Parker, et al. v. NGM Insurance Company, et al

Filing 94

ORDER AND REASONS - IT IS ORDERED that Plaintiffs 64 motion in limine to exclude Dr. Charles Ted Bain is GRANTED, and Dr. Bain is hereby excluded from testifying as an expert in this case. IT IS FURTHER ORDERED that Defendants 46 motion in limi ne to exclude Dr. David Barczyk on timeliness grounds is DENIED AS MOOT. IT IS FURTHER ORDERED that Defendants 65 motion in limine to exclude Dr. Barczyk under Federal Rule of Evidence 702 and Daubert is DENIED AS MOOT. Signed by Judge Susie Morgan. (Attachments: # 1 Attachment 1, # 2 Attachment 2) (bwn)

2014-01-1991
Published 04/01/2014
Copyright © 2014 SAE International
doi:10.4271/2014-01-1991
saetransaf.saejournals.org

Characterization of Force Deflection Properties for Vehicular
Bumper-to-Bumper Interactions
Enrique Bonugli, Jeffrey Wirth, James Funk, Joseph Cormier, Herbert Guzman,
Lisa Gwin, and Mark Freund
Biodynamic Research Corp.

ABSTRACT
This is the complete manuscript and replacement for SAE paper 2014-01-0482, which has been retracted due to
incomplete content.
This paper reports on 76 quasi-static tests conducted to investigate the behavior of road vehicle bumper systems. The
tests are a quasi-static replication of real world low speed collisions. The tests represented front to rear impacts between
various vehicles. Force and deflection were captured in order to quantify the stiffness characteristics of the bumper-tobumper system.
A specialized test apparatus was constructed to position and load bumper systems into each other. The purpose was to
replicate or exceed damage that occurred in actual collisions. The fixture is capable of positioning the bumpers in various
orientations and generates forces up to 50 kips. Various bumper-to-bumper alignments were tested including full overlap,
lateral offset, and override/underride configurations. Force and displacement were recorded and the data was analyzed to
develop system stiffness and crush parameters. These parameters can be used in a collision-based model to calculate
vehicle delta-v (ΔV) and acceleration. The simulation uses an impact mechanics-based numerical algorithm published by
Scott [6]. The paper reports on the test results of various combinations of vehicle categories. Vehicle type includes
passenger, light transport and heavy vehicle bumper systems.

CITATION: Bonugli, E., Wirth, J., Funk, J., Cormier, J. et al., "Characterization of Force Deflection Properties for Vehicular
Bumper-to-Bumper Interactions," SAE Int. J. Trans. Safety 2(2):2014, doi:10.4271/2014-01-1991.

INTRODUCTION
Assessing impact severity in low-speed collisions is often
difficult using current accident reconstruction methods. In many
cases vehicle specific crush stiffness data is not applicable or
difficult to incorporate when dealing with vehicles that have
little to no residual crush. Reconstructionists are routinely given
sparse information regarding the accident vehicles which may
or may not be available for inspection. Photographs, witness
testimony and repair estimates are frequently the primary
source of vehicle information regarding damage.
Traditional vehicle stiffness properties were first studied by
Campbell [5] which defined the plastic deformation of vehicle
structures in terms of equivalent barriers speed (EBS) and
residual crush. The stiffness theory was further developed and
uses what are currently known as stiffness coefficients.
Campbell also described a non-zero intercept term that took
into account the initial energy absorbed with no residual crush.
The theory allows calculation of damage energy which can be
used in conjunction with conservation of momentum and

conservation of energy to determine the ΔV of the vehicles.
However, the stiffness coefficients and intercept have limited
application in low-speed impacts with minimal residual
damage.
Strother et al. examined the use of deformation energy as an
accident reconstruction tool to determine vehicle dynamics for
a specific crash [10]. The method required vehicle specific
crash data to establish deformation energy estimates. Various
force models including the constant force, force saturation, and
bilinear crush force model were explored. He stated the need
for additional testing to supplement the low energy level data.
He cautioned that the use of 30 to 35 mph barrier test data to
estimate low speed collision could yield unrealistic stiffness
estimates.
Another approach has been called the Momentum-EnergyRestitution (MER) method. This method is based on rigid body
impact mechanics and uses impulse, conservation of
momentum, conservation of energy and restitution to
determine the ΔV of the vehicles in a low-speed crash [2,3,7].

