Reduction of Ceramic Wear by Concave Dimples on the Bearing Surface in CoC Hip Implants: A Finite Element Analysis

Abstract

The wear of hip prostheses represents a significant challenge for the longevity and functionality of joint implants. Recent studies have explored surface texturing of prostheses as a strategy to enhance tribological performance. This study aims to evaluate the impact of textured ceramic surfaces with dimples on wear and friction reduction in ceramic-on-ceramic (CoC) prostheses. Materials and Methods: Three-dimensional models of ceramic surfaces with and without dimples were created. Contact pressure was analyzed and wear volume was estimated using Archard’s law. Simulations were conducted using finite element methods (FEM) under various loading conditions. Results: Numerical simulations demonstrated that the wear rate for the dimpled femoral head was 0.2369 mm³/year, compared to 0.286 mm³/year for the smooth counterpart, highlighting a wear reduction of 17.2%. Conclusions: The integration of textured surfaces with dimples in ceramic prostheses can substantially improve their functionality and durability, representing a promising approach to addressing the issues associated with hip prosthesis wear.

1. Introduction

The goal of total hip arthroplasty (THA) is to replace a damaged or compromised joint with an artificial joint [1,2]. This procedure is usually performed for conditions such as arthritis, inflammation, or in more severe cases such as hip fractures [3]. In the United States, more than 285,000 total hip replacements (THA) are performed annually to treat degenerative joint disease [4]. A variety of biomaterials are used in the manufacture of hip implants, including metals, polymers, and ceramics. There are several types of prosthetic joints available, including ceramic-on-ceramic (CoC), ceramic-on-metal (CoM), ceramic-on-polyethylene (CoP), metal-on-metal (MoM), and metal-on-polyethylene (MoP) combinations [5,6,7,8]. In 2014, more than half of new hip replacements in the United States were CoP implants (51%), followed by MoP (42%), MoM (4%), and CoC (3%) [9,10]. Major causes of MoP hips failure include wear of the polyethylene liner, caused by interaction with the Co-Cr femoral component, resulting in the generation of particles that can accelerate contact surface degradation. In addition, biological responses to the presence of wear debris can induce periprosthetic osteolysis, which can compromise the stability of the implant [11]. It has been observed that although cross-linked polyethylene reduces wear to some extent, it can still contribute to osteolysis phenomena [11,12,13]. Minimizing friction and wear rate are essential to increase the longevity of the prosthesis, especially with the use of femoral heads that allow a greater range of motion [14]. The current engineering approach to addressing wear in implants involves improving the mechanical properties of the polyethylene component and creating ultra-smooth bearing surfaces, along with the development of ceramic-on-polyethylene (CoP) and ceramic-on-ceramic (CoC) prostheses. For example, CoC bearing surfaces have an average roughness of less than 5 nm, allowing them to operate in an (elasto-hydro)dynamic lubrication regime, which helps to reduce friction and wear [15]. In an analysis conducted by Buttaro et al. [16], a retrospective review was performed of 939 cases (880 patients) who underwent primary total hip arthroplasty with CoC bearing surfaces. The results showed an exceptional average survival rate of 99.3% over a period of 2–10 years. In addition, Lee et al. [17] reviewed data on 2.78 million AMC ceramic femoral heads implanted worldwide and found a clinical fracture incidence of only 1 in 100,000 for contemporary AMC ceramic femoral heads. Furthermore, a study by Solarino et al. [18] found that CoC is the ideal choice for younger and more active patients due to its reliability and longevity, highlighted by the lack of material-related complications. CoC implants also allow the use of femoral heads larger than 28 mm without increasing the coefficient of friction, which is not always possible with CoCr heads due to concerns about polyethylene wear [19,20]. In a comparative analysis by Higuch et al. [21], the average wear rate on anteroposterior (AP) radiographs was 0.0037 mm/year for CoC compared to 0.0051 mm/year for MoM. Therefore, the lower wear rates of CoC prostheses could indicate a longer implant life and fewer problems related to osteolysis and revision compared to MoP, MoM, and CoP. However, despite the excellent results observed with CoC, the number of revision surgeries is steadily increasing, especially in younger and adult patients, and is expected to double by 2026 [22,23,24,25,26]. This could have a significant social and economic impact if effective preventive measures are not implemented [27,28]. Various surface modification techniques have been developed to extend the life of joint prostheses. These include surface texturing (dimpling) and the application of surface coatings. These methods are typically applied to the surfaces of the femoral head [29,30,31,32,33]. Surface texturization helps to improve tribological performance by increasing the thickness of the lubricating film between contacting components, acting as a lubricant reservoir.

