Limiting performance analysis of the protection of the human head from impact-induced injuries taking into account the duration of the shock pulse

The limiting possibilities of the protection of the human head from impacts by means of helmets are analyzed. The shell (base) of the helmet is assumed to decelerate after an impact against an obstacle with constant acceleration during a given time interval. The minimum of the peak magnitude of the displacement of the head (the object to be protected) relative to the helmet shell is determined, provided that the injury risk index does not exceed a prescribed tolerable value, as well as the corresponding time history of the absolute acceleration of the head. The injury risk index is defined by the HIC functional. This functional is adopted as a standard measure for the head injury risk in crash tests of vehicles, as well as in the tests of shock protection equipment for industries and sports. The time history of the motion of the head and the peak magnitude of the displacement of the head relative to the helmet shell are studied as functions of the shock pulse duration (the deceleration time of the helmet shell). The case of the instantaneous shock, when the shell comes to an instantaneous stop after hitting the obstacle, was considered in 1].