. and Shi et al. for clothing and therapeutic textiles, although these often remain limited to simpler weave or knit geometries and do not account for variations in inlay yarn distribution along the stocking [4, 34, 35, 36].

In the present work, a hybrid finite element model of a medical compression stocking is developed to predict the interface pressure generated in contact with a non‐deformable cylindrical leg, as a first step toward more complex fabric–tissue interaction models. The loop structure is modelled using shell elements, while the inlay yarns are represented by axial connector elements. Different compression zones of the stocking are modelled independently, each characterised by a specific course density that directly controls the mesh configuration and circumferential stiffness. By combining experimentally identified yarn properties with structural parameters measured for each zone, the proposed approach enables prediction of interface pressure under in‐use conditions without full fabric homogenisation. Validation against analytical estimations and experimental pressure measurements confirms the ability of the hybrid finite element model to predict compression levels across the different zones of a medical compression stocking.

2. Materials and Methods

2.1. Inlaid Weft‐Knitted Fabrics for Medical Compression Stockings

The product selected for this study was a women's medical compression stocking (Class II, size M) manufactured by Sigvaris France and designed with a graduated compression profile. According to the French standard for medical compression hosiery, Class II stockings correspond to an interface pressure range of approximately 15–20 mmHg (≈2.0–2.7 kPa) at the ankle. The stocking comprises three main compression zones located at the ankle, calf and thigh. In the present work, the ankle and calf zones were considered.

All compression zones share the same 1 × 1 inlaid weft‐knitted structure. The fabric is composed of polyamide double‐covered elastane yarns used both for the ground yarn forming the loop structure (22/22/22 dtex) and for the inlay yarns (310/22/22 dtex), which provide reinforcement in the circumferential direction, as illustrated in Figure 2a.

FIGURE 2.

Developed hybrid finite element model of inlaid weft‐knitted fabrics for medical compression stockings: (a) shell elements modelling the loop structure assembled in a cylindrical shape; (b) connector elements modelling the inlay yarn describing a helical path; (c) assembly of shell and connector elements modelling the medical compression stocking.

The stocking is designed to fit a specific range of leg perimeters in each compression zone. When the stocking is worn, the difference between the initial fabric perimeter ($P_0$) and the leg perimeter ($P_{\mathrm{leg}}$) imposes a significant circumferential deformation on the fabric. This deformation induces tensile forces within the knitted structure, which are responsible for the generation of interface pressure at the fabric–leg interface.

The initial fabric perimeter ($P_0$) and the reference leg perimeters ($P_{\mathrm{leg}}$), including minimal, maximal, and calculated average values for size M and for the ankle and calf zones, were provided by the manufacturer and are reported in Table 2.

TABLE 2.

Reference leg perimeters for size M of the medical compression stocking, defined by the manufacturer.

Compression zone	$P_{\mathrm{leg}}$ (mm)
	Minimal	Average	Maximal
Ankle	220	230	240
Calf	330	370	410

The course density ($\mathrm{CD}$), which defines the distribution of inlay yarns along the longitudinal direction of the fabric, and directly controls the amount of circumferential reinforcement, was obtained from the structural characterisation reported by Pita Miguelez et al. [33]. This characterisation was carried out on cylindrical knitted samples representative of the ankle and calf zones, produced using the same yarns and machine settings as the commercial product, shown in Figure 1. A fixed longitudinal spacing of 30 mm between coloured reference lines, shown in Figure 1, was used to define the in‐use configuration, both for tensile testing and for the determination of the course density.

FIGURE 1.

Cylindrical knitted samples representative of the ankle and calf compression zones of the medical compression stocking.

The course density was selected as the key structural parameter of the model, as it reflects the local fabric architecture and varies between compression zones. By explicitly integrating this parameter into the finite‐element model, the local architecture of the fabric is directly accounted for.

