Owing to the increased need for bearing couples suitable for meeting the heightened biomechanical demands from younger, heavier, and more active patients, ceramic use has rapidly increased in the past decade. Additionally, the recent tissue reactivity problems associated with metal-on-metal implants may plausibly push demand for ceramics even higher. Certainly, advances in materials science and in manufacturing processes have greatly enhanced long-term performance of ceramic bearings. Nevertheless, fracture remains a substantial concern, at least for liners. Catastrophic failure of a ceramic THA holds devastating consequences for the patient, not the least of which is the increased potential for third-body wear of the revision implant as a result of residual ceramic fragments . Recently, the reported prevalence of liner fracture in CoC bearings has been in the range of less than 1% to greater than 2% [1, 7, 14]. Given the potential for increased burden of morbidity resulting from increasing use of CoC bearing couples in mechanically demanding patients, heightened scrutiny is warranted regarding causation of these catastrophic events. Using physical experimentation to study liner fracture is logistically burdensome both in terms of specimen consumption and researcher time. Computational simulation offers an attractive alternative but, unlike for the more commonly studied modes of failure in THA, involves extraordinarily difficulties technically. Conventional (LEFM) fracture analysis requires a priori knowledge of the location of crack nucleation, and it requires specialized meshes and complex postprocessing routines. Moreover, LEFM analysis of fracture propagation in three dimensions—to address realistic clinical circumstances—is prohibitively laborious. However, important questions relating to the biomechanics of ceramic fracture—specifically the influence of obesity and the role of suboptimally positioned components—remain unanswered. The use of XFEM to address these questions has enabled a paradigm shift in this area.
Despite the exciting capabilities that XFEM offers, several simplifications and limitations merit mention. First, the total percentage of simulations resulting in liner fracture in the present study was of course unrepresentatively much higher than that seen clinically. The vast majority of the fractures simulated in this investigation occurred for microflawed alumina, in which subcritical microfractures were assumed to be homogenously dispersed throughout the entire liner. Although microscopic imperfections are ubiquitous in modern ceramics [15, 39], the probability of such an imperfection being just below critical size and existing precisely at the location of greatest tensile stress (as simulated in the present study) is certainly rather low. As a related matter, the size of a given microflaw will determine the degree of associated reduction of the material’s mechanical properties. The assumed microflaws posited in the present study represent a mechanical decrement approaching alumina’s limiting (initial) stress intensity factor, KI0 . Proof-testing of ceramic implants was initiated to identify the presence of such microflaws immediately after manufacture; therefore, the likelihood is low of implanting a ceramic liner with a microflaw of similar magnitude as represented in the present study. However, the state-space sampling strategy and material property assumptions adopted for the present study design were oriented toward identifying cause-and-effect parametric relationships rather than replicating population-wide experience. (If the great majority of patients undergoing CoC THA were extremely obese individuals with impingement-prone cup orientations and with proclivity for Asian-style squatting, the prevalence of liner fractures would probably be much higher.) Second, we investigated only third-generation (BIOLOX® Forte) alumina ceramic bearings. Although newer, commercially available fourth-generation alumina-composite ceramic demonstrates improved mechanical performance compared with third-generation alumina, the lack of prior experimental or computational data related to fourth-generation fracture characteristics would have hindered model corroboration/validation efforts and therefore precluded use of fourth-generation material properties in this study. Third, stripe wear generation as modeled in the present study did not include the effect of superior rim-loading ensuing from gait-associated bearing microseparation. Although microseparation is a commonly reported mechanism leading to edge-loading and accelerated wear in metal-on-metal bearings , the mechanism responsible for stripe wear formation in ceramic bearings is not as clear. Clinical retrievals  have suggested the majority of wear stripes do not occur from gait, but instead from posterior edge-loading associated with deep hip flexion, similar to the mechanism of stripe wear posited in the present study. Finally, this investigation involved only two fracture-prone maneuvers. Although stooping and squatting have been previously observed  to represent among the greatest challenges to ceramic liner integrity, a seemingly limitless variety of impingement challenges obviously occurs in patient populations. Extension of the present XFEM formulation to investigate additional fracture-prone patient activity maneuvers is an inviting topic for further research.
