تجزیه و تحلیل خستگی از پروتز سمان شونده ران: آسیب سناریو تجمع و تجزیه و تحلیل حساسیت

This work is dedicated to the fatigue analysis of cemented total hip arthroplasty. In particular the damage evaluation scenario is simulated and a sensitivity analysis is performed. To this end, two different damage evaluation algorithms (the elasto-brittle and the continuous damage one) are proposed and implemented in the finite element code ABAQUS®. Some global damage criteria are introduced to quantify the damage accumulation. The continuous damage algorithm is shown to perform better compared to the elasto-brittle damage one in the estimation of the fatigue lifetime of the cement mantle. A sensitivity analysis is then performed as a function of the cement Young's modulus, the stem–cement friction coefficient and the stem Young's modulus. Numerical results show a significant sensitivity to variations of the cement Young's modulus and stem–cement friction coefficient and a moderate sensitivity to the stem Young's modulus.

Forces applied to the prosthesis due to human activity generate complex multiaxial stresses varying in time and resulting in the accumulation of mechanical damage in materials and interfaces [17]. In the literature, finite element models in association with cement damage evaluation algorithms are used to simulate fatigue damage accumulation of a cemented total hip arthroplasty [16] and [6]. In the same way in this work a simulation strategy is described and implemented in the finite element code ABAQUS®[2]. The goal is the simulation of the damage evaluation scenario in the cement mantle together with a fatigue sensitivity analysis [15]. Two different damage rules are introduced in this paper. The first one is the well known Miner rule (elasto-brittle damage evaluation algorithm), originally presented in Verdonschot et al. [16], which does not take into account the damage-induced anisotropy on the cement stiffness. In Verdonschot et al. [16], this produced a conservative estimation of the fatigue lifetime. Some relaxing assumptions were introduced in Dolinski [6], in order to include the effect of the damage-induced anisotropy and a non-linear damage rule was proposed (continuous damage evaluation algorithm). In this paper such an algorithm is fitted to the quasi-three-dimensional finite element model of the implant [4]. Two different global damage criteria are considered in order to study the fatigue behaviour of the cement mantle. The first one is the mean damage accumulated in the cement mantle while the second one is the stem subsidence in the cement mantle. A validation of the quasi-three-dimensional finite element model of the implant is first pursued in term of peak stress in the cement mantle. The proposed global damage criteria are then used to quantify and to analyse the damage initiation and accumulation phenomenon. A sensitivity analysis is finally performed in order to investigate the influence of some parameters such as the cement Young's modulus, the stem–cement friction coefficient and the stem Young's modulus on the fatigue damage scenario.

This work is dedicated to the study of the damage accumulation scenario in the cement mantle of total hip prosthesis. The adopted fatigue damage evaluation algorithms are based on a number of assumptions that should be considered when interpreting the results. First of all the finite element model used to evaluate the stresses at the integration points is a quasi-three-dimensional one. This means that the hoop stress in the cement mantle is recovered as membrane stresses in the corresponding side plate. The maximum hoop stress is comparable to the one obtained by a fully three-dimensional analysis but, of course, cannot take into account the local effect due to the corners or flanges of the stem. Moreover, the effect of rotation of the stem on the formation of a pathway for debris is not captured. Only a particular loading case is considered in this study and the stem is collarless with a particular shape. Other stem designs may lead to less subsidence, particularly when they have flanges or collars. However, note that if cement fatigue is a prominent failure mode, rational design criteria should avoid corners and flanges because when they are present the stem loads the cement mantle primarily at its corners. The mechanical properties of the bone are assumed to remain constant in time and to be linear elastic and isotropic. These assumptions are not realistic but they produce only marginal modification to the stress distribution as checked in Penza et al. [12]. Moreover, creep of acrylic cement reduces the peak stress and thus the cement damage rate in the cement mantle. Due to these limitations the results are only indicative and conclusions should be limited to general trends. Despite the limitations described above, the stress field and the crack pattern formed in the cement mantle are realistic. An unbonded stem–cement interface is considered since it is always associated with cement damage [8]. In this situation the hoop stress is dominant on the bending one and then longitudinally directed cracks are created in the cement mantle. This study demonstrates that the basic assumptions on the cement damage development have a significant effect on the adopted global damage indicators. The elasto-brittle damage algorithm estimates a larger number of cracks compared to the continuous damage one. In the first algorithm the damage does not have any effect on the mechanical properties of the acrylic cement while in the second algorithm the mechanical properties are updated as a function of the mean damage. The damage indicators produced by the continuous damage algorithm seem then to be closer to clinical evidence when frictional interfaces are present. Note that a conservative S–N curve is adopted in this work [9] together with a severe loading condition [1]. Moreover, the actual damage rate is based on uniaxial tensile stress fatigue experiments while in a real situation multiaxial stress condition is present in the cement mantle. All of these factors probably produce an overestimation of the fatigue damage. Cement failure has a minor effect on the stem subsidence within the cement mantle and then it cannot alone be responsible for prosthesis subsidence values sometimes reported in the literature. The fatigue lifetime is sensitive to the bone cement Young's modulus. In fact, an increment of cement bone stiffness produces an increment of the hoop stress in the cement mantle and then a decrement of the fatigue lifetime. However, the stem subsidence remains unchanged because the shear stresses at the interface are not influenced by a variation of the cement Young's modulus. The analyses show that the fatigue lifetime is very sensitivity to the stem–cement friction coefficient. Clearly, a firm and lasting bonding between the stem and the cement mantle reduces the stem subsidence and thus the damage level, although it is difficult to realise clinically. A stem design with flanges or collars could lead to less subsidence and then to a greater fatigue lifetime but it produces very dangerous localised stresses in the cement mantle. Finally, a rather surprising conclusion is that the steel femoral component behaves better than the titanium one with respect to the damage accumulation in the cement mantle. Moreover, the damage evaluation process in the cement mantle does not influence the stress level in the prosthesis and it is below the titanium and steel fatigue limit.