Constitutive modeling the plastic deformation of bone-like materials

Abstract

Bone-like materials such as cortical bone, dentin and nacre possess complex hierarchical structure, which gives rise to superior mechanical performance. Despite numerous efforts devoted to characterizing the mechanical behavior of such materials, there does not exist a general continuum theory describing the plastic deformation of these materials. The present study provides a theoretical framework for the plasticity of bone-like materials. Based on the theoretical framework, a constitutive model is developed. The plastic flow of bone-like materials is modeled by incorporating a shear-dominated mechanism and a dilatation mechanism. We model the shear-dominated mechanism by accounting for the cohesive-frictional nature of bone-like materials, and for the dilatation mechanism, the shear-induced plastic dilatation and the dilatation due to hydrostatic tension are taken into account. Furthermore, the constitutive model incorporates the strain-rate effect on plastic deformation. By fitting the experimental data of uniaxial compression of antler bone, parametric studies are performed and the effect of model parameters on mechanical properties of bone-like materials is discussed. In addition, numerical simulations of cortical bone and dentin under compressive and tensile loadings are carried out; it is found that the model quantitatively captures pressure-sensitive plastic deformation behavior of bone-like materials and a good agreement between numerical simulation and experiment is achieved, substantiating that the continuum model developed in this study can be used to describe the plastic properties of bone-like materials effectively. The plastic deformation of the two-layer structure of dentin subjected to tensile loading is also simulated, and the role of protein-rich intertubular dentin is identified.