Numerical and experimental investigation of bone fracture behavior

Abstract

Bone is one of the essential organs in the human body and performs many vital functions. The bone possesses unique material properties which enable it to perform its tasks of providing structure, safety, and mobility to the human body. The hierarchal microstructure of bone plays a significant role in imparting these material properties to the bone, where constituents at each level play their specific roles in imparting the bone its exceptional material properties. The fracture toughness of bone can either result from extrinsic or intrinsic mechanisms. The intrinsic toughening mechanisms, such as intrafibrillar stretching and intrafibrillar sliding, result from the material's inherent ability to resist elastic and inelastic deformation. The extrinsic toughening methods, such as crack deflection, crack bridging and microcrack formation, originate from the reduction of stress intensity at the crack tip. The fracture process in a bone can be modeled numerically with the help of either discrete or smeared approaches. Discrete approaches such as XFEM and cohesive zone modeling have been employed extensively to study the fracture behavior of bone at various length scales. In these approaches, the discontinuity is modeled with the help of displacement jump functions. These discrete methods can successfully model various toughening mechanisms in bone, such as crack deflection and intrinsic toughening mechanisms. Thus, they give an accurate description of the crack path and fracture process of bone. But these methods cannot model toughening mechanisms such as microcrack coalescence and struggle in problems where a complex crack pattern is present. On the other hand, the smeared crack approaches models crack as a continuous damage band of finite width with no displacement jump across the crack surface. Such models provide a more comprehensive description of the fracture process in the bone, starting from microcrack coalescence to propagation of a macro crack. Further, these models are capable of modeling the other fracture toughening mechanisms observed in the bone, such as crack deflection at interface boundaries. For this reason, continuum damage mechanics methods have been used in the present work to study the fracture process in a trabecular bone at various length scales. The present work has four broad aims, each shown with the help of separate chapters. In the first part of this work, a gradient-enhanced nonlocal continuum damage mechanics model has been presented under the framework of isogeometric analysis to study the fracture behavior of bone. Such a model can generate mesh-independent results at lower computational costs and with lesser geometric errors. Problems given in the literature are solved to validate the applicability of the developed model. Further, the applicability of the framework to model bone fracture is tested by simulating fracture in a cortical bone microstructure. The results of the analysis demonstrate that the proposed model is ca[able of accurately modeling the fracture process in a bone, including the different fracture toughening mechanisms. Further, the proposed damage model is used to study the effect of anisotropy on the fracture characteristics of cortical bone. The model is first expanded to incorporate the material anisotropy resulting from the orientation of osteons in the cortical bone. Then the effect of material anisotropy arising from the differential loading conditions in a bone is also studied. The applicability of the model is tested by solving fracture problems under mode I, mode II and mixed mode conditions. The results clearly show that the fracture behavior of the bone is significantly affected by material anisotropy. The image-based finite element methods are proving to be a helpful tool in fracture risk characterization, especially for atypical femoral fractures. These methods have better accuracy than the industry standard DXA-based tool, the t-score. This is because it takes into account the loading conditions and geometry of the bone for analysis of fracture risk. The developed gradient-enhanced damage model is further expanded to study the patient-specific fracture process in a proximal femur. The given model is compatible with dual-energy X-ray absorptiometry (DXA) as well as computed tomography (CT) images. Further, a stochastic analysis reveals that the uncertainty in geometric parameters has the highest effect on the output of the analysis. Osteoarthritis is a disease of the joints and is usually characterized by the degeneration of cartilage. But it also significantly alters the properties of bone and other components of the joint. The effect of arthritis on bone subchondral fracture behavior is analyzed in the last chapter of the thesis. The fracture process in the trabecular bone samples is analyzed using µ-CT, uniaxial compression testing, and the gradient-enhanced nonlocal damage model. The structural parameters and the bone properties of bone are analyzed for samples taken from two different regions of the tibia, one with degenerated cartilage and one with intact cartilage. It is observed that the alterations in the structural and mechanical parameters of trabecular bone significantly impact the fracture behavior of the arthritic trabecular bone.