2.2. Hybrid Model of Inlaid Weft‐Knitted Fabric

The finite element model was developed based on the previously validated hybrid model for inlaid weft‐knitted fabrics by Pita Miguélez et al. [33]. This approach provides a local‐mesoscopic representation of the fabric architecture by combining continuous (shell) and discrete (connector) finite elements within a unit cell.

Each shell element represents a representative unit cell of the loop structure. The loop structure of the fabric was modelled using four‐node shell elements (S4), which describe the membrane behaviour of the knitted ground structure. When assembled, the shell mesh forms a continuous cylindrical surface representing the tubular geometry of the compression stocking (Figure 2a).

The inlay yarns, inserted along the course direction and responsible for the circumferential reinforcement of the fabric, were modelled using two‐node axial connector elements (CONN3D2), which transfer only axial forces between nodes (Figure 2b). The connector elements link the two lower nodes of adjacent shell elements and are arranged along the circumferential direction, forming two helical paths that reproduce the insertion of the inlay yarns during circular knitting.

The global dimensions of the fabric mesh were defined by the initial fabric perimeter (P ₀), the fabric length ($L$) and the fabric thickness ($t$). The initial fabric perimeters (P ₀) for each compression zone are reported in Table 1. A constant fabric length ($L$ = 50 mm) was used for all compression zones, corresponding to the total modelled length of the fabric. Within this length, a central region of ($L$ = 30 mm) was later defined as an element set for the evaluation of the interface pressure, consistently with the effective fabric length used in the experimental tensile tests presented by Pita Miguélez et al. [33], and in order to reduce boundary effects near the fabric edges. The fabric thickness was approximated as 𝑡 = 1 mm, based on experimental measurements performed on inlaid weft‐knitted fabrics.

TABLE 1.

Identified fabric parameters for the ankle and calf zones of the medical compression stocking.

Compression zone	$P_0$ (mm)	$\mathrm{CD}$ (courses/mm)
Ankle	148	1.467
Calf	196	1.067

The dimensions of the unit cell were defined directly from the local structural parameters of the fabric. The unit cell height ($h$) was defined as the inverse of the course density ($\mathrm{CD}$), which is zone‐specific and corresponds to the in‐use configuration of the fabric. Based on the values reported in Table 1, the resulting unit cell heights were 0.682 mm for the ankle zone and 0.937 mm for the calf zone. The initial connector length ($l_{\text{conn}}$) was set equal to the unit cell height $\left(h\right)$, considering a squared initial configuration of the unit cell. Figure 3 presents the global and local dimensional parameters of the developed model.

FIGURE 3.

Dimensional parameters of the hybrid finite model for medical compression stockings.

By defining the unit cell dimensions from the course density, the number and distribution of unit cells, and therefore of connector elements, vary naturally between compression zones. This configuration directly reflects the local distribution of inlay yarn reinforcement and the associated differences in circumferential stiffness. Since the course density was determined under in‐use conditions, the longitudinal extension of the fabric is implicitly accounted for in the model. Consequently, only circumferential deformation was imposed in the simulations to reproduce the in‐use configuration.

Due to the higher course density and smaller initial fabric perimeter (P ₀) in the ankle zone, the number of unit cells and connector elements per unit length is higher than in the calf zone. This results in a finer mesh for the ankle, with a larger number of connectors contributing to the circumferential tensile response, and a coarser mesh for the calf. This difference in mesh density directly reflects the experimentally observed variation in inlay yarn reinforcement between compression zones.

2.3. Material Properties

Mechanical properties were assigned independently to the loop structure and to the inlay yarn, based on the experimental tensile characterisation presented by Pita Miguélez et al. [33]. This separation allows the hybrid finite element model to account explicitly for the distinct mechanical roles of the two yarn systems within the fabric.

The shell elements (S4), modelling the knitted loop structure, were assigned an isotropic linear elastic law. The elastic modulus (𝐸) and Poisson's ratio (𝜈) were identified by inverse analysis from uniaxial tensile tests performed on weft‐knitted samples without inlay yarns, subjected to circumferential loading, following the NF G30‐102‐B standard. The identified values were 𝐸 = 0.02 MPa and 𝜈 = 0.1, as reported in [33]. These parameters describe the mechanical response of the ground yarn network and were kept constant for all compression zones.

