Abstract
Addressing the needs of patients with lower-limb amputations remains a complex challenge due to the unique biomechanical and personal requirements of each individual. An effective prosthesis must be carefully adapted to ensure optimal comfort, flexibility, and stability. This study presents a finite element analysis aimed at developing an optimal implant model evaluated during lower-limb locomotion, specifically under two scenarios: normal walking and stumbling. The stumbling phase presents increased biomechanical demands, requiring greater balance and structural resilience. The analysis focuses on the influence of varying the liner’s Young’s modulus on the distribution of equivalent Von Mises stresses in the femur and implant. Additionally, the study investigates contact pressure and longitudinal shear stress distributions on the liner, providing a comprehensive comparison across all cases. The findings contribute valuable insights toward the optimization of prosthetic design for improved comfort and safety in everyday movement.
Keywords: Finite element method, Normal walking, Stumbling, CPRESS, CSHEAR, Liner
Subject terms: Engineering, Health care
Introduction
Patients with above-knee transfemoral amputations require prosthetic devices after surgery to regain their self-confidence by completing their form and regaining as much functional mobility as possible. The prosthetic liner is the primary interface between the amputated limb and the prosthesis, contributing to the transfer of weight from the walking motion. It also plays a critical role in determining the quality of adaptation to the prosthesis. Proper adaptation of the liner can significantly affect the patient’s comfort, mobility, and satisfaction with the prosthesis1–3.
Sahli et al.4 concluded that the liner composed of two foam layers (polyurethane and latex) provides the optimal balance between weight support and minimal stress at the stump-prosthetic interface, with contact pressure and shear stress not exceeding 42.12 kPa and 15.4 kPa, respectively. Overall, the liner’s thickness proved effective in reducing stresses at the stump-prosthetic interface across all three-liner configurations. Benkhettou et al.5 demonstrated that contact pressure and immersion measured as displacement in the load direction decreased significantly from 140 and 9 to 10 kPa and less than 1 mm, respectively. These results support the potential of customized multicellular foam liners and highlight the need for future clinical trials to evaluate their clinical efficacy. The findings provide valuable insights into prosthetic design and customization, opening new avenues for the use of foam materials as an alternative to silicone in liner manufacturing. Huang6 reported that while sole hardness had no effect on the first peak force, it significantly influenced the timing of its appearance, the maximum loading rate, and the 50-ms passive impulse. Sole hardness did not affect knee joint motion or ankle joint abduction but influenced flexion, extension, and internal rotation movements. Li et al.7 analyzed the static and dynamic mechanical behavior of a joint model under various conditions using the finite element method. Results indicate that joint stress increases nonlinearly with body weight, with the majority of the knee joint system’s structural force concentrated on the meniscus. Gu et al.8 investigated the damage and failure mechanisms of sandwich cylindrical shells using quasi-static uniaxial compression tests. To predict multi-mode failure, they applied an equivalent monocoque shell theory, effectively simplifying the complex sandwich structure into a quasi-isotropic cylindrical model. This approach provided a practical framework for analyzing failure behaviors under compressive loading. Recent research has advanced the understanding of foam mechanics and prosthetic interface optimization under static and dynamic loading conditions9–11. Bouchahdane et al.12 explored the mechanical behavior of open-cell polyurethane foam (initial density ~ 28.7 kg/m3) under static compression and cyclic fatigue. A novel method was introduced using a custom-designed device to transform the foam structure into an auxetic configuration with a negative Poisson’s ratio, resulting in a significant density increase to approximately 119.59 kg/m3. Complementing this, Yang et al.13 provided key insights into the dynamic response of polyethylene (PE) foam under impact loading, contributing to the development of materials for protective applications. Narimen et al.14 analyzed contact mechanics by identifying CPRESS as the contact pressure, with CSHEAR1 and CSHEAR2 representing frictional shear stresses along two orthogonal local tangent directions15–17. Boudjemaa et al.18 demonstrated that a custom-designed liner significantly reduced stress at critical anatomical locations—the lateral tibia head (LTH), tibia end (TE), and fibular end (FE)—with respective reductions from 55 to 10, 60 to 28 kPa, and 72.3 to 14 kPa. Further finite element analysis by Boudjemaa et al.19 evaluated the effect of integrating a honeycomb structure within orthopedic implants. Models with honeycomb implants showed reduced interface stress (2.15 × 10⁻2 MPa and 2.01 × 10⁻2 MPa) compared to models without the structure (4.5 × 10⁻2 MPa) and those lacking implants altogether (7.97 × 10⁻2 MPa). From a clinical and user-centered perspective, Roberts et al.20 highlighted that individuals with lower limb amputations (LLA) face multifactorial barriers to consistent prosthesis use, categorized into everyday experiences, extrinsic influences, and intrinsic motivations. Finally, Gailey et al.21 compared bone-anchored prostheses (BAP) with traditional socket prostheses (SP), finding improved physical health and quality of life in the BAP group22–24. Although no statistically significant differences were observed in balance confidence or mobility survey scores, large effect sizes suggested clinically meaningful advantages in favor of BAP.
