Non-linear continuous-contact-force model for low-speed front-to-rear vehicle impact

Abstract The most common kind of vehicular accident is the low-speed front-to-rear impact that results in a high proportion of insurance claims and whiplash-associated disorders. The low-speed collisions have specific characteristics that differ from high-speed collisions and must be treated differently. This paper presents a fundamental non-linear continuous-contact-force model for the low-speed front-to-rear impact to simulate the accelerations, the velocities, and the contact force as functions of time. A smoothed Coulomb frictional force is used to represent the effect of braking, which was found to be significant in simulating low-speed front-to-rear impact. The intervehicular contact force is modelled using non-linear damping and spring elements with coefficients and exponents. This paper presents a method of estimating analytically the stiffness and damping coefficients. The exponent of the non-linear contact force model was determined to match the overall acceleration pulse shape and magnitude. The model can be used to determine ∇V values and peak accelerations for the purpose of accident reconstruction and for injury biomechanics studies.