The inlay yarns were modeled using connector elements (CONN3D2) with an axial spring behaviour. The mechanical response of the connectors was derived from uniaxial tensile tests conducted on inlay yarns extracted from the compression stocking. The tests were performed up to rupture using an in‐house experimental protocol adapted for covered elastic yarns, as described in [33]. The force–elongation response of each connector was obtained by converting the experimental force–strain curve of the inlay yarn into a force–elongation relationship, considering the corresponding initial connector length. This procedure allows the nonlinear tensile behaviour of the inlay yarn to be directly incorporated into the finite element model.

2.4. FE Simulations for Interface Pressure Prediction

Finite element simulations were performed using Abaqus/Explicit to predict the circumferential mechanical response of the compression fabric and the resulting interface pressure generated on a rigid leg model. For each compression zone considered in this study, ankle and calf, an independent rigid leg geometry was defined. Three simulations were carried out per zone, corresponding to the minimum, average and maximum leg perimeters defined by the manufacturer and reported in Table 2. This configuration allowed the evaluation of the pressure response over the full range of in‐use circumferential deformations for the selected product size.

The rigid leg was represented by a cylindrical geometry discretised with quadratic rigid shell elements (R3D4) of square shape and fully constrained in all translational and rotational degrees of freedom. The total length of the rigid cylinder was set to 70 mm. A conical transition was added at the lower end of the cylinder in order to facilitate the initial placement of the fabric and to avoid numerical instabilities at the onset of contact.

At the beginning of the simulation, the fabric was positioned below the rigid leg model, as illustrated in Figure 4a. The placement of the fabric was simulated by imposing a prescribed vertical displacement to the fabric nodes, progressively pulling the fabric upward along the longitudinal axis of the leg. Since fabric mesh accounted for the course density identified under in‐use conditions, the longitudinal deformation of the fabric is implicitly considered in the model. Consequently, only the circumferential deformation needed to be imposed during the simulations. The fabric was therefore constrained in the longitudinal direction to prevent axial sliding, while remaining free to deform circumferentially. As a result, the fabric expanded radially to fit the imposed leg perimeter, generating tensile forces within the knitted structure, as shown in Figure 4b,c. The final position of the fabric was defined such that its upper edge was located 10 mm below the top of the cylindrical leg, as shown in Figure 4d, reproducing the experimental configuration for pressure measurements.

FIGURE 4.

Simulation of the vertical sliding of the medical compression stocking over rigid leg. (a) Initial configuration of the simulation, with stocking placed below rigid leg model; (b) and (c) intermediate positions of the stocking sliding over rigid leg (d) final position of the stocking, at the end of the simulation.

A frictionless surface‐to‐surface contact formulation was defined between the external surface of the fabric and the rigid leg. This assumption was adopted to simplify the contact behaviour and to isolate the mechanical response of the textile structure, and is consistent with previous numerical studies on clothing pressure that reported negligible friction effects at the fabric–skin interface [14, 27, 29]. The rigid leg was defined as the master surface and the fabric as the slave surface. Geometric nonlinearity was enabled to account for the large deformations experienced by the knitted fabric. A bulk viscosity damping factor of 0.1 was introduced to ensure numerical stability during the sliding and contact phases.

The simulations were run until a final equilibrium configuration was reached, corresponding to the fully placed fabric in contact with the rigid leg. The interface pressure between the compression fabric and the rigid leg was obtained from the simulation output using the contact pressure variable CPRESS, computed on the master surface of the rigid cylinder.

Due to the sensitivity of contact pressure fields to local contact conditions and mesh compatibility, the interface pressure was evaluated as an averaged quantity. The average interface pressure was calculated from CPRESS values over a predefined element set located in the central region of the fabric–leg contact area, as illustrated in Figure 5. Only compressive contact values were considered in the averaging procedure.

