The pelvic bone is one of most stressed bones in the human body due to its essential task of weight-bearing of upper body. However, pelvic bone fractures usually occur as a result of highrate impact loads, high cycle with low magnitude (e.g., stress fractures) or bone diseases such as pelvic tumors or osteoporosis. Based on these facts, and due to the complexity of injured pelvises for surgeons to treat, the fracture mechanism in this bone and its treatments deserves better understanding. In this research, computer modeling was used to investigate the fracture mechanism in the pelvic bone and to design and optimize the fixation plates of a damaged pelvic bone.

The Finite Element Method (FEM) is a beneficial tool in engineering research to model failure characteristics of solid materials with complex shapes and material properties but not restricted to solid materials. Recently, the extended finite element method (XFEM) employs fracture mechanics to simulate fracture propagation in the bulk materials by allowing cracks to propagate through elements. In this research, the XFEM technique has been implemented to model fracture mechanism in the pelvic bones.

Considering both cortical and cancellous tissues simultaneously in fracture modeling of the bones is one of the requirements in developing a realistic model. Numerous researchers have employed XFEM analysis to model fracture mechanisms in cortical bones on the microscopic and macroscopic scales. However, there are limited studies that modeled fracture in cancellous bone by XFEM analysis. In this research, previously published materials and failure characteristics of cortical bone have been re-implemented on macro-scale level to be utilize in pelvic bone fracture modeling. Modeling the cancellous bone porosity in FE modeling of pelvic bone was impractical because of the details on the micro-scale level of the bone. Alternatively, an equivalent model was developed to produce a behavior similar to that observed in the microscale models.

In order to do so, the experimental results of a published study (Ridha et al. 2013) were used to create a computational model capable of predicting the fracture of one trabecula. The predicted material characteristics of the trabeculae were then utilized in 2D and 3D XFEM models to estimate the behavior of cancellous bone tissue in microscopic scale. Finally, the equivalent model was created based on the obtained material behavior of cancellous bone specimen. The results of the equivalent model were found to be in excellent agreement with the micro-scale XFEM models.

Thus far, material behaviors and failure parameters of cortical and cancellous bones have been estimated. Also, an equivalent model from cancellous tissue in micro-scale level has been developed and evaluated with micro-scale modeling of cancellous specimen. The modeling resulting from cortical and cancellous tissues were integrated into the pelvic bone. Various loading conditions have been investigated to simulate different types of fracture in the pelvic bone.

Finally, the estimated material properties of cancellous and cortical tissues were assigned to a T-shaped damaged bone fixed by a customized bone plate. The fixation plate and screws characteristics were optimized by means of FE analysis (FEA) and the Design of Experiments (DoE) method. In order to do so, the DoE model was developed. Fixation plate thickness, plate material and the number of screws were selected as variables and reduction of stress shielding and stiffer fixation were considered as model objectives. The ANOVA (analysis of variance) method was employed to determine the significant factors mentioned above, along with their effect values. The fixation plate material and thickness were determined as the first and second effective parameters respectively for design of implants, and their optimized values were found.

The contributions of my work were, developing XFEM models of cancellous bone specimens that are capable of accurately predicting the onset and propagation of cracks under mechanical loading, developing an equivalent constitutive model of cancellous bone to utilize in fracture modeling of bones in macro scale, developing an XFEM model that is capable of predicting different types of fracture in pelvic bone under various loading conditions and evaluating and optimizing the mechanical stability and stress shielding of the fixation system in T-shaped acetabular fracture by conjunction of Finite Element Analysis (FEA) and Design of Experiment (DoE).