A new viscoelastic model for human brain tissue using Lode invariants based rate-type thermodynamic framework

We develop new rate-type constitutive relations on a set of orthonormal tensor basis and the corresponding set of Lode invariants, which require only 9 material parameters to predict the mechanical response of the human brain tissue. The mode-dependent response of the tissue is captured by invoking the Hill-stable elastic potential of Prasad and Kannan (2020) and constructing a new form for the rate of dissipation, thus introducing the mode-of-deformation dependent modulus terms and the mode-of-deformation-rate dependent viscosities into the rate-type thermodynamic framework of Rajagopal and Srinivasa (2000). Through the analysis-driven construction of the rate of dissipation, we incorporate maximum change in the viscosities with respect to the mode-of-deformation rates and limit the number of material parameters. Our model satisfactorily predicts the complicated load-unload cycles (pre-conditioned and conditioned) and the stress relaxation data under multiple modes of deformation and multiple rates for the Corona Radiata (CR) region of the brain tissue. It also captures the tension–compression asymmetry in the response and the higher relaxation time in compression loading than in shear loading.