Increasing the thickness of the lubricant film by creating dimples on the surface of the femoral head allows direct contact between the surfaces to be avoided, reducing the risk of dry friction. This system helps to trap wear particles under mixed lubrication conditions, preventing damage to the bearing surface during movement. Roy et al. [34] documented a significant 22% reduction in friction and 53% reduction in wear on textured surfaces compared to non-textured surfaces. Vaidyanathan et al. [35] found that the use of a textured CoCrMo femoral head in conjunction with a UHMWPE liner resulted in a reduction in coefficient of friction of up to 36% and a reduction in wear of up to 69%. Finite Element Methods (FEM) provide an effective alternative to laboratory testing [36,37,38,39]. These methods allow faster and more cost-effective simulations of different loading and kinematic scenarios. However, some studies, such as that of Jamari et al. [40], have used simplified models that do not always accurately reflect physiological conditions. Despite the lack of studies on the wear volume of CoC prostheses, there is a great deal of experimental and numerical research on the textured surfaces of MOP and COP prostheses [41]. The aim of this research is to analyze the contact pressure on the surface of the acetabular cup with and without the addition of dimples in a ceramic-on-ceramic (CoC) configuration. The analysis is performed using 3D dry contact models with simplified loading conditions to obtain immediate results. In addition, the wear rate for both models is estimated using Archard’s law to validate the null hypothesis that the introduction of dimples would significantly reduce the wear rate.

2. Materials and Methods

The CoC hip implant has a 32 mm diameter head made of Biolox Delta zirconia matrix [42] with a Young’s modulus of 350 GPa and a Poisson’s coefficient of 0.26. The acetabular insert has an internal diameter of 32.49 mm, a thickness of 8 mm, and an external diameter of 40 mm. It is made of zirconia with a modulus of elasticity of 210 GPa and a Poisson’s coefficient of 0.26. In addition, the distance between the acetabular insert and the femoral head is 0.245 mm (Figure 1). The two components were manufactured and assembled using the 3D modelling software Autodesk Inventor 2024 [43,44].

Based on the geometric parameters of dimples reported in the literature [41], a model was created with the addition of circular dimples as shown in Figure 2. Using Autodesk Inventor’s geometric modeling commands, dimples were created that are 0.5 mm in diameter and 0.25 mm deep. The industrial technology for creating dimples on ceramic surfaces using lasers is known as laser surface texturing (LST) or laser surface treatment. This process modifies the surface properties of the material, resulting in microstructures that improve tribological properties such as reduced friction and wear.

One of the important parameters describing the geometry of textured features is the aspect ratio ɛ [45]. It is defined as the ratio of the depth (h) to the equivalent diameter (d) of the textured feature. Deep pits with an aspect ratio ɛ > 0.1 act as lubricant reservoirs, reducing friction and wear in mixed lubrication conditions and providing lubricant to contact surfaces in deficient conditions. They also provide trapping of wear debris that would otherwise scratch the surface. Conversely, for aspect ratios ɛ < 0.1, there is a micro-hydrodynamic support effect which increases the pressure and thickness of the lubricant film between the bearing surfaces, reducing contact and, consequently, friction and wear (Figure 3).

