## 1 Introduction  
A total knee replacement (TKR) is a surgical method through which the knee joint is replaced by artificial material to deliver pain and recover locomotion functions of the involved patients [1]. However, periprosthetic fractures commonly occur when using the implant. The fractures can occur in the femur, tibia, or patella, affecting the areas within 15 cm from the joint surface, or within 5 cm from the intramedullary stem [2; 3]. Thus, the management of these post-surgical complications remains a clinical and scientific challenge. Understanding of fracture mechanics of the human knee structures allows a better decision support for clinical interventions. Numerous studies addressed these complex injuries involving the femur [4; 5; 6; 7; 8]. Reported findings showed that the successful nature of the TKR treatment links to both mechanical and biological aspects [9]. However, the dominant mechanical failure remains an important issue. Additionally, it is well-acknowledged that cracks play a vital role in the failure process. According to [10; 11], periprosthetic fracture following TKR occurs most regularly in the femur, mostly in the supracondyl sector. [PERSON] [12] clinically indicated that the interface crack (e.g., cement and implant) could be noticed as a hint of loosening, and its behavior needs to be elucidated for better management. Tibia fractures were also studied [10; 13; 14]. Most studies focused on the mechanical behavior at the bone-implant interface. [PERSON] et al. [14] aimed to elucidate the relationship of tibial tunnel (TT) with fracture pattern and implants. The simulation of different types of osteosynthesis and the process of bony healing was also performed in [PERSON] et al. [15]. However, the periprosthetic fractures in tibias, as a result of an implant, needs further investigations to better understand the role of cracks and their propagation path, which leads to the failure process. Moreover, the fatigue crack initiation and age-related effects of the bone properties are not yet extensively investigated. From a clinical perspective, the fractures in tibias can happen at any stage of surgery, mostly during skeletal retraction, tibial insertion, or elimination of the pre-existing prosthesis in revision surgery [10]. As stated by the most often used classification system [5; 10], which is based on the anatomical area of the fracture and the condition of the tibial component fixation, the tibial fracture is categorized into four types (I-IV) and three subtypes (A, B, C). Type-I tibial fracture can be found in the tibial plateau, type II is assigned inferior to the tibial plateau in the vicinity of the prosthetic stem, type III occurs distal to the stem of the tibia, and type IV concerns the tibial tubercle. Additionally, subtype A is located to a fracture with a stable prosthesis on radiographs, subtype B is determined as fractures with radiographic proof of component loosening, and subtype C could be seen as intraoperative fractures. To quantify the resistance of a material to cracking under monotonic loading conditions, fracture toughness is commonly used [16]. Bone is considered to be a heterogeneous hierarchical material [17; 18]. Under cyclic loading conditions, multiple micro-cracks can first occur and then coalesce into \"macro-crack\", prior to leading to final failure--which is the separation of the bone in pieces. Most of the time, micro-cracks are eliminated by remodeling [16]. If fatigue damage in bone accumulates more speedily than the eliminated procedure by remodeling, fatigue failure could occur. [PERSON] et al. [19] indicated that mechanical fatigue damage accumulates more rapidly in these \"compressive\" areas than in the \"tensile\" areas of the cortical bone. Specimens were tested at strain ranges from 0.005 to 0.01, under physiological loading rates.