Agarwal Mohit, Pelegri Assimina A
Mechanical and Aerospace Engineering Rutgers, The State University of New Jersey, New Brunswick, NJ, USA.
Heliyon. 2024 Feb 8;10(3):e25379. doi: 10.1016/j.heliyon.2024.e25379. eCollection 2024 Feb 15.
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.
据称，诸如脑白质等软固体上的剪切力和扭转载荷会表现出坡印廷效应。这是一种与软材料相关的典型非线性现象，即软材料倾向于在垂直于剪切或扭转平面的方向上伸长（正坡印廷效应）或收缩（负坡印廷效应）。在本研究中，已构建了一种新颖的三维微观力学有限元模型（FEM），用于描述双相建模脑白质（BWM）代表性体积单元（RVE）中的坡印廷效应，其中轴突束嵌入周围的细胞外基质（ECM）中，以模拟脑物质对纯简单剪切的响应。在提出的BWM三维有限元模型中，采用非线性奥格登超弹性材料模型来解释轴突和ECM材料相。建模的双相RVE中的轴突与周围的ECM相连。在这个概念验证（POC）有限元模型中，分析了三种简单剪切加载配置和一个纯剪切情况。计算了应力和变形响应图的均方根偏差（RMSD），以了解轴突-ECM取向和加载条件对坡印廷行为程度的影响。垂直于剪切平面的法向应力（S11、S22或S33）的变化突出了轴突纤维-基质相互作用的重要性。从模拟的案例集合中，注意到一种过渡性的主导趋势，因为简单剪切的轴突表现出明显的坡印廷行为，但在纯剪切脑模型中的剪切变形积累在较高应变百分比极限下表现出最高的坡印廷行为。在较低应变极限下，横跨轴突束方向和垂直于轴突束方向施加的简单剪切成为主导的坡印廷效应配置。在高应变下，应力-应变%图显示纯剪切轴突中有轻微的应变硬化效应和弯曲应力，证实了脑组织响应中的强非线性。