In this study, an aspect ratio of ɛ = 0.5 was chosen, contributing to a higher load capacity and a reduction in the coefficient of friction. The materials considered in this analysis were modelled with isotropic linear behavior as they are characterized as brittle materials that do not exhibit yielding behavior [43,46,47,48] (

Table 1. Mechanical properties of materials.

Components	Young’s Modulus [GPa]	Poisson’s Ratio
Femoral head	350	0.26
Liner	210	0.26

).

2.1. FEA Modeling

The classical workflow for an FEM analysis in (Ansys^® R 2024) software consists of four steps: (1) pre-processing (PREP 7); (2) solving (SOLU); (3) post-processing (POST 1 or POST 26); (4) validation. In the pre-processing step, materials are selected, and the geometry of the model is created. During the solution step, boundary conditions are applied, and solution options are set. In the post-processing step, results are obtained, and analysis is performed Figure 4.

While the acetabular insert and the femoral head were discretized with a mesh size of 1 mm, the contact area was refined using the Contact refinement command. A finer mesh of 0.5 mm was used to better represent the stress distribution in this area (Figure 5).

These parameters were subsequently validated by convergence analysis, which showed an error in the contact pressure results of less than 1% using a mesh of 0.5 mm and 0.6 mm. The element order was set to Quadratic (SOLID 187), and the error limits were set to Standard Mechanical. The most used elements are hexagonal and tetrahedral. Hexagonal elements are generally preferred due to their higher accuracy but are more expensive to calculate [49,50,51,52]. The choice between the two types of elements depends on the level of accuracy required. A mesh that is too coarse leads to imprecise solutions but low computational cost, while a fine mesh gives very accurate results, may become computationally impractical. Tetrahedral elements were therefore used in this study because they allow easier meshing, resulting in a total of 15,479 nodes and 9452 elements.

2.2. Boundary Conditions

Regarding contact conditions, the femoral head is modelled as ‘Target Body’, as it is the strongest material, while the acetabular insert is defined as ‘Contact Body’. Eight-node linear 3D elements (CONTA 174) were used for the contact, while four-node linear 3D elements (CONTA 170) were used for the target. A frictional contact between the two surfaces was then assigned using a Ceramic-Ceramic friction coefficient of 0.12 [53,54] (Figure 6).

The calculation is simplified through the study of Bergmann et al. [55] and shows that the resultant force is equivalent to the vertical component. Therefore, only this component is considered in this analysis for an individual weighing 80 kg. In this study, various activities shown in

Table 2. Loads acting on the joint as daily activities vary and as a function of body weight.

Activity	Maximum Contact Force (% of Body Weight) or Activity Factor
Going upstairs	2.6
Going downstairs	2.51
Fast walking	2.5
Slow walking	2.42
Sitting down	1.56

were considered. Then, the equivalent forces for the individual activities were applied to the upper surface of the insert.

The lower part of the femoral head was fully constrained in all directions, while a vertical load was applied to the upper surface of the insert Figure 7.

In this study, the normal contact case is defined to represent the basic interaction between surfaces, concentrating on axial loading conditions during femoral head articulation within the acetabulum. While rotation plays a critical role in real-life scenarios, more detailed analyses can incorporate rotational dynamics in subsequent studies. Future finite element analyses may explore how dynamic loading and rotational forces impact contact mechanics and wear over time, particularly in the context of dynamic testing conditions.

A total of 10 cases (five model a, five model b) were analyzed for the various activities shown in Table 2.

2.3. Calculation of the Wear Rate

Using Archard’s formulation [56,57], wear can be calculated. This assumes that the two contact surfaces are not perfectly smooth but consist of asperities. It is also assumed that only the higher asperities carry the normal load W during the sliding motion.

Given a small sliding section ds and a small load increment dW, we assume that the volume of material removed dV is proportional to these quantities and inversely proportional to the hardness H of the “soft” material:

$$\mathrm{d}V=k{\displaystyle \frac{\mathrm{d}W \mathrm{d}s}{H}}$$

(1)

where k is a dimensionless proportionality constant (incorporating the fraction of asperities broken and transported as wear particles).