This study aims to design an optimal implant model suited for two fundamental lower-limb locomotion scenarios: normal walking and stumbling. Lower-limb amputation presents significant biomechanical and rehabilitation challenges, particularly in restoring natural gait and stability. Although extensive research has been devoted to prosthetic design and material optimization, many existing models still lack adaptability to complex locomotion conditions. Most prior studies have focused primarily on normal walking cycles, often neglecting irregular events such as stumbling, which impose abrupt mechanical loads and increased muscular coordination demands. These limitations underline a persistent research gap in evaluating prosthetic performance under dynamic and unpredictable conditions.
The present study therefore aims to design and numerically evaluate an optimal implant model capable of maintaining comfort, stability, and structural integrity during both normal walking and stumbling scenarios. By employing finite element analysis, this work seeks to quantify stress distributions, contact pressures, and shear behaviors across prosthetic components particularly the liner–bone–socket interface to establish design recommendations that enhance safety and long-term functionality for transfemoral amputees.
Materials and methods
The finite element method (FEM) is a powerful engineering method for modeling continuous media by discretizing them into discrete finite elements to facilitate the analysis of physical systems25–27. FE analysis has also found applications in fields other than engineering and is widely used in implantology, traumatology, and general biomechanical analysis, especially in the disciplines of medicine and dentistry28–30. From a traumatological point of view, FEM plays an important role in the analysis of biomechanical behavior and stress distribution, as well as in the creation of individualized treatment plans31–33. This increases the importance of the method in the field of implantology and the development of prosthetic devices. In this study, FEM software packages were used for numerical modeling and analysis of the problem; appropriate geometry, mesh structure, and material properties were defined and finite element analysis was performed under specified loading and boundary conditions.
Geometries
A finite element model of a virtual patient was developed to simulate an above-knee amputation scenario. The model incorporates detailed representations of the limb, including bone, soft tissues, an implant, and implant support structures. Additionally, a prosthetic system comprising a liner and a socket was integrated into the model. The prosthetic liner and socket were custom-designed using Autodesk Meshmixer, enabling precise adaptation of the liner to the residual limb anatomy. This approach facilitates accurate simulation of the biomechanical interactions between the residual limb and the prosthetic components. The liner was defined with a thickness of 6 mm, while the socket thickness was 2 mm as shown in Fig. 1.by Abaqus 6.17 software. One simulate this model by varying the Young Modulus of liner from (0.1; 0.2; 0.3 and 0.4 MPa).Fig. 1.
Fig. 1.
Schematic representation of the model, (a) bone with implant, (b) different components.
The contact interactions between the femur, liner, and implant components were modeled using a surface-to-surface formulation with a friction coefficient of 0.3, while soft tissues were represented as hyperelastic materials and the liner as an isotropic linear-elastic material. In conventional prosthesis-insert-skin interfaces, micro movements are small, typically in the order of 0.5 to 2 mm, depending on the insert stiffness and loading conditions; in our simulation, 0.5 mm was used.
The implant was designed based on the EF model and consisted of two main components. The upper component, measuring 45.5 mm in height and 45 mm in diameter, functioned as a support structure for the soft implant, as illustrated in Fig. 2.
Fig. 2.
Schematic representation of implant geometry.
