Mathematical Model for Closed Head Impact

In order to understand better the head injury mechanism and to clarify the unsettled question as to whether the shear strain or the reduced pressure is the primary injury etiology during a given impact, a realistic model capable of predicting both the shear strain and the reduced pressure effects should be devised. The approach to such a realistic but complicated boundary value problem in biomechanics is achieved through the application of the finite element method. By use of the finite element displacement formulation, the human head is modeled as a viscoelastic core bonded to a thin viscoelastic shell, which simulates the brain and the skull, respectively.

For purpose of comparison, two configurations-a spherical shape and a prolate ellipsoid-have been used to describe the geometry of the human head. By applying an impact load over a small area of the shell, the head injury mechanisms-such as cavitation, caused by excessive tensile stress, and rotation, produced by large shear strain-along with their possible damage locations, are simulated. Linear viscoelastic properties are assumed for both the core material and the shell. The equations of motion for the problem are in the form of second-order matrix differential equations. Solutions are obtained through the matrix iterative method.