Integrating over the total sliding distance S and the total load W gives Archard’s volumetric law:

$$V=\int dV={\int }_0^W{\int }_0^{S}K\hspace{0.17em}{\displaystyle \frac{dW\hspace{0.17em}ds}{H}}={\displaystyle \frac{K\hspace{0.17em}W\hspace{0.17em}S}{H}}$$

(2)

In the case of the femoral head and insert coupling, where R is the radius of the head with a circumference of length 2πR, Archard’s formula can be rewritten as:

$$V_{tot}={\displaystyle \frac{K\hspace{0.17em}W\hspace{0.17em}S}{H}}={\displaystyle \frac{K\hspace{0.17em}W\hspace{0.17em}\left(2\pi R\right)}{H}}$$

(3)

Equation (3) is scaled to reproduce actual daily loading conditions (10,000 cycles) and then adjusted to an annual period with an additional scaling factor of 365. A factor of 1000 was also applied to convert the results to mm³ per year. The final equation of Archard’s law applied in this study is Equation (4), where the contact area $S_l$ was calculated by subtracting the area of the femoral head from the hemispherical area of the insert, resulting in a contact area of 1608.5 mm².

$$V=k_w\ast {\sigma }_c\ast A\ast S_l\ast 1000\ast 365\ast {10}^3$$

(4)

where:

• $k_w$: wear coefficient in mm³/Nm.
• ${\sigma }_c$: contact pressure in MPa
• $A$: contact area in mm²
• $S_l$: sliding distance in mm.

The wear coefficient k_w can be obtained from experimental studies such as pin-on-disc tests or hip wear simulators [57], considering the surface roughness Ra. In the present study, a k_w value of 1 × 10⁻⁸ is used for a ceramic-ceramic contact in a CoC joint. The results of the FEM simulation, such as contact pressure and sliding distance, can then be used to calculate the wear volume during different activities using Equation (4).

3. Results

Numerical simulation of this model was conducted to determine the maximum value of contact pressure and sliding distance, assuming static loading conditions to simplify the analysis. Using Archard’s wear rate formulation, it is possible to estimate the volume of wear that occurs on the inner surface of the acetabular liner. The situation involving the maximum load is the activity of climbing stairs, in which the body weight increases by 2.6 percent. Figure 8 shows the contact stress found during stair-climbing activity. From these findings, it can be seen that the maximum stress values are located in the central region of the inner surface of the liner, while the minimum values are located in the circumferential area.

For the model without dimples (model A) a maximum contact stress of 0.7047 MPa is reached, whereas for the model with dimples (model B) 0.5419 MPa is reached. Furthermore, the maximum stress observed at the femoral head for model A is 0.5043 MPa, while for model B lower values of 0.3097 MPa reached Figure 9.

From Figure 9 the maximum stress value is reached in the c zone for both models. While the lowest contact stress values are reached in zone a, 0.4292 MPa for model A and 0.4184 MPa for model B. Regarding the sliding distance, the relative values in mm are shown in

Table 3. Sliding distance values for model A and model B.

	Sliding Distance (mm)
Without dimples	0.01832
With dimples	0.00874

.

In the case of a dimpled model, the sliding distance is less than in the case of a model with a smooth femoral head.

Wear Volume

The wear volume (V) of the surface modified femoral head was calculated using the modified Archard wear equation. This method allows the quantitative measurement of material loss from artificial implant components, which is critical in assessing their performance and durability over time. To estimate the annual wear volume, a condition of 10,000 load cycles per day, a femoral head surface roughness of 0.008 μm and a radius of 16 mm was assumed. Figure 10 shows that the wear rate of a femoral head is higher during stair-climbing activities. In this activity, the model with dimples exhibits a lower wear rate (0.2369 mm³/year) compared to the smooth head model (0.286 mm³/year). Therefore, the dimples may help distribute pressure more evenly across the contact surface between the femoral head and the insert. This contributes to reducing localized stress peaks, which are often responsible for excessive wear. Furthermore, the dimples reduce the contact area, distributing the load over a larger surface. As a result, a smaller contact area can lead to lower wear, as there is less direct material in contact to wear away. The dimples can also act as traps for debris, reducing friction and wear caused by direct contact between surfaces.

