A Semi-Empirical Constitutive Model for Post Yield Behavior of Bone in Tension

Among the material properties that can be assessed through mechanical testing, toughness quantifies the energy required for failure and is therefore most suited for characterizing bone quality. As much of the toughness of bone occurs after yielding, post yield behavior of bone is attracting more and more attention [1, 2]. Although a lot of experimental studies have been conducted on post yield behavior of bone, little efforts have been made to develop constitutive relation for post yield behavior of bone tissues. Elucidating the underlying mechanism of post-yield behavior of bone is critical for further development of clinical strategies to predict and prevent age and disease related bone fractures. In addition, such understanding could help bridge the gap between biology and mechanics of bone since cellular activities are directly related to the ultrastructural architecture and composition of the tissue. Moreover, an accurate constitutive model is always required in numerical modeling and simulating the mechanical behavior of bone under different loading conditions. Based on the results reported in the literature and obtained in our laboratory, this study intends to develop and verify a semi-empirical constitutive model of the post-yield and failure behavior of the cortical bone tissue in tension.