FIGURE 5.

Element set selected for contact pressure evaluation over rigid leg model.

To reduce boundary effects near the fabric edges, interface pressure was evaluated over a central element set of 30 mm, corresponding to the active measurement length used in experimental tensile tests. This evaluation region is consistent with the effective sensing area of the PicoPress probe and ensures a representative pressure measurement.

Finally, a mesh‐sensitivity analysis was conducted to ensure numerical convergence and compatibility between the fabric mesh and the rigid leg mesh. The fabric mesh, defined from the structural parameters described in Section 2.3, was kept constant throughout the analysis. The discretisation of the rigid leg was progressively modified by varying the characteristic element size of the rigid surface ($h_{\text{rigid}}$). Since both the fabric and the rigid leg meshes were composed of square elements, the element height and width were identical for each mesh. The circumferential mesh‐size ratio, calculated with Equation (2), was therefore controlled by adjusting the rigid element size relative to the fixed fabric mesh.

$$R_{\text{mesh}}=h_{\text{rigid}}/h_{\text{fabric}}$$ (2)

The circumferential mesh‐size ratio was varied between 2:1 and 10:1. For each configuration, the average interface pressure was computed to identify a stable discretisation range and to ensure accurate contact interactions.

2.5. Validation of the Finite Element Model

The predictive capability of the finite element model was assessed by comparison with analytical estimations based on Laplace's law and with experimental interface pressure measurements obtained using a PicoPress sensor. These two validation approaches allow verification of the numerical predictions against both a theoretical reference and experimental data under controlled conditions.

For the analytical validation, the average interface pressure predicted by the finite element model was compared with the pressure estimated using Laplace's law. The analytical pressures were derived from the experimental tensile characterisation reported by Pita Miguélez et al. [33]. Uniaxial tensile tests were performed along the circumferential direction on the cylindrical fabric samples described in Section 2.1, following the NF G30‐102‐B standard. For each compression zone, the fabric was stretched up to the maximum leg perimeter defined by the manufacturer (Table 2). From the resulting force–perimeter curves, the tensile forces corresponding to the three reference leg perimeters used in the simulations, minimum, average and maximum, were extracted. Considering the cylindrical geometry of the experimental samples and of the rigid leg model used in the simulations, as well as the uniform circumferential deformation imposed, Laplace's law could be applied to estimate the corresponding interface pressures. These analytical pressure values, calculated with Equation (1), were then compared with the average interface pressures obtained from the finite element simulations, as described in Section 2.4, for each compression zone and leg perimeter.

Experimental validation was performed using interface pressure measurements acquired on rigid cylindrical leg models with a PicoPress sensor (Microlab Elettronica, Padua, Italy) [37], positioned at the mid‐height of the cylinder, as illustrated in Figure 6. The PicoPress probe has a finite sensing area with a diameter of 5 cm and therefore provides an averaged pressure value over its contact region. For consistency with the experimental setup, the numerical validation was based on the average interface pressure extracted from the central element set of the fabric–leg contact area, defined at the same axial location as the sensor. Experimental measurements were performed only for the maximal leg perimeter defined by the manufacturer (Table 2), corresponding to the available 3D‐printed rigid leg models and representing the most critical in‐use configuration in terms of deformation. For each compression zone, five samples were tested and the mean measured pressure value was retained for comparison with the finite‐element predictions.

FIGURE 6.

Interface pressure measurements with PicoPress sensor (a) 3D‐printed cylinders for each compression zone: Black for ankle, blue for calf. (b) Placement of the pressure sensors, between the fabric and the rigid leg model.