Sitting is the activity that causes the least wear, with values of 0.0358 mm³ for the model without dimples and 0.01369 mm³ for the model with dimples. These results are consistent with previous clinical studies and suggest that the empirical relationships developed may be useful in the design of hip prostheses.

4. Discussion

The prevention of aseptic loosening of artificial joints poses a significant challenge in orthopedic surgery. It is crucial to improve the lubrication properties of friction surfaces and reduce the generation of wear particles [58,59,60]. This necessity can be justified on three main grounds. First, high friction can generate elevated shear stresses at the bone-implant interface. This mechanism is often responsible for aseptic loosening, which can compromise implant stability [61,62]. Therefore, it is essential to mitigate friction to prevent such events. Second, numerous studies have shown that high molecular weight polyethylene (UHMWPE) liners wear at rates between 0.1 and 0.2 mm per year [63], resulting in a thick reduction of approximately 1–2 mm over a decade. In situations where the liner is thin, increased wear can lead to higher friction with the femoral head. This friction is associated with conditions such as metallosis, which can lead to osteolysis [64,65]. Finally, wear particles generated during friction serve as stimuli for the immune system, provoking an adverse foreign body response. Histological and biochemical studies conducted on wear particles from UHMWPE and metallic components, collected from surrounding tissues during revision surgeries, have demonstrated how these particles can negatively affect the biological response and longevity of the implant [66,67,68].

Conversely, the adoption of materials with different mechanical and tribological characteristics in the coupling of femoral heads and acetabular cups has allowed for better control over wear rates and friction [69]. In recent years, the implementation of ceramic-on-ceramic (CoC) prostheses in total hip arthroplasties has shown significant advancements in addressing the previously mentioned issues [70,71,72]. Ceramic surfaces are characterized by a high level of smoothness, which substantially reduces friction during joint movement. In comparison to traditional materials such as metal and polyethylene, the use of ceramic surfaces in prosthetic devices allows for a reduction in the interaction between surfaces, leading to decreased wear over time and thereby ensuring a longer lifespan of the implant. A particularly crucial aspect is the adoption of femoral heads with a larger diameter (≥36 mm), which not only enhances the stability of the implant by reducing the risk of dislocation but also improves the distribution of forces within the joint, minimizing contact and friction between the bearing surfaces [73]. This approach has demonstrated significant improvements compared to lower-diameter prosthetic systems, which are generally associated with higher wear rates [74,75,76].

Furthermore, recent studies have shown that even under conditions of poor lubrication, ceramic heads can maintain good performance characteristics, limiting both friction and the accumulation of wear debris in the joints [77,78,79]. An important innovation has been the introduction of laser surface texturing (LST), which allows the creation of microstructures (dimples) on various materials, including metals and ceramics, thereby contributing to the reduction of friction and wear. A study conducted by Joshi et al. [80] showed that LST significantly reduces the coefficient of friction, achieving a reduction of up to 60% in textured samples compared to polished ones. Numerous experiments in total hip arthroplasty have been conducted to optimize the tribological characteristics of joints through texturing techniques [81,82,83].

