8 - Prediction of Size Effects in Bone Brittle and Plastic Collapse

Abstract

The overall plastic yield and brittle failure behaviors of three-dimensional trabecular bone are investigated by a microstructural modeling approach based on the homogenization of the initially discrete architecture. The multiaxial yield behavior is analyzed to formulate a multiaxial plastic yield criterion. Furthermore, the brittle fracture of the lattice is modeled under triaxial stress states to construct the failure surfaces, defined in the tension–tension quadrant. In plastic yielding, the analyses are performed assuming an elastic perfectly plastic lattice, and a micromechanical model based on homogenization scheme is applied to a representative unit cell to determine the macroscopic plastic yield surfaces in stress space. This general framework is applied to evaluate the yield and failure properties of trabecular bone, which are of key interest in understanding and predicting the fracture of bones and bone implant systems. The effective strength of trabecular bone is evaluated in the two situations of fully brittle (fracture with no tissue ductility) and fully ductile failure (yield with no tissue fracture) of the trabecular tissue.