The accuracy of the finite element predictions was quantified using the absolute error (AE) and the percent relative error (PRE). For both analytical and experimental validations, AE and PRE were calculated according to Equations (3) and (4), where $\mathrm{I}{\mathrm{P}}_{\mathrm{FE}}$ is the average interface pressure predicted by the finite element model and ${\mathrm{IP}}_{\mathrm{ref}}$ corresponds either to the analytical pressure estimated using Laplace's law or to the experimental pressure measured with the PicoPress sensor.

$$\mathrm{AE}\left[\mathrm{KPa}\right]=\mid {\mathrm{IP}}_{\mathrm{ref}}-\mathrm{I}{\mathrm{P}}_{\mathrm{FE}}\mid$$ (3)

$$\mathrm{PRE}\left[\%\right]=\frac{\mid {\mathrm{IP}}_{\mathrm{ref}}-\mathrm{I}{\mathrm{P}}_{\mathrm{FE}}\mid }{{\mathrm{IP}}_{\mathrm{ref}}}*100$$ (4)

3. Results

3.1. Mesh Sensitivity Analysis

A mesh sensitivity analysis was performed to assess the influence of the rigid leg mesh on the predicted interface pressure. The analysis was carried out for the ankle zone, with the average leg perimeter. The fabric mesh was kept constant, while the rigid leg discretisation was progressively modified by increasing the element size of the rigid surface.

The predicted average interface pressures obtained for the different mesh‐size ratios are presented in Figure 7a. The horizontal axis represents the mesh‐size ratio, where a value of 2 corresponds to a ratio of 2:1 between rigid and fabric element sizes. The error bars indicate the standard deviation of the contact pressure over the entire fabric–leg contact area, providing a measure of pressure heterogeneity.

FIGURE 7.

Mesh sensitivity analysis, with error bars representing standard deviation of pressure values at the fabric‐leg interface. (a) Complete analysis considering mesh size ratios between 1.5:1 and 10:1. (b) Focus on mesh size ratios between 2.5:1 and 8:1.

The results show that the mesh‐size ratio has a strong influence on the homogeneity of the predicted interface pressure. Very fine ratios (e.g., 1.5:1 or 2:1) and very coarse ratios (e.g., 9:1 or 10:1) produce higher variability across the contact area. This variability is due to poor element matching between the two surfaces, leading either to under‐resolution (for coarse meshes) or to instability in contact force transmission (for overly fine meshes).

Mesh ratios between 2.5:1 and 8:1, shown in Figure 7b, resulted in more stable and homogeneous pressure distributions, with lower standard deviation values. Among these, a ratio of 8:1 was selected for the subsequent simulations, as it provides an optimal compromise between numerical stability, accuracy of the predicted interface pressure when compared to Laplace's predictions, and computational efficiency.

3.2. Predicted Interface Pressure

The finite element results were first analysed in terms of interface pressure distribution and average pressure levels for the different compression zones. Figure 8 presents the contact pressure maps obtained on the rigid leg surface at the end of the simulations for the three reference leg perimeters, minimal, average and maximal, and Table 3 presents the averaged interface pressure for the different leg perimeters and compression zones.

FIGURE 8.

Simulated interface pressure profiles for different compression zones and leg perimeters.

TABLE 3.

Averaged interface pressures (IP) for the three reference leg perimeters, minimal, average and maximal, for ankle and calf.

Compression zone	IP ($P_{\mathrm{leg}}\min$) (KPa)	IP ($P_{\mathrm{leg}}\mathrm{avg}$) (KPa)	IP ($P_{\mathrm{leg}}\max$) (KPa)
Ankle	2.08	2.16	2.29
Calf	1.32	1.39	1.56

As expected, contact pressure develops only in the region where the fabric is in contact with the cylindrical part of the leg, while negligible pressure values are observed outside the active compression zone. This confirms the correct definition of the boundary conditions, contact formulation, and fabric placement procedure adopted in the simulations.

Consistent with previous numerical studies on compression garments, the contact pressure fields exhibit local heterogeneities associated with the discretisation of the contact interface and the intrinsic sensitivity of contact algorithms [13, 20, 32, 35]. For this reason, the quantitative analysis focuses on the average interface pressure, computed over the central element set defined in Section 2.4. The use of an averaged pressure value over a representative contact region is commonly adopted in numerical and experimental studies of compression garments in order to obtain consistent and comparable pressure estimations [20, 32, 38].