One of the main purposes of texturing is to create structures on the surface called dimples, which serve various functions: they act as reservoirs for lubricants; they increase hydrodynamic pressure during movement; they trap wear debris or foreign materials in the concavities; they reduce the contact area; and they minimize friction and wear [84]. However, the effectiveness of wear reduction depends on the optimization of geometric parameters such as the density, pitch, and size of the dimples. Roy et al. [85] demonstrated that a dimple diameter of 400 μm with a density of 15% improves friction and wear performance compared to other geometries. On the other hand, Huang et al. [86] reported enhanced lubrication effects from smaller-sized concavities with a high pore density, due to the uniform distribution of lubricants within the micro-dimples. This also confirms the role of dimples as lubricant reservoirs. The lubricant is expelled from the concavities to minimize contact under load conditions. However, surface roughness may increase with dimple density. Moreover, from a geometric perspective, circular shapes have been commonly used since they can be easily fabricated with high precision. Ito et al. [29] studied the tribological performance of a textured Co–Cr–Mo surface, observing a 17% reduction in friction and a 36% reduction in polyethylene wear. Meanwhile, a study by Shen et al. [87] reported a significant improvement in tribological performance by creating a trapezoidal shape of the dimples. However, few studies have been reported on the application of dimples on ceramic heads. Research in this area is limited compared to other implant surfaces, such as those made of metal or polyethylene. This could be attributed to the technical challenges associated with creating dimples on ceramic materials, which may influence the tribological performance and durability of the implants. The use of laser technology has made it possible to texture ceramic surfaces in recent years [88]. In this study, the finite element method was employed to investigate the effect of dimples on a ceramic surface in a CoC coupling [89,90,91,92,93,94,95]. The results indicated that the addition of dimples led to a significant reduction in wear rate of approximately 17% compared to a model without dimples. Clinically, dimples on ceramic heads improve lubrication and reduce the contact area, mitigating vibrations and resulting in quieter operation with decreased squeaking. These findings align with previous literature. For instance, Tewelde et al. [96] reported a wear volume reduction of up to 87% on smooth metal surfaces using various texture configurations. Similarly, Sagbas et al. [97] demonstrated a 29% decrease in friction coefficient and a 39% reduction in wear volume when comparing smooth CoCrMo pins with textured UHMWPE disks. Concerning ceramic surfaces, only physical experiments have been conducted. For example, an analysis by Min Ji et al. [98] showed that various surface textures reduced the friction coefficient by 24% compared to untextured surfaces during ceramic-ceramic friction tests.

Limitations

Although this study showed a significant improvement in wear rate reduction by introducing textured surfaces with dimples, it is important to consider some relevant limitations of the model used. The simulations performed were carried out under static conditions, which do not reflect the actual behavior of the implants during the physical activity of the patients. This is a crucial issue since the joints are subjected to repeated load cycles and different motion conditions, factors that could significantly affect the tribological performance of the ceramic surfaces. To address these limitations, in vitro studies are proposed to validate numerical simulations. In addition, controlled tests under dynamic conditions would provide useful empirical data to better understand how textured surfaces interact with synovial fluid. Another aspect to consider is the strength and fatigue of the material. Textured surfaces may behave differently under cyclic loading over time; therefore, longitudinal studies would be valuable in assessing their durability. It is therefore necessary to develop models that simulate mechanical fatigue over time and to analyze the effect of wear-induced particle accumulation on the integrity of ceramic materials.

5. Conclusions

This study highlighted the importance of dimpled textured surfaces in ceramic hip replacements and demonstrated significant and quantifiable results. A 17.2% reduction in wear rate was observed, with wear values of 0.2369 mm³/year for textured femoral heads compared to 0.286 mm³/year for smooth femoral heads. In addition, during stair-climbing activity analysis, the textured model showed a maximum contact pressure of 0.5419 MPa, which was lower than that of 0.7047 MPa for the smooth model, demonstrating better load distribution. The sliding distance was reduced from 0.01832 mm in the dimpleless model to 0.00874 mm in the dimpled model, indicating better tribological behavior. Finally, the dimples were shown to act as lubricant reservoirs, further reducing friction. These results suggest that the incorporation of dimples into ceramic prostheses represents an innovative approach to improving the durability and function of hip prostheses.