# Mechanical and Fatigue Behavior of Cellular Structure
###### Abstract  
Repetitive loads acting on the hip joint fluctuate according to the type of activities produced by the human body. Repetitive loading is one of the factors that leads to fatigue failure of the implanted stems. The objective of this study is to develop lightweight femoral stems with cubic porous structures that will survive under fatigue loading. Cubic porous structures with different volumetric porosities were designed and subjected to compressive loading using finite element analysis (FEA) to measure the elastic moduli, yield strength, and ultimate tensile strength. These porous structures were employed to design femoral stems containing mechanical properties under compressive loading close to the intact bone. Several arrangements of radial geometrical porous functionally graded (FG) and homogenous Ti-6 Al-4V porous femoral stems were designed and grouped under three average porosities of 30%, 50%, and 70% respectively. The designed stems were simulated inside the femoral bone with physiological loads demonstrating three walking speeds of 1, 3, and 5 km/h using ABAQUS. Stresses at the layers of the functionally graded stem were measured and compared with the yield strength of the relevant porous structure to check the possibility of yielding under the subjected load. The Soderberg approach is employed to compute the safety factor (N\({}_{\text{f}}\) > 1.0) for each design under each loading condition. Several designs were shortlisted as potential candidates for orthopedic implants. stem design; implants; hip replacement; femur bone; total hip arthroplasty; loading; muscular forces; walking speeds; fatigue analysis; computational analysis +
Footnote †: journal: Applied  
Total hip arthroplasty is keep raising drastically over the next 30 years. THA in USA is expected to increase from 930,575 in 2020 to 1,537,422 in 2050 with an annual growth rate of 1.7% [15; 16]. The revision hip replacement surgery after 20 years varies from 40% for young of less than 50 years old, 30% for ages between 50 and 59 years old, and 15% for ages between 60 and 75 years old [16]. Early hip arthroplasty revisions with a diagnosis of infection and inflammatory reaction, fracture, instability, other mechanical complications, and aseptic loosening over the years 2012 to 2019 are 32.5%, 24.3%, 21.7%, 4.8%, and 4.2%, respectively [15; 17]. The femoral stem's prefabricated design allows using different biocompatible materials with properties fitting the functional requirements [2; 18] and increasing the expectations to last longer than before. Studies have proven that the Ti-6 Al-4V (Ti alloy) is a perfect biomedical material for hip implants in terms of strength, biocompatibility, corrosion resistance, lightweight, and flexibility [19; 20; 21]. The stiffness of the Ti-6 Al-4V alloy is 5-10 stiffer than femur bone [11; 20]. Thus, stems with porous structure designs were developed to reduce the stiffness, enhance the trabecular bone tissue ingrowth that facilitates the integration of the implanted stem with the hosting bone [22] and significantly reduce the stress shielding [11]. The applied forces on the implanted stem that depend on the different human activities such as running, stair climbing, jogging, and walking at various speeds produce dynamic stresses leading to fatigue fracture [23]. Many researchers focused on transferring part of the applied stresses on the stem to the bone to reduce the stress shielding and micromotion without considering the fatigue failure due to the dynamic stresses in their studies. Most of the previous studies were found predicting the fatigue limit using FEA for bulk stems under concentrated compression loads, but few studies were found carried out for stems with porous structure [24; 25]. No literature was discovered on computing the fatigue life for porous stems using different physiological loads. In our previous study [11], mechanical performance, stress shielding, and micromotion of the designed femoral stems were studied and investigated.