For both compression zones, the predicted interface pressure increases with increasing leg perimeter. Larger leg perimeters impose higher circumferential strains on the fabric, leading to increased tensile forces within the knitted structure and, consequently, higher interface pressures. In addition, higher pressure levels are systematically obtained in the ankle zone compared to the calf zone. This behaviour reflects the higher density of inlay yarn reinforcement modelled in the ankle region through a larger number of connector elements, resulting in greater circumferential stiffness and resistance to deformation, as reported in previous experimental and numerical studies on inlaid compression fabrics [33, 34, 39].

The predicted average interface pressure ranges from 2.08 to 2.29 kPa for the ankle zone and from 1.32 to 1.56 kPa for the calf zone, as summarised in Table 4, which is consistent with the expected pressure gradient expected for graduated medical compression stockings. When considering averaged interface pressure values, these results are within the pressure range specified for French Class II medical compression stockings. They demonstrate the ability of the hybrid finite element model to reproduce zone‐dependent compression levels based on local structural parameters.

TABLE 4.

Absolute error (AE) and percent relative error (PRE) between finite element predictions and analytical (Laplace) and experimental (PicoPress) interface pressure values for the ankle and calf compression zones.

Compression zone	$P_{\mathrm{leg}}\max$		$P_{\mathrm{leg}}\max$		$P_{\mathrm{leg}}\max$
	FE—Laplace		FE—Laplace		FE—Laplace		FE—sensor
	AE (KPa)	PRE (%)	AE (KPa)	PRE (%)	AE (KPa)	PRE (%)	AE (KPa)	PRE (%)
Ankle	0.11	5.02	0.16	6.90	0.12	4.98	0.24	9.49
Calf	0.11	7.70	0.26	15.76	0.4	20.41	0.39	20

Finally, it was observed that the standard deviation of the contact pressure increases for larger circumferential deformations, particularly for the maximal leg perimeter. The highest variability was obtained for the calf zone at the maximal leg perimeter, reflecting the increased sensitivity of the contact formulation under large deformation conditions, despite the mesh optimisation identified through the sensitivity analysis. Similar trends have been reported in previous finite‐element studies of compression garments and are commonly attributed to the combined effects of contact nonlinearity and mesh discretisation [13, 20, 32].

3.3. Validation of the Numerical Model

The predictive capability of the hybrid finite element model was assessed by comparison with analytical interface pressure estimations derived from Laplace's law and with experimental measurements obtained using a PicoPress pressure sensor. Validation was performed under in‐use conditions corresponding to the reference leg perimeters defined by the manufacturer for the selected medical compression stocking.

Figures 9 and 10 present the comparison between the average interface pressure predicted by the finite element model and the analytical values obtained from Laplace's law for the ankle and calf compression zones, respectively. Results are shown for the three reference leg perimeters: minimal, average and maximal. In addition, experimental PicoPress measurements are included for the maximal leg perimeter only, corresponding to the available experimental configuration and representing the most critical in‐use condition.

FIGURE 9.

Comparison between finite element predictions, analytical interface pressure estimations obtained from Laplace's law, and experimental PicoPress measurements for the ankle compression zone and the three reference leg perimeters.

FIGURE 10.

Comparison between finite element predictions, analytical interface pressure estimations obtained from Laplace's law, and experimental PicoPress measurements for the calf compression zone and the three reference leg perimeter.

For both compression zones, the finite element predictions reproduce the expected increase in interface pressure with increasing leg perimeter, reflecting the increase in circumferential deformation imposed on the fabric. Higher pressure levels are consistently predicted in the ankle zone than in the calf zone, which is in agreement with the higher density of inlay yarn reinforcement and the greater circumferential stiffness of the ankle region, as reported in previous experimental and numerical studies [9, 10, 15].

