A compressible hyper-viscoelastic material constitutive model for human brain tissue and the identification of its parameters

In this paper, we have introduced a compressible hyper-viscoelastic constitutive model for human brain tissue. The model is calibrated with the reported experimental data from different regions of the brain. The parameters of the model are determined in a simultaneous calibration for tension, compression, shear, and compression–relaxation tests data. They are obtained in an iterative procedure in conjunction with a finite elements (FE) modeling of the tissue, as well as, with the Nelder–Mead Simplex optimization procedure. In the calibration procedure, the compressibility of the material is taken into account, and the respective time-dependent volumetric parameter is also determined. Additionally, the Drucker stability condition is enforced to assess the physical meaning of the extracted constitutive parameters. This proposed model provides an improved prediction of the experimental data and tissue response under various loading conditions. The results show that, under inhomogeneous deformation, the suggested approach will lead to a better material calibration of brain tissue compared to the simple mathematical model fitting.