A quasi-brittle continuum damage finite element model of the human proximal femur based on element deletion

In this paper, a simple and practical finite element (FE) model coupled to a quasi-brittle damage law to describe the initiation and progressive propagation of multiple cracks based on element deletion is developed to predict the complete force-displacement curve and the fracture pattern of a human proximal femur under quasi-static load. The motivation of this work was to propose a FE model for possible clinical use with a good compromise between complexity and capability of the simulation. The model considers a limited number of parameters that can predict proximal femur fracture in more adequate physical terms than criteria-based fracture models. Based on experimental results, different damage laws for cortical and trabecular bone are proposed to describe inelastic damage accumulation under excessive load. When the damage parameter reaches its critical value inside an element of the mesh, its stiffness matrix is set to zero, leading to the redistribution of the stress state in the vicinity of the damaged zone (crack initiation). Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. To illustrate the potential of the proposed approach, the left femur of a male (age 61) previously investigated by Keyak and Falkinstein (Model B: male, age 61) was simulated till complete fracture under one-legged stance quasi-static load. The proposed finite element model leads to more physical results concerning the shape of the force-displacement curve (yielding and fracturing) and the profile of the fractured edge.