The Exact Solution of the Translational Acceleration of a Low Modulus Elastic Medium in Rigid Spherical Shells—Implications for Head Injury Models

Abstract

The exact solution in the form of a finite series has been obtained for the problem of low modulus elastic medium contained in rigid spherical shells subjected to translational acceleration about its diametrical axis. Laplace transformation technique and the shifting theorem were used to obtain the Green’s functions for the potentials when the external acceleration is a Dirac delta function. The solutions are formally extended to external accelerations which are general functions of time by the convolution integral. The shear stress distribution for a unit step function acceleration is illustrated. The results obtained are used to judge the adequacy of this and other similar models for the study of closed head injury mechanism.