Experimental and numerical comparisons between finite element method, element-free Galerkin method, and extended finite element method predicted stress intensity factor and energy release rate of cortical bone considering anisotropic bone modelling

Abstract

Stress intensity factor and energy release rate are important parameters to understand the fracture behaviour of bone. The objective of this study is to predict stress intensity factor and energy release rate using finite element method, element-free Galerkin method, and extended finite element method and compare these results with the experimentally determined values. For experimental purpose, 20 longitudinally and transversely fractured single-edge notched bend specimens were prepared and tested according to ASTM standard. All specimens were tested using the universal testing machine. For numerical simulations (finite element method, element-free Galerkin method, and extended finite element method), two-dimensional model of cortical bone was developed by assuming plane strain condition. Material properties of the cortical bone were considered as anisotropic and homogeneous. The values obtained through finite element method, element-free Galerkin method, and extended finite element method are well corroborated to experimentally determined values and earlier published data. However, element-free Galerkin method and extended finite element method predict more accurate results as compared to finite element method. In the case of the transversely fractured specimen, the values of stress intensity factor and energy release rate were found to be higher as compared to the longitudinally fractured specimen, which shows consistency with earlier published data. This study also indicates element-free Galerkin method and extended finite element method predicted stress intensity factor and energy release rate results are more close to experimental results as compared to finite element method, and therefore, these methods can be used in the different field of biomechanics, particularly to predict bone fracture.