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

Fig. 7 modeling the oblique impact of a torus shape object with a spherical shell using Finite Element.
SOLID 164 elements have been used for mesh generation. It is required to use a
unique type of element for meshing the parts which are in contact with each other.
Element SOLID 164 is normally used in modeling three dimensional structures in
explicit dynamics cases. There are 2876 elements in the model from them, 300
elements are for the skull and 2000 elements for the brain. Half of the torus shape
object has been modeled by 576 elements. Skull behavior is considered as linear
elastic. [4]
kg
ν sh = 0.25 And Esh = 13.79Gpa
ρ sh = 2140 3
m
Mechanical properties of brain are considered similar to water. [4]
kg
B = 2.18Gpa
ρ f = 1002 3
m
The impactor is steel with the following properties:
kg
ν e = 0.25 ρ e = 7850 E 207
3 e = Gpa
m
After meshing and defining the components of head and impactor, the contact
between head and impactor is defined as face to face contact. Head is the target and
torus object is the impactor. Twelve different cases are considered. The attack angles
are changing as 0, 15, 30, and 45 degrees. The velocity of spherical shell is changing
as 1.5, 2, 2.5 m/s. The torus object is stationary. Figure 8 displays the timedisplacement
curve of shell center from FE analysis.
5. CONCLUSIONS:
Figure 8: Time-displacement curve of shell center for V= ⎛ o m ⎞
⎜α = 0 , Vsh
= 2 ⎟
⎝ s ⎠
Analytical equations were obtained for fluid filled spherical shell. The analytical
model is based on separation of the contact Hertzian deformation from the membrane
and bending deformation in order to express approximate values for impact key
parameters. For a wide range of thicknesses which includes the type of human skull,