Keywords: Vehicle, Accident, Reconstruction, Deformation, Finite element method

Transcription

1 Key Engineering Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Virtual Reconstruction of Vehicle Crash Accident Based on Elastic-Plastic Deformation of Auto-body Zhang Xiaoyun 1,a, Jin Xianlong 1,b, Qi Wenguo 1,c and Sun Yi 1,d 1 High Performance Computing Center, Shanghai Jiao Tong University, Shanghai, P. R. China a general_zhang@sjtu.edu.cn, b jxlong@sjtu.edu.cn, c wenguoqi@sjtu.edu.cn, d sunyi@sjtu.edu.cn Keywords: Vehicle, Accident, Reconstruction, Deformation, Finite element method Abstract: The finite element method, which has been widely used in crashworthiness analyses and structural optimization design, is not practical in the traffic accident reconstruction because of the limitation of computation ability. Elastic-plastic deformation of the vehicle and the collision object are the important information produced during the course of the traffic accidents, and the information can be fully utilized by using the finite element method to increase the computing precision. Now, with the development of high performance computing technology, the finite element method based on parallel computing could be used in the accident reconstruction, both the direction and the crash velocity of pre-impact could be found accurately, and these results can provide a scientific foundation for accident judgement. In this paper, one typical traffic accident was studied using the finite element method. According to the simulation results, the deformation of the key points on the frontal longitudinal beam and the mudguard could be measured in the post process of the software. By comparing the results of the real accident and the simulation tests, the best simulation test could be found, thus the most accurate relative angle and the initial velocity could be found. Introduction Traffic accidents have become serious social problems that threaten people and their property at an accelerating rate, particularly in the developing countries such as China. Vehicle collision analyses and accident reconstructions have become increasingly popular in recent years due to the seemingly expanding rate of civil litigation, thereby commanding a need to investigate a collision by analytical methods. The major questions that certainly arise are the determination of the vehicle's impact speed and trajectory. Due to the variety, complexity and instantaneity of the traffic accidents, the precision of doing quantitative analyses of accidents manually is quite low. With the development of simulation technology, the numerical simulation methods can lay a theoretical foundation for the reconstruction of vehicle accidents. The whole process of a vehicle accident can be divided into three phases: (1) post impact - the usual starting point of the reconstruction developed from information obtained from the accident scene (2) impact - determination of the vehicle's impact speeds, impact directions and impact location and (3) pre-impact - determination of speeds and trajectories (usually the unknowns). The main method of accident analyses is to find out the vehicle motions in collision phase through vehicle rest positions in post-collision phase, and then the vehicle motions in pre-collision phase, based on the collection, recording, investigation and analysis of the accident scene. The elastic-plastic deformation of vehicles and other collision objects are the important information of one traffic accident. The computer programs now available for the reconstruction of vehicle accidents seldom consider the information. But the explicit finite element algorithm using a very small integration time step takes not only the strain rate of materials in high speed but also the elastic and plastic characteristics into consideration. So, research on reconstruction of vehicle accidents based on finite element method can achieve a relatively high precision of calculation. In addition, for an effective presentation of the results, 3-D animations can be created using the post-processing software based on the finite element method. At the same time, direct observations of the deformation behavior of key energy absorbing parts, such as mudguard and the front All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-05/03/16,16:33:45)

2 1018 Advances in Engineering Plasticity and Its Applications longitudinal beam, in different types of accidents can be taken. This can t be finished well by other accident reconstruction methods. But for the restriction of computational power of computers, the finite element method had never got good applications in accidents reconstruction. Now with the continuous development of computer science, the performances of computers have been greatly enhanced, making the finite element method applicable in accidents reconstruction possible. Basic Description and Definitions Consider the body shown in Fig. 1, where a point in b initially at X ( α = 1,2,3) in a fixed rectangular Cartesian coordinate system moves to a point x i ( i =1,2,3) in the same coordinate system. Since a Lagrangian formulation is considered, the deformation can be expressed as equation (1). α ( X t) Fig. 1 Notation xi = xi α, at time t=0, the initial conditions as equation 2 and 3. x ( X α,0) xα ( X,0) V ( ) x i = i α = i X α where Vi defines the initial velocities. To seek a solution to the momentum equation (1) (2) (3) σ + ρf = ρ& x& ij, j i i (4) here σ ij is the Cauchy stress,? is the current density, f is the body force density, acceleration. Mass conservation is trivially stated x& & i is ρ V = ρ 0 (5) where V is the relative volume. The energy equation E& = Vs ( ijε & ij p + q)v & (6) is integrated in time and is used for equation of state evaluations and a global energy balance. And in equation 6, s ij and p represent the deviatoric stresses and pressure [1]. Application of the divergence theorem and noting that ( ijδx i ) σ ij, jδxi σ ijδ i, j σ = (7), j leads to the weak form of the equilibrium equations:

