Generalised Mooney–Rivlin models for brain tissue: A theoretical perspective

Abstract

A vivid research on brain tissue has proven that in simple shear tests the relation between the shear stress and shear strain is linear for strains in a range which is significative in the physiological and pathological regime. Since Mooney–Rivlin materials satisfy this peculiar property when subjected to simple shear deformations, the celebrated mathematical model introduced first by Mooney, and then developed by Rivlin, has been often used to describe the mechanical behaviour of brain tissue. Recently, it has been shown that a most general strain energy density for incompressible isotropic elastic materials exhibiting a linear relationship between shear stress and shear strain in simple shear deformation consists of the sum of the Mooney–Rivlin model and an arbitrary function of the difference of the first two principal invariants of the deformation tensor. For this reason, a strain energy function of this form is called a generalised Mooney–Rivlin model. In this note we design theoretically a procedure aiming at the determination of the generalised Mooney–Rivlin model which fits best the experimental data.