Research of non-linear frictional contact model in vehicle-pedestrian accidents based on computer simulation

Abstract

In numerical simulation of vehicle–pedestrian accidents, pedestrian rest positions are greatly influenced by the friction coefficient between pedestrian and ground. Current researches on vehicle–pedestrian accident reconstruction often regard pedestrian–ground friction coefficient as a constant value. However, clothing fabric belongs to viscoelastic material. Some researches show that friction coefficient of viscoelastic material can be influenced by normal contact force. In this paper, a contact model between clothing fabric and asphalt road is built by computer simulations. The calculation based on this contact model indicates that the pedestrian–ground friction coefficient in accidents is not constant. Relationship between friction force and contact pressure is non-linear. Meanwhile, according to the simulation results of a real-world vehicle–pedestrian accident, influence of vehicle– pedestrian contact stiffness on pedestrian projection has been discussed, and simulation errors under different pedestrian–ground friction coefficients are calculated. Simulation results show that compared with traditional pedestrian–ground contact model, the non-linear pedestrian–ground contact model can obtain smaller simulation error with higher stability, which has validated the rationality of this contact model.

Abbreviations
${\tau }_f$	=	Shear stress at surface contact points
A	=	Real contact area
$\mathit{a}$	=	RMS roughness of the surface
$\mathit{\kappa }$	=	Constant related to the average height of the surface
${\mathit{\beta }}_{\mathit{x}}$	=	Correlation length of the surface in X-direction
${\mathit{\beta }}_{\mathit{y}}$	=	Correlation length of the surface in Y-direction
Z1	=	Height matrix of surface 1
Z2	=	Height matrix of surface 2
${\overline{z}}_1$	=	Average height of peaks on surface 1
${\overline{z}}_2$	=	Average height of peaks on surface 2
$h_0$	=	Distance between two rough surfaces
$\xi$	=	Characterised distance between rough surfaces
$\Delta \mathit{Z}$	=	Distance matrix between rough surfaces
$\epsilon$	=	Ratio of real contact area to nominal contact area
$R_{\mathrm{eq}}$	=	Gaussian contact radius
$A_{\mathit{ij}}$	=	Real contact area of a single rough peak
$\Delta L$	=	Accuracy of contact area calculation
$\mathit{T}$	=	Contact matrix between rough surfaces
$F_{\mathit{ij}}$	=	Local contact force of a single rough peak
$E_1$	=	Elastic modulus of surface 1
$E_2$	=	Elastic modulus of surface 2
${\upsilon }_1$	=	Poisson ratio of surface 1
${\upsilon }_2$	=	Poisson ratio of surface 2
$f$	=	Friction force
$\mu$	=	Friction coefficient
${\mu }^{\prime }$	=	Feature friction coefficient
$E^{\mathrm{\text{'}}}$	=	Constant related to material property parameters

Keywords:

• Pedestrian–ground friction
• accident reconstruction
• rough surface contact
• computer simulation
• contact stiffness

Disclosure statement

The authors declare that there is no conflict of interest.

Additional information

Funding

This research did not receive any specific grant from any funding agencies in the public, commercial or not-for-profit sectors.