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

Impact duration (Tp) can be obtained by numeric Integration from the forcedisplacement
curve. The motion could be considered as a simple harmonic motion
with an effective linear stiffness:
(12)
Fmax
1
K effec = =
∆x ⎛ ⎞
⎜ 1 1
+
⎟
⎜ 2 1
K
⎟
⎜ sh 3 3 K H . F ⎟
⎝ max ⎠
Now considering the related equations, the value of Tp could be obtained as:
T
P
= π
m
K
Where
sh e m m m
1 1 1
= +
*
Head Injury Criteria (HIC) which is as explanation of impact severity can be obtained
from the following equation:
2.
5
⎡ ⎡ 1 t ⎤
2 ⎤
HIC = max(
t1,
t2
) ⎢(
t2
− t1
) ⎢ ( ) ⎥ ⎥ (14)
⎢ ( )
⎣ ⎣ − ∫ a t dt
t t1
2 t1
⎦ ⎥⎦
The term max(t1, t2) explains that the time distance between t1 and t2 must be so that
the next term in brackets gains its maximum value. With the following assumption for
the head acceleration
(15)
F ⎛ max t ⎞
a( t) = Sin⎜π
⎟
msh ⎝ TP
⎠
and by replacing equation 15 in 14 and for 0 < t < TP
, by simultaneous solution of
the following equations, the time distance which maximize equations 14 would be:
( )
( HIC)
*
effec
(13)
∂ HIC
∂t2
= 0
∂
∂t1
= 0 (16)
After obtaining the values of t1 and t2, the peak value of HIC is specified.
4. VALIDATION USING FEM.
For FE analysis of current model, LS-Dyna module of ANSYS software has been
used. For modeling a spherical shell as human head, two concentric spheres have been
considered. Initially two smaller spheres as brain and one bigger sphere as skull were
drawn. Then one of the smaller spheres was deducted from the larger one. The model
was divided to two identical parts which were symmetrical with regard to the sagittal
plane to reduce the computer run time. By defining points and constructing surfaces,
the model was divided to four equal parts to create the mesh. MDT software is applied
to model the torus shape object which has two different radii in impact region. After
constructing the model in MDT, the file is saved as .sat format and introduced to
ANSYS. The model is an object with two radii of 0.03m and 0.045m in the impact
zone. The distance of the spherical shell from the torus body is 0.5mm.