ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

of 24 shell elements, while the interior fluid was modeled by 384 eight noded brick
elements. Impact loading was simulated by applying a pressure-time history to a
circular cap with sector half angle 15º on the exterior of the shell. A Hanning squared
function was used, which is a reasonable approximation of actual impact loading. 4 [3]
Fig. 1: Diagram of Young and Morfey’s fluid-filled spherical shell model. [3]
A sensitivity study was performed, consisting of a range of simulated impacts with
varying impact duration Tp, while all other parameters, including the peak impact force
F0, were held constant. As impact duration was lowered Young and Morfey observed
that the intracranial pressure behavior began to deviate from the “quasi-static” response.
The quasi-static response is analogous to the hydrostatic pressure at a certain depth
within a fluid-filled container, which is caused by gravity. In a similar fashion, during
comparatively long duration impacts (typically 3 ms or greater), the skull is
predominantly subjected to rigid-body linear acceleration. As so, the intracranial
pressure can be described by Equation 1:
[Equation 1]
Where: r (/m) is the distance in the x-direction from the central (coronal) plane of the
brain, P(r) (/Pa) is the pressure at this point, and m (/kg) is the mass of the skull-brain
system. [3] Hence for a quasi-static response one expects peak positive pressure in the
brain to occur directly beneath the point of impact (the coup), varying linearly through
to a peak negative pressure (of equal magnitude) diametrically opposite the impact (the
contrecoup). This pressure behavior is prevalent in both numerical and cadaveric head
impact literature, in which it is unusual to investigate low duration impacts.
For quasi-static behavior the magnitude of the peak positive and negative pressures do
not depend on impact duration, only on the maximum load. A portion of Young and
Morfey’s results are presented below, see Fig. 2. For comparatively long to medium
duration impacts (10 ms to 3 ms) the intracranial pressures at the coup and contrecoup
rise and fall with the applied load and the peak pressures remain constant, clearly
indicating quasi-static behavior as was expected. However as impact duration is reduced
to 1 ms, the peak pressures observed become significantly greater than predicted by the
4 Hanning squared pressure time history given by:
where
[Equation 2]
[Equation 3]
t is time, Tp is the duration of the applied load, F0 is the maximum force in the x-direction, a is the inner
radius of the skull, and φ is the loading area sector half angle. [3]