Computational Solid Mechanics Laboratory, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA.
J Mech Behav Biomed Mater. 2018 Jul;83:63-78. doi: 10.1016/j.jmbbm.2018.04.011. Epub 2018 Apr 13.
Being extremely soft, brain tissue is among the most challenging materials to be mechanically quantified. Despite recent advances in mechanical testing of ultra-soft matters, there still exists a need for robust procedures to analyze their behavior at large deformation. In this paper, it is shown how failing to taking into account the precise boundary conditions can result in substantial variation from the "assumed" ideal behavior, even for the case of simple loading conditions such as the uniaxial mode. For an accurate analysis, the mathematical modeling is combined with the finite element simulation to interpret the mechanical behavior of the brain tissue based on the comprehensive experiments conducted by Budday et al. (2017). It is demonstrated herein that only an Ogden hyperelastic model with both negative and positive nonlinearity constants can predict the mechanical behavior of the brain tissue in tension and compression, and the tension-compression asymmetry might arise from the difference in compressibility behavior in tension and compression. This hypothesis is utilized for modeling the mechanical behavior of the brain tissue in uniaxial loading condition and exhibits excellent agreement with the experiments. This study also provides a comprehensive explanation for nonlinear analysis of soft matters, in general, and the brain tissue, in particular, with thoroughly describing the concept of hyperelasticity and modeling incompressible or compressible behaviors utilizing the Ogden strain energy function.
脑组织极为柔软，是最难进行力学量化的材料之一。尽管最近在超软物质的力学测试方面取得了进展，但仍需要稳健的程序来分析它们在大变形下的行为。本文展示了如果不考虑精确的边界条件，即使在简单的加载条件下（如单轴模式），也会与“假设”的理想行为产生实质性的差异。为了进行准确的分析，将数学建模与有限元模拟相结合，根据 Budday 等人（2017 年）进行的综合实验来解释脑组织的力学行为。本文证明，只有具有负和正非线性常数的 Ogden 超弹性模型才能预测脑组织在拉伸和压缩下的力学行为，拉伸-压缩不对称性可能源于拉伸和压缩下的压缩行为的差异。该假设用于模拟单轴加载条件下脑组织的力学行为，与实验结果吻合得非常好。本研究还为软物质的非线性分析提供了全面的解释，特别是对脑组织，详细描述了超弹性的概念，并利用 Ogden 应变能函数来模拟不可压缩或可压缩的行为。