Mechanical properties
The mechanical properties of the bone, soft tissues, implant, implant support, liner, and socket were modeled as linearly elastic, homogeneous, and isotropic materials, with the corresponding values detailed in Table 1. This simplification enables consistent comparison and computational efficiency in finite element analysis, while providing a reasonable approximation of the materials’ behavior under loading conditions.
Table 1.
Details material properties.
Loading and boundary conditions
The boundary conditions were defined to reproduce realistic mechanical constraints during lower-limb locomotion. As illustrated in (Fig. 3), the distal end of the socket was fully constrained (encastre), meaning all translational and rotational degrees of freedom were fixed. This condition simulates the mechanical support provided by the ground reaction force transmitted through the prosthetic pylon during stance.
Fig. 3.
Applied forces and boundary conditions.
A dynamic load (F dynamic) was applied at the proximal end of the femur, corresponding to the resultant forces transmitted through the hip joint during gait. The load components Fx, Fy, and Fz represent the mediolateral, anteroposterior, and vertical directions, respectively, and were applied as time-dependent functions derived from experimental gait data (Fig. 4).
Fig. 4.
Variation of forces applied on the model during two activities: (a) normal walking, (b) stumbling (Moulgada et al.38,39).
Mesh
The meshing process utilized C3D4 tetrahedral elements across all components, including the bone with implant, stump, liner, and socket. Tetrahedral meshes are valued for complex geometries and freeform shapes due to their flexibility in adapting to irregular contours and curved surfaces.
They enable rapid and automatic generation while ensuring high quality for reliable simulations40–44 (in Fig. 5).
Fig. 5.
Mesh of the components (a) bone with implant, (b) liner, (c) soft tissue, (d) socket.
The C3D4 element supports three translational degrees of freedom per node, allowing for accurate stress and deformation analysis under multi-axial loading conditions.
The convergence study demonstrated that the key output variables Von Mises stresses in the bone and implant and contact pressures and shear stresses on the liner became insensitive to further mesh refinement beyond the second refinement level.
The relative differences between successive refinements were below 2% for all monitored metrics, confirming numerical stability. Therefore, the mesh containing approximately 158,000 C3D4 elements (ROI element size ≈ 1 mm) was selected for all subsequent analyses as it offered the best compromise between accuracy and computational cost.
Table 2 provides a summary of the total number of elements and the corresponding element types assigned to each component of the finite element model, ensuring adequate resolution and accuracy across the different anatomical and prosthetic structures.
Table 2.
Mesh properties in FEM.
| Component | Number of elements | Element type |
|---|---|---|
| Soft tissue | 42,076 | C3D4 |
| Bone with implant | 12,700 | C3D4 |
| Liner | 17,933 | C3D4 |
| Socket | 25,002 | C3D4 |
Results and discussion
Distribution of Von Mises stresses in the stump with an implant
The model was simulated by varying the Young’s modulus of the liner across four values: 0.1, 0.2, 0.3, and 0.4 MPa.
Figure 6 illustrates the distribution of Von Mises stresses on the soft tissues around a limb (stump) implant under two activities: normal walking and stumbling. The stresses are displayed for four different liner stiffness values. During normal walking, stress levels in the soft tissues are lower compared to stumbling. Increasing the liner stiffness results in changes in stress distribution. While stumbling, highest stress levels are noticed.
Fig. 6.
Von Mises stress distribution (MPa) on the stump with implant for different soft tissue Young modulus values in the liner during: (a) normal walking and (b) stumbling.
In the soft tissues, increased stiffness leads to a concentration of high-stress areas. In both cases, the increase in linear stiffness affects stress distribution in the soft tissues, suggesting that the material properties of the liner have a significant impact on force transfer to the surrounding tissues during movement.
Figures 7 and 8 illustrate the Von Mises stress as a function of the normalized distance along a path for two activities: normal walking and stumbling. The curves represent different linear stiffness. Observations show that for normal walking, stress values fluctuate along the distance and are highest for thicker liners. For stumbling, the overall stress values are higher than for normal walking, especially for the thinnest liners. Thicker liners appear to help distribute stress more evenly. This indicates that thicker liners could be beneficial in situations where component durability is important.
Fig. 7.
Von Mises stress as a function of normalized distance.
Fig. 8.
Comparison between Von Mises stress in normal walking and stumbling.
