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

AN ANALYTICAL MODEL TO INVESTIGATE HUMAN HEAD
IMPACT AND ITS GOVERNING EQUATIONS
1. ABSTRACT
S. M. Rajaai 1 , M. Haghayegh 2 , and S. M. Baghaei 3
An analytical method to predict the response of the inclined impact of a fluid filled
elastic spherical shell having an arbitrary thickness with an elastic toroid is
investigated in this paper which can be considered as a model for analytical
evaluation of blunt impact on human head. The study is performed as a combination
of Hertzian contact theory and the local effect of membrane and bending of the shell
in order to state the implicit equation to determine the transmitted force. With respect
to the analytical responses, it is concluded that transmitted force decreases and the
contact duration increases by increasing the attack angle in constant initial velocity. In
addition, a closed form solution has been presented to obtain the impact parameters
including the duration, the maximum transferred load and the maximum acceleration
of the shell which are particularly important for the researchers. Therefore, the
investigation of important quantities of the impact phenomena would be possible by
using the closed form solution. The concluded results are validated by finite element
method to verify the response of the model. A good agreement between analytical
responses and numerical results reveals the accuracy of analytical equations.
2. INTRODUCTION
Research including financial expenses is being performed in private and public
sectors of the society to identify the reasons of occurrence and the prevention methods
of head injuries. Although there is not an exact statistics for the death rate as a result
of these injuries, but it is estimated around 15 to 30 persons out of each 100000
around the globe. If the mean value of death rate as a result of head injury is
considered 22 out of 100000 people, and the world population considered as 6 billion,
the death count from head injury would be around 1.2 million persons in the whole
world [1]. Extensive research in the form of cadaver studies and analytical methods
has been performed to identify the response of the human head to the impact. The first
analytical models have been proposed by Anzelious [2] and Catinger [3], in which the
head was modeled by a fluid filled spherical container. Angin [4] proposed an
analytical model which contained the membrane and bending characteristic of the
shell. Kenner and Goldsmith [5] continued these studies for the limited time loads.
Finally Young [6] proposed a model in which a sphere filled with viscous fluid hit
with a solid sphere and obtained implicit and explicit equations for the maximum
transferred force, the impact duration, maximum head acceleration, and inner brain
pressure. In the present paper, some equations will be derived for calculating general
1
Associate Professor, School of Engineering, Islamic Azad University, Abhar Branch, Abhar, Iran
2
Master graduate, School of Mechanical Engineering, Iran University of Science and Technology,
Tehran, Iran
3
PhD Graduate, School of Mechanical Engineering, Iran University of Science and Technology,
Tehran, Iran