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A mathematical model of an airbag restraint system for automobile drivers, including the simulation of the simultaneous collapse of the steering column, has been developed. The model is designed to work in conjunction with a three-dimensional occupant model. It is capable of assessing the relative effects of airbag size, pressure, deployment rate, venting area, contact force, steering column collapse force, and column collapse distance. The results of the model are compared with experimental runs in which anthropometric dummies were used as test subjects. Good correlation was obtained for torso kinematics. The model can be conveniently used for a parametric study to aid the design of airbag restraint systems.

Normal motion of the lower limbs is discussed in this paper. The biomechanics of human gait has been studied experimentally using an instrumented walkway and analytically by means of mathematical models. Experimental methods for measuring ground reaction forces and limb kinematics are discussed. If limb kinematics are known, they can be used to compute the resultant joint forces and moments, using equations of motion which are algebraic in form. To obtain limb kinematics from the differential equations of motion, the problem is generally redundant, the degree of redundancy being equal to the number of unknown joint moments. The computation of muscle, ligament and bone contact forces from known resultant loads is also a redundant problem because there are more unknowns than there are available equations. For these there is no general consensus regarding the best objective function to be minimized.

Numerical analyses frequently accompany experimental investigations that study injury biomechanics and improvements in automotive safety. Limited by computational speed, earlier mathematical models tended to simplify the system under study so that a set of differential equations could be written and solved. Advances in computing technology and analysis software have enabled the development of many sophisticated models that have the potential to provide a more comprehensive understanding of human impact response, injury mechanisms, and tolerance. In this article, 50 years of publications on numerical modeling published in the Stapp Car Crash Conference Proceedings and Journal were reviewed. These models were based on: (a) author-developed equations and software, (b) public and commercially available programs to solve rigid body dynamic models (such as MVMA2D, CAL3D or ATB, and MADYMO), and (c) finite element models.

As early as the 1950's, Gurdjian and colleagues (Gurdjian et al., 1955) observed that brain injuries could occur by direct pressure loading without any global head accelerations. This pressure-induced injury mechanism was "forgotten" for some time and is being rekindled due to the many mild traumatic brain injuries attributed to blast overpressure. The aim of the current study was to develop a finite element (FE) model to predict the biomechanical response of rat brain under a shock tube environment. The rat head model, including more than 530,000 hexahedral elements with a typical element size of 100 to 300 microns was developed based on a previous rat brain model for simulating a blunt controlled cortical impact. An FE model, which represents gas flow in a 0.305-m diameter shock tube, was formulated to provide input (incident) blast overpressures to the rat model. It used an Eulerian approach and the predicted pressures were verified with experimental data.