Finite element modelling of fracture in long bones

Abstract

The finite element method (FEM) has shown to be an effective and viable tool for simulating the events of a high-speed impact. As materials and methods for protecting the vehicle occupant advance, so must the capabilities of the FEM codes. One shortcoming that must be addressed is the way in which fracture (more appropriately failure) is currently modelled. Two problems exist when using the method of element erosion; 1) it is impossible to predict proper crack propagation with reasonably sized elements and 2) the stress distribution is inaccurately represented at the crack tip when elements are removed. To address this issue, a new fracture algorithm has been written and implemented into DYNA3D. This algorithm allows for prediction of both crack propagation and direction. Crack propagation is predicted using either a Crack Tip Opening Angle (CTOA) criteria or a plastic energy criteria. Crack growth direction is determined from the principle stresses of the elements surrounding the crack tip. The algorithm allows for a crack to split existing elements thus creating new elements and nodes respectively. The fracture algorithm has been validated for several classical fracture mechanics problems using standard engineering materials. The algorithm has been applied toward the prediction of the fracture modes of a long bone under different loading conditions. A model of the human tibia was subjected to pure tension, pure compression, pure torsion, and simple bending. The fracture algorithm was able to predict the proper modes of failure for tension, torsion, and simple bending. The algorithm had difficulty predicting the proper failure mechanism in compression. Future developments will focus on the application of the fracture algorithm to all material types in DYN A3D and the implementation of a better failure initiation criteria for bone.