An Ogden hyperelastic 3D micromechanical model to depict Poynting effect in brain white matter

Abstract

Shear and torsional load on soft solids such as brain white matter purportedly exhibits the Poynting Effect. It is a typical nonlinear phenomenon associated with soft materials whereby they tend to elongate (positive Poynting effect) or contract (negative Poynting effect) in a direction perpendicular to the shearing or twisting plane. In this research, a novel 3D micromechanical Finite Element Model (FEM) has been formulated to describe the Poynting effect in bi-phasic modeled brain white matter (BWM) representative volume element (RVE) with axons tracts embedded in surrounding extracellular matrix (ECM) for simulating brain matter's response to pure and simple shear. In the presented BWM 3D FEM, nonlinear Ogden hyper-elastic material model is deployed to interpret axons and ECM material phases. The modeled bi-phasic RVEs have axons tied to the surrounding ECM. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear case were analyzed. Root mean square deviation (RMSD) was calculated for stress and deformation response plots to understand the effect of axon-ECM orientations and loading conditions on the degree of Poynting behavior. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane underscored the significance of axonal fiber-matrix interactions. From the simulated ensemble of cases, a transitional dominance trend was noticed, as simple sheared axons showed pronounced Poynting behavior, but shear deformation build-up in the purely sheared brain model exhibited the highest Poynting behavior at higher strain % limits. At lower strain limits, simple shear imparted across and perpendicular to axonal tract directions emerged as the dominant Poynting effect configurations. At high strains, the stress-strain% plots manifested mild strain stiffening effects and bending stresses in purely sheared axons, substantiated the strong non-linearity in brain tissues’ response.