Contact pressure at the stump
Figures 9 and 10 present the distribution of contact pressure at the stump–prosthetic interface for varying liner stiffness levels under two activity conditions: normal walking and stumbling. The results clearly indicate that contact pressure is influenced by liner stiffness. During normal walking, a progressive increase in contact pressure intensity at the external interface of the stump is observed with increasing liner stiffness. This trend underscores the mechanical influence of liner material properties on load transfer and pressure distribution at the interface during gait. The highest contact pressure reached 28.68 kPa for the liner with a Young’s modulus of 0.4 MPa. The lowest maximum contact pressure recorded at 17.36 kPa was noted for a liner with lower stiffness, having a Young’s modulus of 0.1 MPa. During stumbling, we detected that contact pressure intensity at the stump’s external interface rises as the liner’s stiffness increases. The peak contact pressure reached 58.24 kPa with a liner that has a Young’s modulus of 0.4 MPa. The lowest recorded maximum contact pressure was 32.54 kPa, Perceived with a more flexible liner, having a Young’s modulus of 0.1 MPa.
Fig.9.
Contact pressure distribution (MPa) on the stump for all liner stiffness cases during two activities.
Fig.10.
Comparison between CPRESS Stresses in normal walking and stumbling.
Figure 11 illustrates the variation of the contact pressure at the stump–prosthetic interface across all liner stiffness cases during both normal walking and stumbling. In the case of normal walking, it was observed that increased linear stiffness correlates with higher contact pressure at the interface. Specifically, the stiffest liner, with a Young’s modulus of 0.4 MPa, exhibited peak contact pressures of approximately 48 kPa. In contrast, the softest liner, with a Young’s modulus of 0.1 MPa, resulted in significantly lower contact pressures, with maximum values around 26 kPa. These results highlight the crucial role of linear stiffness in modulating interface load distribution during gait. In general, there is a clear link between increased stiffness and higher contact pressure during walking. For stumbling, pressure stress shows increased variation with continual variation. The stiffer liner with a Young’s modulus of 0.4 MPa creates higher maximum pressures, exceeding 80 kPa, while the less stiff liner with a Young’s modulus of 0.1 MPa shows a peak pressure recorded 43 kPa. The pressure stress is considerably higher during stumbling than during regular walking, it’s reasonable to assume result of the irregular movements that occur during stumbling. In both activities, sleeves with higher stiffness typically result in higher contact pressures. Stumbling introduces more extreme variations and pressure spikes than normal walking, that the residual stump-prosthesis interface experiences more strain. Therefore, selecting a sleeve with the right level of stiffness is crucial to effectively manage pressure and ensure comfort for prosthetic users, especially during activities with chaotic movements.
Fig. 11.
The variation of contact pressure at the stump-prosthetic interface for all liner stiffness cases during two activities: (a) normal walking, (b) stumbling.
Longitudinal shear stress
Figures 12 and 13 illustrate the distribution of shear stress (MPa) at the stump–prosthetic interface for all tested liner stiffness values, comparing two locomotion scenarios: normal walking and stumbling. During normal walking, it was observed that shear stress intensity at the stump’s external interface increased with the liner’s stiffness. The highest longitudinal shear stress, 8.48 kPa, was recorded for the liner with a Young’s modulus of 0.4 MPa, while the lowest value, 5.55 kPa, corresponded to the liner with the lowest stiffness (0.1 MPa). A similar trend was observed during stumbling, with shear stress intensifying as linear stiffness increased. The maximum longitudinal shear stress reached 12.82 kPa for the 0.4 MPa liner, compared to a lower value of 10.43 kPa for the 0.1 MPa liner. These findings indicate that increasing liner stiffness leads to elevated shear stress transmission at the stump–prosthetic interface under dynamic loading conditions.
Fig. 12.
Shear stress distribution (MPa) at the stump–prosthetic interface for all liner stiffness cases during two activities: (a) normal walking and (b) stumbling.
Fig.13.
Comparison between CSHEAR Stresses in normal walking and stumbling.