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
In order to estimate the ΔV for a vehicle in a specific crash the
MER method requires a value for the coefficient of restitution
(ε) and an estimate of the energy absorbed by each vehicle
during the crash. An analysis of a low-speed crash with the
MER method provides a ΔV for the crash but does not provide
the acceleration vs. time information for the vehicles during the
crash.
A third approach is to treat the vehicles as rigid structures and
model the bumpers as a spring/dashpot systems and then
solve the governing differential equations with the appropriate
initial conditions [2,7,12]. The solution gives the accelerations
of both vehicles during the crash. In order to simulate a specific
crash with a spring/dashpot model the appropriate stiffness
and damping coefficients must be used.
Happer et al. [6] described a method for using the IIHS low
speed crash test reports to establish an upper limit for crash
severity. A comparison of damaged components between the
test vehicle and the vehicle being investigated is made. If
lesser damage is demonstrated on the vehicle being
investigated when compared to the test vehicle then the
closing velocity for the test can be used as an upper limit BEV
for the subject vehicle. The BEV can in turn be used in the
Carpenter [3] single-degree-of-freedom (SDOF) MER method,
once b1 values have been determined. This method is useful
when IIHS tests are available for a particular vehicle.
Scott developed a numerical collision model to simulate
low-speed collinear vehicle-to-vehicle impacts. In the analysis
the impact force was directly related to the physical properties
of the bumpers that were involved in the crash [8,9]. The
approach allows the crash severity of a low-speed crash
involving specific vehicles to be estimated, including the crash
pulse. This approach takes into account the variability of the
force-deformation characteristics of the bumper systems. A
numerical simulation is performed which satisfies Newton's
Second Law at discrete time increments The structural
characteristics of both vehicles' bumpers are combined and
input as a system Impact Force-Deformation (IF-D) function.
The deformation is the sum of the deformation of the two
bumpers involved in the crash (i.e. mutual crush). The IF-D
function can be a theoretical curve, or be based on measured
force-deflection data for specific bumpers. Tests were
conducted to measure IF-D curves which were then used in the
analysis to determine the ΔV and the acceleration vs. time
information for vehicles involved in crashes.
Validation of the quasi-static bumper loading method described in
this paper has been conducted by Scott et al. A series of matching
quasi-static and dynamic tests were performed and compared.
The study concluded that quasi-static force deflection
measurement can be used to reconstruct and quantify the vehicle
dynamics in low speed bumper-to-bumper collisions.
This retrospective study provides a large number of forcedeformation curves taken from tests covering a wide range of
bumper systems. The testing is grouped into categories and

summarized as linear IF-D functions. These functions could be
used for the calculation of vehicle delta-v and acceleration in
low-speed collisions when specific test data is not available. In
that case the delta-v and acceleration are calculated in an
analysis of the collision using a model based on Newton's
Laws of Motion developed by Scott et al. The IF-D function
characterizes the vehicle interaction.

