Numerical modelling of cancellous bone damage using an orthotropic failure criterion and tissue elastic properties as a function of the mineral content and microporosity

Abstract

Background and objective: Elastic and strength properties of lamellar tissue are essential to analyze the mechanical behaviour of bone at the meso- or macro-scale. Although many efforts have been made to model the architecture of cancellous bone, in general, isotropic elastic constants are assumed for tissue modelling, neglecting its non-isotropic behaviour. Therefore, isotropic damage laws are often used to estimate the bone failure. The main goals of this work are: (1) to present a new model for the estimation of the elastic properties of lamellar tissue which includes the bone mineral density (BMD) and the microporosity, (2) to address the numerical modelling of cancellous bone damage using an orthotropic failure criterion and a discrete damage mechanics analysis, including the novel approach for the tissue elastic properties aforementioned. Methods: Numerical homogenization has been used to estimate the elastic properties of lamellar bone considering BMD and microporosity. Microcomputed Tomography (μ-CT) scans have been performed to obtain the micro-finite element (μ-FE) model of cancellous bone from a vertebra of swine. In this model, lamellar tissue is orientated by considering a unidirectional layer pattern being the mineralized collagen fibrils aligned with the most representative geometrical feature of the trabeculae network. We have considered the Hashin's failure criterion and the Material Property Degradation (MPDG) method for simulating the onset and evolution of bone damage. Results: The terms of the stiffness matrix for lamellar tissue are derived as functions of the BMD and microporosity at tissue scale. Results obtained for the apparent yield strain values agree with experimental values found in the literature. The influence of the damage parameters on the bone mechanics behaviour is also presented. Conclusions: Stiffness matrix of lamellar tissue depends on both BMD and microporosity. The new approach presented in this work enables to analyze the influence of the BMD and porosity on the mechanical response of bone. Lamellar tissue orientation has to be considered in the mechanical analysis of the cancellous bone. An orthotropic failure criterion can be used to analyze the bone failure onset instead of isotropic criteria. The elastic property degradation method is an efficient procedure to analyze the failure propagation in a 3D numerical model.