3 Key Engineering Materials Vols δπ = ρx& δx dv + σ δx dv = 0, ρf δx dv t δx ds (8) i i ij i j i i i i V V a statement of the principle of virtual work. Typical Traffic Accident Reconstruction V 2 S According to characteristics of crash accidents, the indices to evaluate the accident were given as x 1, x 2,, x n,which reflected the deformation of the key points in the main energy-absorbing parts during the crash. The key points were chosen at the round hole ( 20mm)and the bolt hole, which were easy to locate. The deformation of the center of the round hole can be measured using the deformations of the 3 points on the circle of the hole, and the deformation of the bolt hole can be measured using the information of three coordinates of the nodes in that place. Using the measurement values of these indices from the survey of the accident scene: x 1 e, x and using the calculation values of these indices from computer simulations, the x 2 e,, ne index E is defined to reflect the difficulty level of accident reconstruction. ( Σ( x x ) ( x x ) ( Σx x ) E = 1 / (9) ie ic ie ic ie ie In the equation above, the closer to 1 of the value of E, the closer of the reconstruction to the real situation. So the equation to calculate the index E was set as the object function, the initial velocity and the direction of the car were set as the variables, which would be optimized. That was to choose a right combination of the initial velocity and the direction of the car to make the index E the maximum. Traffic Accident Scene. In December 2001, there was an accident happened to one car in Hainan province, China. It can be shown in fig.2, the geometry of the wall was measured. Threecoordinate-measuring instrument was used to measure the deformation of the car body. First the body ordinate system was set at the back of the car, where there was no deformations, then 11 key points were selected at the front of the car where major deformation occurred: 7 bolt hold on the frontal longitudinal beam, 4 round hole on the mudguard. Because these two main energyabsorbing parts were hardly affected by the rough surface of the wall, they should be more reliable than the front wall. Figure 4 was the geometry of the frontal longitudinal beam and the mudguard and the coordinates on the figure was the three-dimensional coordinates before deformation. Fig. 2 Scene of one typical accident Fig.3 Measure the deformation of auto-body Fig.4 The CAD model of the energy-absorbing parts

4 1020 Advances in Engineering Plasticity and Its Applications Finite Element Modeling. The vehicle model was first disassembled and grouped into several main groups: the frame, front inner, cabin, doors, etc. The three dimensional geometric data of each component were obtained by using Unigraphics16.0 software. Next, these files were imported into Hypermesh 5.0 for meshing and model assembly. Finally, the model was translated into LS-DYNA input files. It is known that the work of modeling the whole vehicle is very huge, the total structure is made up of more than 100 parts, which are connected by joints (including spot welding, arc welding), bolt connecting, rivet connecting and adhesives gluing. Many types of elements were used to describe the geometric shapes, connecting properties etc, including shell element, beam element, rod element, hexahedron element, spring element, rigid nodes and specific welding nodes which can fail when some specific conditions are met. A 3-D dummy model used to simulate the dynamic behavior of the occupant in the full frontal crash, was created. All parts of the model are connected using spherical and revolute joints [2-4]. In this simulation, the deformation of the engine is not considered, but is treated as a rigid part. The doors are connected to the body using hinges and door locks. According to the photo of the traffic accident scene, the finite element model of the wall was also included in the whole model. Fig.5 shows the finite element model of the commercial vehicle and the wall. Fig.6 shows the finite element model of the mudguard and the front longitudinal beam, and the numbers are the Node ID of the key points. Fig. 5 The FE model of the commercial vehicle and the wall Fig. 6 The FE model of the mudguard and the front longitudinal beam Simulation Result. The measurement of the deformation of the longitudinal beam and the mudguard are listed in the table 1. No Measurements (mm) Tab. 1 The measurement of the deformation of the key points According to the photo of the accident scene and the memory of the driver, the range of the initial velocity and the angle between the car and the wall are confirmed in the table 2. Then the data of deformation of the eleven key points were calculated for the first round and super computer was used for the calculation.