For the two distinct ceramic liner geometries (28 mm versus 36 mm), both the causative factors for liner fracture propensity and the individual fracture characteristics differed. The 28-mm liners fractured only at the head egress site with fracture initiation occurring very near the cup edge (Fig. 7A). Fracture risk in this group increased with increased cup inclination (Appendix Fig. A3), similar to the behavior simulated using LEFM . (Additionally, earlier LEFM work had identified increased fracture risk with increased anteversion.) Because increased cup inclination and increased anteversion generally protect against neck-on-liner impingement, fracture risk in the 28-mm implant was not strongly correlated with component impingement per se. These findings stand very much in contrast to the fracture characteristics of the 36-mm implant, in which the vast majority of fractures initiated at a location intermediate between the cup edge and cup pole (Fig. 6). Additionally, fracture risk in the 36-mm implant was strongly correlated with component positions that favored impingement (ie, decreased inclination and decreased anteversion).
The percentage of simulations resulting in fracture increased dramatically when BMI was increased from 25 kg/m2 (normal weight) to 33 kg/m2 (moderately obese) and beyond for both flaw-free and microflawed alumina properties. Given the increased intraoperative challenge of component positioning  as well as the increased risk of malpositioning  with obese patients, the current data suggest that meticulous positioning of CoC THA implants is even more important for obese patients than for those of normal weight. Finally, the present data suggest that edge-loading-associated stripe wear and fracture risk exhibit much more than simply chance association. Because edge-loading and stripe wear have been linked to squeaking in ceramic THAs [35, 37, 38], the present results suggest that squeaking may possibly herald potential catastrophic fracture of the liner. Although the association between squeaking and fracture has been remarked on in the laboratory simulator setting , to the authors’ knowledge, a formal relationship has not yet been documented clinically. Hopefully the present study may help stimulate increasing vigilance in that regard.
Clearly, XFEM opens exciting new vistas for systematic biomechanical study of ceramic liner fracture. This computational formulation seems especially fertile for application in a design optimization context. Although XFEM has been preliminarily applied to the study of native bone fracture , to the authors’ knowledge, the present work represents the first application of XFEM to orthopaedic implants.
In summary, an advanced computational platform, XFEM, was used for systematic analysis of ceramic-bearing fracture in THA. The parametric study corroborated recent clinical observations of increased risk of ceramic liner fracture for obese patients. A strong association was identified between scraping/stripe wear severity and fracture risk for instances of both normal and elevated body weight. For both obese and normal-weight simulations, fracture risk was substantially higher for 36-mm cups with decreased anteversion.
Dr Cheryl Liu and the SIMULIA/Abaqus technical support team provided invaluable engineering collaboration during initial development of the XFEM model.
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XFEM background and model development
The eXtended Finite Element Method
The eXtended Finite Element Method (XFEM, also known as the partition of unity method ) involves numerical enrichment of a model’s geometry so as to allow for solution of the governing differential equations in regions of physical discontinuity such as across fracture surfaces. The XFEM formulation was initially introduced in 1999 to address shortcomings associated with conventional FE treatment of physical discontinuities, especially material cracks . When XFEM is used for fracture analysis, standard displacement fields are enriched near a crack tip by including both discontinuous fields and crack-tip asymptotic fields (Fig. A1).
Development of the FE/XFEM Fracture Model
The determination of femoral head stripe wear magnitude and ceramic liner fracture propensity involved a multistep approach, previously described . Stresses developed during hip articulation (with or without the occurrence of component impingement) were determined from a global dynamic FE model of THA mechanics. These stresses were then subsequently passed to a separate XFEM submodel of the liner, allowing for fracture initiation and propagation to be simulated. A previously developed and physically validated  FE model of the overall THA construct was used for the global analysis. The computational zoning for the global model had been optimized for bearing contact and edge-loading  and had been validated by comparison with a corresponding Hertzian analytical contact stress solution reported by Sanders and Brannon .
