Application of fractional-derivative standard linear solid model to impact response of human frontal bone

The impact of a rigid body on a thin plate with a buffer is investigated in this paper. A buffer is assumed as a linear spring fractional derivative dashpot which exhibits the viscoelastic features. The fractional-derivative standard linear solid model is suggested for describing the shock interaction of the impactor with a circular elastic plate. We assume that a transient wave of transverse shear is generated in the plate and the reflected wave does not have sufficient time to interact with the plate before the impact process is completed. The ray method is used outside the contact spot, but the Laplace transform method is applied within the contact region. The time-dependence of the contact force is determined. A numerical example is carried out by considering crash scenarios in frontal impacts of the human head which could estimate brain injury risks.