Two nonlinear constitutive models were used to describe the dynamic viscoelastic behavior of brain tissue. Small disc-shaped samples of bovine brain tissue were tested in simple shear using forced vibrations (0.5 to 200 Hz) with finite amplitudes (up to 20% Lagrangian shear strain). The samples response to simple, double, and triple harmonic inputs was determined in order to characterize the nonlinearities up to the third-order. A quasilinear viscoelastic model was proposed to describe the spatial nonlinearity. A fully nonlinear viscoelastic model with product-form multiple hereditary integrals was proposed to describe the spatial as well as the temporal nonlinearities. The fully nonlinear model demonstrated superiority at high frequencies (above 44 Hz). Under finite strains, the linear complex modulus showed nonrecoverable asymptotic strain conditioning behavior. Discrepancies observed in previously published studies and the threshold of functional failure of the neural tissue were shown to be related to this strain conditioning effect.
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