For all global analyses, physical properties of third-generation alumina were used. The liner and head were modeled as linearly elastic (elastic modulus = 380 GPa, Poisson’s ratio = 0.23, density = 3.98 gm/cm3) with radial clearance of 0.034 mm and a friction coefficient of 0.04 . Each of these 200 global FE simulations was executed using Abaqus/Explicit (Version 6.10; Dassault Systèmes Simulia Corp, Providence, RI, USA).
Stresses obtained from the global solutions of the Abaqus/Explicit analyses of THA impingement/subluxation were then passed as boundary conditions to the (described previously) (implicit) XFEM submodels. Whereas LEFM analysis would have required extensive ad hoc meshing to reflect the discontinuous material behavior at the initial fracture location , the XFEM models were simply partitioned into two distinct so-called “enrichment zones” (see Fig. 1C). For each such enrichment zone, XFEM allows one but only one crack to initiate and propagate within that zone. For the ceramic liner analyses, one enrichment zone was set to correspond to the egress region of the cup, ie, the region associated with head subluxation and edge-loading stress concentrations; the second enrichment zone was that associated with the neck-on-cup impingement region.
Liners without microflaws were modeled as having a damage initiation criterion (flexural strength) of 580 MPa (of maximum principal stress), whereas the flexural strength of alumina with microflaws was taken to be 150 MPa . For both material variants, mixed-mode (tension/in-plane shear/out-of-plane shear) fracture was used with the strain energy release rate (ie, the change in potential energy per unit change of crack surface area) taken as 42 J/m2 (flaw-free) or 2.6 J/m2 (with microflaws) . The resulting 400 distinct XFEM submodels were then executed using Abaqus/Standard.
Corroboration of the XFEM model was conducted using two separate series. For the first series, correspondence between the XFEM model and a traditional LEFM fracture mechanics formulation  was demonstrated for 28-mm alumina bearings. For this series, inclination was varied between 30° and 60° for cups in 10° of anteversion. Fracture propensity was investigated using a stooping fracture challenge, applying otherwise identical loading and boundary conditions as those for the LEFM study.
The second corroboration series, by contrast involving direct experimental comparisons, investigated the neck-on-liner impact force required to induce fracture in ceramic liners. For both the 36- and 28-mm liners (Fig. A2), the habitual site of neck-on-liner impingement was determined from a global analysis of the stooping maneuver for cups positioned in 45° inclination and 0° anteversion. Then, to approximate a previously reported experimental liner fracture series , the femoral neck was displaced toward that impingement site along an axis formed between the center of the neck and the impingement site. For each liner geometry, several simulations were performed in which the displacement of the neck was varied relative to the liner. The resulting impact forces varied between 12 and 30 kN. Impact forces required to initiate fracture were then compared with experimentally determined values .
Results of Model Corroboration
For the 28-mm LEFM/XFEM corroboration series, fractures initiated always at the site of head egress as a result of impingement-induced edge loading (Fig. 7A), behavior very similar to that determined using the LEFM approach (Fig. 7B). Additionally, fracture risk determined for the XFEM formulation increased abruptly for cups abducted greater than a threshold of 35°, a similar threshold to that for abrupt increase of fracture propensity in the LEFM analysis (Fig. A3).
For the neck-on-liner impingement fracture corroboration series, a threshold impaction force of 23.6 kN was computed with cause of fracture for the 28-mm liner (Fig. A4A). A similar fracture threshold force (24.5 kN) was computed for 36-mm liners (Fig. A4B). The corresponding fracture threshold force measured experimentally  was 23 kN, lending very strong credence to the credibility of the computational results.