A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach

Abstract

Cortical bone can be considered as a heterogeneous composite at microscopic scale, composed of osteons that act as reinforcement fibres embedded in interstitial matrix. Cement lines constitute the interface between osteons and matrix, and they often behave as the weakest links along which microcracks tend to propagate. However, current simulations of crack growth using XFEM combined with usual orientation criteria as implemented in commercial codes do not capture this behaviour: they predict crack paths that do not follow the cement lines surrounding osteons. The reason is that the orientation criterion used in the implementation of XFEM does not take into account the heterogeneity of the material, leading to simulations that differ from experimental results. In this work, a crack orientation criterion for heterogeneous materials based on interface damage prediction in composites is proposed and a phantom node approach has been implemented to model crack propagation. The method has been validated by means of linear elastic fracture mechanics (LEFM) problems obtaining accurate results. The procedure is applied to different problems including several osteons with simplified geometry and an experimental test reported in the literature leading to satisfactory predictions of crack paths.