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.

A review on experimental and numerical investigations of cortical bone fracture

“…Some researchers considered the anisotropic bone modeling, microstructural effects, the non-linear model of the cortical bone to numerically predict the K C of cortical bone more efficiently. 19,65–67,69–72,76…”

“…15,19,31 Additionally, these studies also included the effect of storage media on the K C . 15,19,31 and the energy required for plastic deformation before the fracture of cortical bone. 31 Numerous experimental studies determined the effect of several parameters, that is, sugar, age, hydration, mineralization, preservative method, fatigue loading, strain rate, porosity, anisotropy, demineralization, deproteinization, type of specimen, indentation, shear deformation, bone composition, etc., on fracture parameters of cortical bone.…”

“…Numerically predicted fracture parameters of cortical bone have shown a wider range of data than experimentally determined fracture parameters of cortical bone. Fracture toughness in terms of critical SIF varied between 1 and 5 MPa.m 1/2 for longitudinally, and transversely fractured specimen 19,82 ; however, the mode-I energy release rate ( G I ) varied between 500 and 7000 J/m 2 due to the different locations, and numerical techniques (FEM, EFGM, and XFEM) considered to analyze the cortical bone fracture. 12–14,19,65–67,76,81,82,84 Experimentally and numerically determined fracture parameters of cortical bone are also presented in Table 1.…”

“…5,10–15 All the experiments were performed with different osteon orientations of the specimen (longitudinally and transversely fractured). 16–20 Hence, a thorough study of the cortical bone fracture is needed to develop suitable numerical and experimental analyses to determine the fracture parameters of the cortical bone. Numerical analysis cannot be done without experimentally determined material properties and loading of cortical bone.…”

“…Therefore, initially, material properties of cortical bone were determined experimentally, and then in-depth numerical analysis (finite element method (FEM), element free Galerkin method (EFGM), and extended finite element method (XFEM)) was performed to understand the fracture behavior of the cortical bone. 19…”