A Discrete Spheropolygon Model for Calculation of Stress in Crowd Dynamics

Abstract

Several models have been presented to evaluate flow rates in pedestrian dynamics, yet very few focus on the calculation of the stress experienced by pedestrians under high density. With this aim, a pedestrian dynamics model is implemented to calculate the stress developed under crowd conditions. The model is based on an extension of a granular dynamics model to account contact forces, ground reaction forces and torques in the pedestrians. Contact stiffness is obtained from biomedical journal articles, and coefficient of restitution is obtained by direct observations of energy loss in collisions. Existing rotational equations of motion are modified to incorporate a rotational viscous component, which allows pedestrians to come to a comfortable stop after a collision rather than rotating indefinitely. The shape of the pedestrian is obtained from a bird’s eye, cross sectional view of the human chest cavity and arms, which was edited to produce an enclosed shape. This shape is them approximated by a spheropolygon, which is a mathematical object that allows real-time simulation of complex-shape particles. The proposed method provides real benefits to the accuracy on particle shape representation, and rotational dynamics of pedestrians at micro-simulation level. It provides a new tool to calculate the risk of injuries and asphyxiation when people are trapped in dense crowds that lead to development of high pressure.