Modified Bilston Nonlinear Viscoelastic Model for Finite Element Head Injury Studies

This paper proposes a modified nonlinear viscoelastic Bilston model (Bilston et al., 2001, Biorheol., 38, pp. 335–345). for the modeling of brain tissue constitutive properties. The modified model can be readily implemented in a commercial explicit finite element (FE) code, PamCrash. Critical parameters of the model have been determined through a series of rheological tests on porcine brain tissue samples and the time-temperature superposition (TTS) principle has been used to extend the frequency to a high region. Simulations by using PamCrash are compared with the test results. Through the use of the TTS principle, the mechanical and rheological behavior at high frequencies up to $104rad∕s$ may be obtained. This is important because the properties of the brain tissue at high frequencies and impact rates are especially relevant to studies of traumatic head injury. The averaged dynamic modulus ranges from $130Pato1500Pa$ and loss modulus ranges from $35Pato800Pa$ in the frequency regime studied $(0.01rad∕sto3700rad∕s)$⁠. The errors between theoretical predictions and averaged relaxation test results are within 20% for strains up to 20%. The FEM simulation results are in good agreement with experimental results. The proposed model will be especially useful for application to FE analysis of the head under impact loads. More realistic analysis of head injury can be carried out by incorporating the nonlinear viscoelastic constitutive law for brain tissue into a commercial FE code.