Figure 14 illustrates the variation in shear stress at the stump–prosthetic interface during both normal walking and stumbling, for different values of linear stiffness. The results highlight how changes in linear material stiffness influence shear stress distribution under dynamic loading conditions. In the case of normal walking, shear stress values peak at 8 to 9 kPa around 0.2 s, then gradually decrease. For stumbling, shear stress fluctuates more rapidly and reaches values exceeding 16 kPa. The liner with a stiffness of 0.4 MPa shows the largest fluctuations, while other liner values have lower peaks. These two graphs demonstrate the impact of linear stiffness on shear stress levels during different activities, with greater fluctuations noticed during stumbling compared to normal walking.
Fig. 14.
Variation of shear stress at the stump–prosthetic interface for all liner stiffness cases during two activities: (a) normal walking and (b) stumbling.
Distribution of contact pressure on the liner
Figures 15 and 16 illustrate the contact pressure distributions across all liner cases and comparisons during two activities. For normal walking, the highest noted contact pressure in the liner with a Young’s Modulus of 0.4 MPa reached up to 22.98 kPa, while the lowest contact pressure across all cases was in the liner with a Young’s Modulus of 0.1 MPa, attaining 14.67 kPa. In the case of stumbling, the liner with a Young’s Modulus of 0.4 MPa exhibited the highest contact pressure, reaching 34.14 kPa, whereas the liner with a Young’s Modulus of 0.1 MPa showed the lowest contact pressure, at 23.89 kPa.
Fig. 15.
Distribution of contact pressure on the liner with varying stiffness during two activities: (a) normal walking, (b) stumbling.
Fig. 16.
Comparison between CPRESS stresses in normal walking and stumbling.
Figure 17 illustrates the variation of contact pressure over time for different liner thicknesses during two activities (normal walking and stumbling). In the case of normal walking, pressure stress remains relatively stable over time for all liner thicknesses. The highest-pressure stress is around 25–30 kPa for a liner with a Young’s modulus of 0.4 MPa, while the liner with a Young’s modulus of 0.1 MPa has the lower pressure stress recorded at 15–20 kPa. The differences between liner types remain consistent throughout the period. For stumbling, pressure stress fluctuates more compared to normal walking.
Fig.17.
Variation of contact pressure in all cases of the liner during two activities: (a) normal walking, (b) stumbling.
The liner with a Young’s modulus of 0.4 MPa shows a high initial peak recorded at 40 kPa, followed by fluctuations. The pressures converge and diverge over time, indicating a less stable pattern than that of normal walking. All liner types show peaks, but the liner with a Young’s modulus of 0.1 MPa consistently remains the lowest throughout the activities.
Distribution of longitudinal shear stresses on the liner
Figures 18 and 19 present the longitudinal shear stress distributions for all liner stiffness cases during both normal walking and stumbling. During normal walking, the highest longitudinal shear stress was recorded for the liner with a Young’s modulus of 0.4 MPa, reaching 3.89 kPa, while the lowest value, 2.72 kPa, was observed for the liner with a Young’s modulus of 0.1 MPa. Under stumbling conditions, the maximum longitudinal shear stress increased to 5.43 kPa for the stiffest liner (0.4 MPa), whereas the softest liner (0.1 MPa) exhibited the lowest stress at 3.98 kPa. These findings underscore the influence of liner stiffness on shear stress transmission at the stump–prosthetic interface under varying gait dynamics.
Fig. 18.
Distributions of longitudinal shear stress on the liner with varying stiffness during two activities: (a) normal walking, (b) stumbling.
Fig. 19.
Comparison between CSHEAR stresses in normal walking and stumbling.
Figure 20 illustrates the variation of shear stress over time for different liner thicknesses during two activities (normal walking and stumbling). In the case of normal walking, the shear stress values remain stable, with a slight upward trend at the beginning. A liner with a Young’s modulus of 0.4 MPa shows the highest shear stress values, around 4.6 kPa. A lower stiffness of the liner, with a Young’s modulus of 0.1 MPa, results in lower shear stress values, around 3 kPa. For stumbling, the shear stress is more variable, with peaks at specific intervals. Liners with a Young’s modulus of 0.4 and 0.3 MPa show the highest stress values, particularly at the beginning. The range of shear stress is broader during stumbling, ranging from around 1 kPa to 7 kPa. Both graphs suggest that the type of liner affects the shear stress—liner with a Young’s modulus of 0.4 MPa has the highest stress in both activities (Table 3).
