An IGA based nonlocal gradient-enhanced damage model for failure analysis of cortical bone

Abstract

The fracture behavior of a cortical bone is significantly affected by its hierarchal structure and a high degree of material anisotropy. Recently, continuum damage models have proven to be an effective tool to characterize such kind of material behavior. However, these models suffer from drawbacks such as mesh dependency, spurious damage growth, and incorrect prediction of damage initiation during the initial stage of loading process. To this end, the objective of this work is to develop a nonlocal gradient-enhanced damage model in an isogeometric setting to predict the fracture behavior of a cortical bone. The numerical framework is formulated considering an additional diffusion equation in conjunction with the standard equilibrium equation. The material is assumed to be transversely isotropic to incorporate the anisotropy in damage evolution. The versatility of the proposed framework is tested by solving problems for different modes of fracture. For numerical simulations, samples are taken from different quadrants of bovine cortical bone, and the effect of anisotropy on the damage characteristics of the bone are investigated.