Development of a micromechanical computational finite element model of a brain axon

This study intends to contribute to the research of human brain injury through the development of a computational finite element (FE) model of a brain axon at the microscopic level. This is accomplished using SIMULIA's Abaqus FEA software to perform a dynamic analysis of the axon fiber/matrix model. The FE model is based on the repeating unit cell (RUC) theory applied to composite materials by Abolfathi et al. (2008), the hyperelastic theory applied to brain injury by Meaney (2003), and the undulation data reported by Bain et al. (2003). Limitations noted in the most recent micromechanical study published by Karami et al. (2009), motivate the current study by presenting a need to refine the axon fiber/matrix composite model in order to reduce the discrepancy between the finite element model and the experimental results of Bain et al. (2003). The primary goal of this study is to introduce the construction of a computational model of a brain axon to lessen the gap between experimental and computational results.

The geometry of the model is defined by constructing an RUC of a hexagonal distribution of axons in a matrix. Periodicity and rigid body constraints are applied to the structure, and a hyperelastic material model is assigned. The composite structure is based on an undulation ratio of 1.131 and a fiber volume fraction ratio of 53 percent, as reported in the studies of Bain et al. (2003) and Arbogast and Margulies (1999). Finite displacements are applied to obtain stresses and strains in the structure.

The axon fiber/matrix composite model only converged at small displacement values. In order to resolve the problem, the model was simplified as an elastic material model without the fiber. The reoccurrence of convergence problems indicated that the problem lies in the manner in which periodicity constraints are applied in Abaqus by means of node sets. Since the nodes do not move uniformly, the model does not accurately predict the stresses and strains for the applied displacement. Thus, future work can address the incorporation of periodicity constraints and more specifically, the definition of node sets, in an alternative manner.