A mass spring model applied for characterizing mode I fracture in orthotropic materials

Abstract

We describe a mass spring system (MSS), which is also referred as lattice model in the literature, predicting the load-displacement curve of the orthotropic materials. We have developed the MSS model of a double cantilever beam to capture the energy release rate in a mode I fracture of the orthotropic materials using two different formulations: maximum strain energy and maximum strain. Further, we have considered determination of fracture energy of cortical bone, as a case study, using the compliance based beam method (CBBM). This method avoids monitoring of crack length during fracture and provides the complete R-curve along with the plateau, which is the fracture energy. We have also obtained the R-curve from the load-displacement curve predicted by the MSS model and determined the fracture energy of cortical bone. As the maximum percentage error in fracture energy predicted by the MSS model for dehydrated and hydrated bone is 1.02 per cent and 1.15 per cent, respectively, the results are in good agreement with the experimental results. Thus, we have shown the ability of the MSS model to produce quantitative results as well in comparison to the models presented in the literature for simulation of a fracture, which give essentially qualitative results. We have used the validated MSS model for characterizing the load-displacement behavior of cortical bone for increasing mineralization and porosity.