Hyperelastic modeling of the human brain tissue: Effects of no-slip boundary condition and compressibility on the uniaxial deformation

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.