## 4 Discussion  
Understanding of crack propagation behavior within biological organs (e.g., femur, tibia) is of great clinical relevance to prevent the fractures [18]. Numerical methods such as eXtended Finite Element Method were considered as potential tools to provide quantitative and objective indicators (e.g., crack path, critical stress intensity factor, and critical strain energy release rate) for characterizing the crack propagation within bone structures [25; 26; 27]. Consequently, understanding the fracture mechanics of the human knee structures allows better decision support for clinical interventions. In this present study, the simulation of the tibia bone crack propagation under total knee replacement was simulated and evaluated. This study provided, for the first time, a detailed view on the full crack path of the tibia bone within the TKR implant. In particular, an age-related factor effect analysis in this process was conducted. In our study, two strategies to identify the location of the initial crack were adopted. The first strategy related to the fixed-point location from clinical observation and the associated outcomes indicated that the propagation still happens with smaller values of the stress intensity factor and energy release rate, than those in the literature. This finding suggested a larger range of values for these factors, when propagating cracks within the human bone structures. In fact, this strategy was less sensitive to the value range of the stress intensity factor and the energy release rate. The second strategy dealt with the use of experimental data to calibrate an age-related point identification process. In fact, the automatic identification of the crack initiation point, based on the maximal stress under tensile loading, gives a more consistent range of values for the stress intensity factor and the energy release rate. Obtained outcomes indicated that the strategy to identify the crack initiation point is a very important factor. This present study suggested that the second strategy was the best strategy to perform crack analysis in the human system, thanks to its damage-based crack initiation approach. In addition to the crack initiation, the material law of the bone tissue also plays an important role in the propagation process. In the present study, a homogeneous linear elastic law was used. However, with the presence of the implant, we observed the discontinuity at the bone-implant interface, leading to a disruption of the crack path. This finding confirmed the important role of the patient-specific material properties of the bone to analyze the crack propagation behavior. Age-related micro-damage accumulation during surgery or daily life activities might affect the material properties of bone [33]. A scratch might inevitably occur on its surface, leading to an accumulation of stress at those points and the formation of a location for crack growth propagation. Additionally, the S-N curve observation revealed that older individuals would experience a lesser decline in the fatigue cycles to failure than younger ones, with a certain increase in the applied stress. In fact, the higher the stress, the faster was the gradual accumulation of damage. The present study compared the full crack path and fracture behavior of two age models (27-year-old and 56-year-old) with different material properties. The obtained outcomes also suggest that age (i.e., bone strength) plays an important role in the tibia crack and fracture. Our finding was in agreement with the literature work [20]. However, it is important to note that the strength of the bone tissue is an important factor for crack and fracture prevention. Thus, rehabilitation should be conducted after the TKR procedure, to improve the bone strength and joint flexibility. In the framework of finite element modeling, the choice of the element formulation plays an important role for an accurate analysis. It is well-known that higher-order elements such as quadratic elements give more accurate results than linear elements.