Fig. 20.
Variation of shear stress in all liner cases during two activities: (a) normal walking and (b) stumbling.
Table 3.
Global summary of stress outcomes across liner stiffness and activities.
| Activity | Liner stiffness (Young’s modulus, MPa) | Contact pressure (kPa) | Shear stress (kPa) | Key observations |
|---|---|---|---|---|
| Normal walking | 0.1 | 14.67 (Lowest) | 1–3 (Peak: 3.0) | Lowest mechanical load, stable stress |
| 0.2 | ~ 18–20 | 1–4 (Peak: 4.0) | Moderate pressure, gradual shear rise | |
| 0.3 | ~ 20–22 | 2–5 (Peak: 5.0) | Higher load transfer, steady shear | |
| 0.4 | 22.98 (Highest) | 3–6 (Peak: 6.0) | Highest stress, sustained peaks | |
| Stumbling | 0.1 | 23.89 (Lowest) | 1–5 (Peak: 5.0) | Broad shear range, early peaks |
| 0.2 | ~ 28–30 | 2–6 (Peak: 6.0) | Fluctuating stress, higher variability | |
| 0.3 | ~ 32–34 | 3–7 (Peak: 7.0) | Sharp initial peaks, high load | |
| 0.4 | 34.14 (Highest) | 4–7 (Peak: 7.0) | Max stress, critical for tissue risk |
Conclusion
The aim of this study was to evaluate the influence of liner stiffness, in combination with the implant, on the distribution of Von Mises stresses, shear stresses, and pressure at the stump–prosthetic interface during two activities: normal walking and stumbling. The following observations were made:
Liners with higher stiffness of 0.4 MPa were associated with increased Von Mises stresses, contact pressures, and shear stresses compared to softer liners (0.1 MPa). These effects were more pronounced during stumbling, where stress magnitudes and variations were greater due to the irregular nature of the motion.
For both normal walking and stumbling, contact pressures and shear stresses tended to increase with linear stiffness, with the stiffest liners showing the highest values. These findings may have implications for user comfort and the potential for soft tissue irritation.
Softer liners exhibited a more uniform stress distribution, which could enhance comfort and reduce localized loading. However, stiffer liners may provide improved durability and stability—an aspect that warrants further investigation under different loading scenarios.
Between the two evaluated activities, stumbling generated considerably higher mechanical constraints than normal walking, reflecting the greater loading demands and instability involved.
Overall, balancing linear stiffness is essential for optimizing prosthetic performance. Future work should focus on developing and characterizing liner materials that achieve an optimal compromise between comfort, load distribution, and long-term durability.
Acknowledgements
This study has been supported by the Recep Tayyip Erdoğan University Development Foundation (Grant number: 02025007002613).
Author contributions
Guerchouh Nawel: Conceptualization, Investigation, Methodology Sahli Abderahmane: Conceptualization, Formal analysis, Resources Moulgada Abdelmadjid: Validation, Investigation, Data curation Zagane Mohammed El Sallah: Resources, Investigation, Supervision Murat Yaylacı: Formal analysis, Methodology, Funding acquisition, Project administration Şevval Öztürk: Writing—review & editing, Visualization Boudjemaa Ismail: Validation, Investigation Ecren Uzun Yaylacı: Writing—review & editing, Visualization Ayberk Dizdar: Software, Formal analysis Yılmaz Güvercin: Writing – review & editing, Supervision.
Funding
This work was supported by Recep Tayyip Erdoğan University Scientific Research Projects Unit under Grant FBI-2024-1589.
Data availability
The data that support the findings of this study are available on request from the authors. Corresponding author, Prof. Dr. Murat Yaylacı, E-mail: murat.yaylaci@erdogan.edu.tr.
Declarations
Competing interests
The authors declare no competing interests.
Consent to participate
No external participants have contributed to the work discussed in this manuscript.
Consent for publication
The authors give their full consent to the editor to publish this article if accepted.
Ethics approval
The authors declare that the research was conducted according to ethical standards. This article does not contain any studies with human or animal subjects.
Footnotes
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The data that support the findings of this study are available on request from the authors. Corresponding author, Prof. Dr. Murat Yaylacı, E-mail: murat.yaylaci@erdogan.edu.tr.