Application of energy derivative method to determine the structural components' contribution to deceleration in crashes
Journal article, 2018

Objective: For occupant protection, it is important to understand how a car's deceleration time history in crashes can be designed using efficient of energy absorption by a car body's structure. In a previous paper, the authors proposed an energy derivative method to determine each structural component's contribution to the longitudinal deceleration of a car passenger compartment in crashes. In this study, this method was extended to 2 dimensions in order to analyze various crash test conditions. The contribution of each structure estimated from the energy derivative method was compared to that from a conventional finite element (FE) analysis method using cross-sectional forces. Method: A 2-dimensional energy derivative method was established. A simple FE model with a structural column connected to a rigid body was used to confirm the validity of this method and to compare with the result of cross-sectional forces determined using conventional analysis. Applying this method to a full-width frontal impact simulation of a car FE model, the contribution and the cross-sectional forces of the front rails were compared. In addition, this method was applied to a pedestrian headform FE simulation in order to determine the influence of the structural and inertia forces of the hood structures on the deceleration of the headform undergoing planar motion. Result: In an oblique impact of the simple column and rigid body model, the sum of the contributions of each part agrees with the rigid body deceleration, which indicates the validity of the 2-dimensional energy derivative method. Using the energy derivative method, it was observed that each part of the column contributes to the deceleration of the rigid body by collapsing in the sequence from front to rear, whereas the cross-sectional force at the rear of the column cannot detect the continuous collapse. In the full-width impact of a car, the contributions of the front rails estimated in the energy derivative method was smaller than that using the cross-sectional forces at the rear end of the front rails due to the deformation of the passenger compartment. For a pedestrian headform impact, the inertial and structural forces of the hood contributed to peaks of the headform deceleration in the initial and latter phases, respectively. Conclusions: Using the 2-dimensional energy derivative method, it is possible to analyze an oblique impact or a pedestrian headform impact with large rotations. This method has advantages compared to the conventional approach using cross-sectional forces because the contribution of each component to system deceleration can be determined.

pedestrian protection

acceleration control


frontal impact

vehicle design, finite element method


Kei Nagasaka

Nagoya University

Koji Mizuno

Nagoya University

Robert Thomson

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Safety

Traffic Injury Prevention

1538-9588 (ISSN) 1538-957X (eISSN)

Vol. 19 6 651-656

Subject Categories

Applied Mechanics

Vehicle Engineering

Building Technologies





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