The analytical pressures calculated using Laplace's law follow the same overall trends, predicting higher pressures for larger leg perimeters and higher values in the ankle than in the calf. However, Laplace's law systematically provides higher pressure values than the finite element model. This behaviour has been widely reported in the literature and is attributed to the simplifying assumptions of Laplace's law, which considers a homogeneous membrane and a uniform cylindrical geometry and does not account for local variations in fabric structure, anisotropy, or contact conditions [14, 15, 17].

Quantitatively, the agreement between finite element predictions and Laplace estimations is good for the minimal leg perimeter, with relative errors of approximately 5.0% for the ankle and 7.7% for the calf, as reported in Table 4. Larger discrepancies are observed for the calf zone, which is characterised by a larger curvature radius and stronger geometric transitions. These factors increase the sensitivity of the contact formulation and may lead to a moderate underestimation of the interface pressure by the finite element model for larger leg perimeters.

Experimental interface pressure measurements obtained using the PicoPress sensor are included in Figures 9 and 10 for the maximal leg perimeter. Due to the finite sensing area of the PicoPress probe, which provides an averaged pressure over its contact region, validation was performed using the average interface pressure extracted from the central element set of the fabric–leg interface in the finite element simulations. For both compression zones, the finite element model correctly predicts higher interface pressure in the ankle than in the calf, in agreement with experimental observations.

The experimentally measured pressures are systematically higher than the finite element predictions. This behaviour is consistent with previous studies reporting that the finite thickness of the PicoPress sensor may lead to a slight overestimation of interface pressure when measurements are performed on rigid or curved surfaces [40, 41]. Similar levels of deviation have been reported for finite element validation of compression garments using PicoPress measurements. Ye et al. reported deviations ranging from approximately 10%–20% depending on the material model and compression class [20, 31], while Shi et al. reported an average error ratio of approximately 11.0% ± 7.8% [4].

Overall, the hybrid finite element model exhibits error levels comparable to, and in several cases lower than, those reported in previous numerical studies of medical compression garments. The observed deviations highlight the intrinsic sensitivity of contact pressure predictions to local geometry and mesh compatibility, particularly in regions with lower structural stiffness. These results confirm the ability of the proposed model to predict interface pressure under realistic in‐use conditions while maintaining a direct link between fabric structure and macroscopic compression performance.

4. Conclusions

This work presented a hybrid finite element model for predicting the interface pressure generated by medical compression stockings under in‐use conditions. The proposed approach is based on an explicit mesoscopic representation of inlaid weft‐knitted fabrics, combining shell elements to model the looped ground structure with axial connector elements to model the inlay yarn reinforcement.

The course density is directly introduced into the mesh definition and controls the size and distribution of the unit cells. This modelling choice links the local fabric architecture to the macroscopic mechanical response and enables the pressure variations between compression zones to be predicted without the use of homogenised material descriptions.

The mechanical interaction between the stocking and the limb was simulated by sliding the ankle and calf compression zones over rigid cylindrical leg models. The reference leg perimeters were defined from manufacturer data for the selected product size. A frictionless contact formulation was used to impose the circumferential deformation corresponding to in‐use conditions, while the longitudinal deformation was implicitly accounted for through the experimentally identified course density.

The mechanical parameters assigned to the loop structure and to the inlay yarn were obtained from experimental tensile characterisation and applied consistently across compression zones. The predicted interface pressures were compared with analytical estimations based on Laplace's law and with experimental measurements obtained using a PicoPress sensor.

For both compression zones, the finite element model reproduced the expected increase in interface pressure with increasing leg perimeter and correctly predicted higher pressure levels in the ankle than in the calf. The deviations between numerical predictions and analytical or experimental reference values remained within the range reported in the literature for finite element models of compression garments.

Because the mechanical parameters of the yarn systems and the structural parameters of the fabric are explicit inputs, the proposed modelling framework can be readily adapted to different materials, knit designs and stocking sizes without repeated experimental recalibration.

Funding

The authors have nothing to report.

Ethics Statement

The authors have nothing to report.

Consent

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.