Differential versus integral formulation of fractional hyperviscoelastic constitutive laws for brain tissue modelling

For years, interest has been constantly growing in biological tissue modelling. Particularly, the mechanical study of the brain has become a major topic in the field of biomechanics. A global model of this organ, including a realistic mesh and suitable constitutive laws for the different tissues, would find applications in various domains such as neurosurgery, haptic device design or car manufacturing to evaluate the possible trauma due to an impact.Several constitutive models have already been designed; regarding the strong strain-rate dependence of the stress–strain curves available in the literature, we decided to describe brain tissue as a viscoelastic medium through the use of the fractional derivation operator. Thanks to this approach, we can derive a convolution-based model with the Mittag–Leffler function as the regularized kernel.