A theory of biological composites undergoing plastic deformations

Abstract

Natural biological composites such as bone, dentin, nacre and enamel exhibit anisotropic microstructures, giving rise to orientation-dependent mechanical properties. Although the mechanical properties of these materials have been studied extensively, there is limited progress on modeling the common features associated with the orientation-dependent plastic deformation of biological composites. In this study, we develop a continuum theory for elastic-viscoplastic deformations of anisotropic biological composites. The pressure-sensitive and plastically dilatant plastic flow is incorporated into the theory, and the plastic spin related to the kinematics of the underlying substructure during macroscopic plastic deformation is explicitly taken into account. A special set of constitutive equations are implemented in a finite element program. Furthermore, the material parameters have been calibrated and numerical simulations of elastic-plastic deformation in bone are performed. It is found that the theory can capture the major features of plastic deformation of biological composites. The numerical simulations are in good agreement with experiments, demonstrating that the model is capable of predicting the complex plastic deformation of bone.