5 Key Engineering Materials Vols E 30 km/h 38 km/h 46 km/h 54 km/h 62 km/h 70 km/h 78 km/h 86 km/h Tab. 2 The first round calculation E was calculated according to the formula 9 and the values in the black regions ( 0. 6) in the table 2 were found to be close to 1, the other data was ignored. Then the second round of calculation was carried out in these regions, and the simulation result of the second round were listed in the table 3. In the first round of the simulation, the step of the velocity and the angel are 8km/h and 8, in the second round of the reconstruction, the steps reduced to 4km/h and 4. E 30 km/h 34 km/h 38 km/h 42 km/h 46 km/h 50 km/h 54 km/h Tab. 3 The second round calculation Also, E was calculated and the values in the black regions ( 0. 94) in the table 3 were found to be closer to 1. Then the third round of calculation was carried out in these regions, and the steps of the velocity and the angle reduced to 2km/h and 2. E 38 km/h 40 km/h 42 km/h 44 km/h 46 km/h 48 km/h 50 km/h Tab. 4 The third round calculation After the third round calculation, we can found that when the velocity is between the 48km/h and 50km/h, and the direction is between 15 and 17, E calculated was near 1. E was the maximum when the direction was 17 and the velocity was 50 km/h. The simulation result of the auto-body was shown in figure 7. And the deformation of the front longitudinal beam was shown in figure 8. It can be said that the simulation with the combination of the velocity and direction was quite coincident with the real accident. The result was quite accurate with the compensation of the computing time. On the other hand, the time can be shortened greatly with the genetic algorithm and the theory of the response surface methodology.

6 1022 Advances in Engineering Plasticity and Its Applications Fig.7 Simulation result of 17 and 50km/h Fig.8 The deformation of the front longitudinal beam Result Verification. Because of the clear tire marks on this accident scene, we can get the model of these marks by making use of EOS System s PhotoModeler which is a photogrammetry software by solving the collinear equations to obtain the object points set (see Fig. 9). So the angle between the direction of vehicle motion and the plane of wall can be measured from this model, and its result is 16.89º. Then this model would be imported into the PC-CRASH, one accident reconstruction software, and the velocity before the vehicle impacted the wall could be computed, the data is 50km/h. This is very close to the result obtained by the FE method. But the method mentioned above doesn t utilize the information of vehicle deformation. It relies on the tire marks thoroughly. It s well known that nowadays many vehicles are installed with ABS so that the tire marks can hardly be got after braking. Furthermore, the weather condition or people can destroy tire marks easily. By FE method to resolve the velocity and angle according to vehicle deformation, and doesn t need any exterior conditions such as the tire mark. So more reliable result could be got with the finite element method. Fig.9 Solving the direction of movement by the software of PhotoModeler Conclusion This article makes use of the finite element method to reconstruct a typical accident base on the vehicle deformation. The finite element method doesn t depend on the marks of the accident scene that may be destroyed easily, and it should take the elastic-plastic performance and strain rate into account adequately, so its result is more accurate. With the development of high performance computing technology, the restriction in computing time will be reduced greatly and the application of the finite element method in the field of accident reconstruction will be more extensive. Acknowledgements The authors would like to thank the financial support from the National Natural Science Foundation of China (No ) and the Ph.D. Programs Foundation of Ministry of Education of China (No )

7 Key Engineering Materials Vols References [1] Livemore software technology corporation: LS-DYNA theoretical manual (1998). [2] Jin X L, Zhang X Y and Sun Y. Research on the Improvement of Energy Absorbed Structure of a Commercial Vehicle with Computer Simulation Techniques, The 2 nd International Forum of Automobile Traffic Safety, December, 2002, Changsha, P. R. China, Journal of Hunan University, Vol. 29(2002), p.114~123 [3] Zhang X Y, Jin X L and Ge L. National Regulation Oriented Crashworthiness Simulation of Vehicle Steering System. Journal of System Simulation, Vol.15 (2003), p. 228~230 [4] Zhang X Y, Jin X L and Sun Y. Research on Improvement of Automotive Engine Hood with Computer Simulation Techniques. Journal of System Simulation, Vol.15 (2003), p.1600~1602

8 Advances in Engineering Plasticity and Its Applications / Virtual Reconstruction of Vehicle Crash Accident Based on Elastic-Plastic Deformation of Auto-Body /