Impact Response of a Fractionally Damped Spherical Shell

Abstract

In the present paper, the problem on normal low-velocity impact of a solid upon an isotropic spherical shell is studied without considering the changes in the geometrical dimensions of the contact domain. At the moment of impact, shock waves (surfaces of strong discontinuity) are generated in the target, which then propagate along the shell during the process of impact. Behind the wave fronts up to the boundary of the contact domain, the solution is constructed with the help of the theory of discontinuities and one-term ray expansions. The ray method is used outside the contact spot, but the Laplace transform method is applied within the contact region. As a result, the exact solution of the contact force is determined as a function of time. This model is intended to be used in simulating crash scenarios in frontal impacts, and to provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks.

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

“…Since experimental results by Zhu et al [58] show that human skull structure belongs to a weakly damped structure, then the fractional derivative standard linear solid model has been utilized in [31] to describe the impact response of human frontal bone under high-energy impact conditions, such as motor vehicle collisions or shock interactions of sportsmen on sports fields, which is important for the analysis of human brain injury of sportsmen or automobile accident occupants.…”

“…In the present paper, the approach suggested in [31] and [59] is generalized to the case of collision of two elastic or viscoelastic spherical shells to model the dynamic response of a human head impacted by another head or by some spherical object. To determine the impact force that is actually being transmitted to bone will require numerical analysis.…”