Two-Way Coupled Multiscale Model for Predicting Mechanical Behavior of Bone Subjected to Viscoelastic Deformation and Fracture Damage

Abstract

This paper presents a two-way linked computational multiscale model and its application to predict the mechanical behavior of bone subjected to viscoelastic deformation and fracture damage. The model is based on continuum thermos-mechanics and is implemented through the finite element method (FEM). Two physical length scales (the global scale of bone and local scale of compact bone) were two-way coupled in the framework by linking a homogenized global object to heterogeneous local-scale representative volume elements (RVEs). Multiscaling accounts for microstructure heterogeneity, viscoelastic deformation, and rate-dependent fracture damage at the local scale in order to predict the overall behavior of bone by using a viscoelastic cohesive zone model incorporated with a rate-dependent damage evolution law. In particular, age-related changes in material properties and geometries in bone were considered to investigate the effect of aging, loading rate, and damage evolution characteristics on the mechanical behavior of bone. The model successfully demonstrated its capability to predict the viscoelastic response and fracture damage due to different levels of aging, loading conditions (such as rates), and microscale damage evolution characteristics with only material properties of each constituent in the RVEs.