A Semi-Empirical Elastic-Plastic-Visco-Damage Constitutive Model of Cortical Bone

Bone quality can be characterized by toughness of bone which quantifies the energy required for failure. As much of the toughness of bone occurs after yielding, 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. However, the underlying mechanism of the post-yield behavior of cortical bone is so far poorly understood, which makes it difficult to establish physically sound constitutive models for cortical bone that could accurately predict the mechanical behavior of the tissue. The absence of the constitutive equations has significantly hindered the application of bone mechanics in solving biomedical problems. Besides, an accurate constitutive model is always required in numerical modeling and simulating the mechanical behavior of bone under different loading conditions. Based on the experimental results obtained in our lab, the objective of this study was to develop and verify a constitutive model of cortical bone under compression, which accounted for damage accumulation, plastic deformation and viscoelastic properties.