The purpose of this study was to determine experimentally the constitutive equations for brain tissue. Three series of experiments were performed in which the brain tissue was treated as a linear, quasi-linear and nonlinear isotropic viscoelastic material. Finite element analysis was performed and verified that simplifying assumptions made for developing constitutive equations were reasonable.

Human and bovine brain samples were used to characterize linear behavior of brain tissue in the first series of tests. Single step tests with shear strains of up to 40% were performed to obtain stress-relaxation material functions for human and bovine brain tissue.

The second series of experiments determined shear properties of bovine brain material by performing a set of single step loading stress-relaxation tests at the strain levels of up to 100%. For these tests, the theory of quasi-linear viscoelasticity (QLV) was employed to determine material properties.

The third series of experiments involved nonlinear testing using single, two and three step loading stress-relaxation tests. The integral polynomial form of the third order Green-Rivlin constitutive equation was applied to model nonlinear behavior of the brain tissue. This representation describes the material behavior of brain tissue for the shear strains of up to 100%.

The range of applicability for each viscoelastic theory was determined for brain material. It was found that for the strains of up to 40% a linear viscoelastic model is sufficient to describe material behavior. For the strains of up to 60% a quasi-linear model may be employed to describe the nonlinear behavior of brain tissue. At the strains of 60% and greater a time nonlinearity of brain material becomes significant and a nonlinear theory of viscoelasticity must be employed.