Modeling of viscoelastic deformation and rate-dependent fracture damage in rat bone

Bone is a complex hierarchical structural material whose organ-level response is highly influenced by its constitutive behavior at the microstructural level, which can dictate the inelastic nonlinear deformation and fracture within the organ. In the current study, a combined experimental-computational approach was sought to first obtain the local constitutive properties. Later, a multiscale modeling framework utilizing a novel rate-dependent nonlinear viscoelastic cohesive zone (NVCZ) model was used to explore the fracture behavior at the microstructure of the bone and its influence on the global scale (organ-level) response. Toward this end, nanoindentation testing was conducted within the cross-section of a rat femur bone specimen. An inverse optimization process was used to identify the isotropic linear viscoelastic (LVE) properties of cortical bone by integrating the test results with a finite element model simulation of the nanoindentation testing. Model results using different numbers of spring-dashpot units in the generalized Maxwell model showed that four spring-dashpot units are sufficient to capture the LVE behavior, while solely LVE constitutive relation is limited to fully characterize the rat femur. The LVE constitutive properties were then used along with the rate-dependent NVCZ fracture within the representative volume element (RVE), which was two-way coupled to the global scale bone. A parametric study was conducted by varying the fracture properties of the NVCZ model. The model demonstrated the capability and features to represent inelastic deformation and nonlinear fracture that are linked between length scales. This further implies that the inelastic fracture model and the two-way coupled modeling can elucidate the complex multiscale deformation and fracture of bone, while model validation and further advancements with test results remain a follow-up study and are currently in progress.