METHOD
General
Bumper-to-bumper interactions were simulated using a test
fixture developed to quasi-statically load two bumper systems
as described by Scott [8,9]. The working model assumes each
of the vehicles involved in the collision to be a rigid body with
the exception of the interacting bumper and vehicle
components. Many of the tests conducted were designed and
modeled based on a real world low speed collision and were
used to analyze the crash mechanics for that specific crash
configuration. The bumper components were aligned using
information available to the reconstructionist for the particular
crash being investigated. Information available to the
reconstructionist often included scene photographs,
photographs of one or both vehicles involved in the crash,
witness testimony, repair estimates, accident reports, and/or
appraisal reports. For example, in some cases the front license
plate or license plate fastener of the striking vehicle created an
imprint onto the rear bumper cover of the struck vehicle. This
physical evidence was used to align the bumper at the point of
initial contact. Exemplar vehicles were procured for each
bumper system in order to obtain external bumper cover and
bumper reinforcement bar heights. In some instances bumper
dive measurements due to heavy braking were also
documented to ensure proper vertical bumper alignment.
The interacting bumpers are treated as a one system and
therefore produce the stiffness characteristics for the system
as a whole. The exemplar test components were fixed to the
test apparatus rigidly and in a substantially similar mounting
configuration when compared to their respective vehicles
including all relevant bumper brackets. All tests were
conducted using original equipment manufacturer (OEM) parts
and brackets.
A total of 85 quasi-static force deflection bumper tests were
reviewed. The bumper tests were sorted and grouped in a
variety of category permutations for comparative analysis. Nine
of the 85 did not form a significant category grouping and were
not used in the analysis.
Each force deflection test consisted of two general phases, a
compression phase and rebound phase. The front bumper
system of one vehicle and the rear bumper system of another
were compressed together in order replicate and/or exceed the
damage seen on the vehicles being investigated. Only
compression phases were comparatively analyzed for this
study.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

Test Apparatus
The test fixture is comprised of one fixed and one moveable
steel plate as shown in Figure 1. Each bumper system is
mounted to one of the steel plates. The moveable plate is
guided along two tracks on roller bearings and is powered by
two 4 inch diameter hydraulic cylinders operating at 2400psi.

Inc.) inside a Dell® workstation connected to a 3-channel
bridge conditioner and amplifier system (136-1DC, Endevco,
Inc.).

Documentation
All tests were documented using real-time digital video. The
video cameras were synchronized in time with the force
displacement data. Digital still photography was used to
document the pre- and post-test condition of the bumper
components. Comparative photographs were taken at similar
angles and focal distances as the photographs of the vehicles
being investigated.

Test Categories

Figure 1. Photograph of the test apparatus designed to mount two
bumper systems for a quasi-static compression test.

Override/underride configurations were tested in addition to the
bumper-to-bumper interactions. The test fixture was modified
by removing the fixed steel plate from the I-beam track. An
exemplar vehicle, in its entirety, is then rigidly anchored to the
fixture and ground as shown in Figure 2. In this configuration
the suspension of the vehicle was allowed to respond normally
in the vertical direction.

Figure 2. Photograph of the test apparatus modified for an override/
underride condition. The fixed steel plate has been removed and a
whole vehicle is rigidly anchored to the ground and fixture.

Instrumentation
The test machine was instrumented with two force transducers
(1210AO-25k, Interface, Inc.) and a displacement transducer
(Temposonics, E-Series, MTS, Inc.). The data acquisition
system consisted of a 16-channel board (PCIMIO16E2, NI,

Each test was categorized by vehicle type, vertical bumper
alignment, horizontal bumper alignment, and whether or not
the struck vehicle was equipped with a trailer hitch ball mount.
The vehicle type was defined by the vehicle the bumper
system originated from. The categories chosen were cars,
which included passenger vehicles such as two or four door
sedans and coupes, light transport vehicles (LTV's) including
pickups, sport utility vehicles (SUV), and minivans, and heavy
vehicles which included all commercial vehicles with a GVRW
of 10,000 lbs or greater. For each test there was a striking and
struck vehicle. Table 1 lists the test categories and the number
of tests in each category.
Table 1. Test categories organized by vehicle type, vertical and
horizontal alignment.

RESULTS
Car-to-Car (CC), Full Vertical Overlap, Full
Horizontal Overlap
The car-to-car, full overlap category included a total of 18 tests
as shown in Figure 3. Manufacturers represented within this
category were General Motors, Ford, Chrysler, Honda, Toyota,
Suzuki, Mercedes, Mitsubishi, Hyundai, Jaguar, Volkswagen,
Nissan and Volvo. A linear best fit slope for each test was

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
determined based on a zero y-intercept to peak force criterion.
In many cases, the peak force may represents a global
maximum rather than the force at peak deformation as shown
in Figure 4. The maximum values located within the
compression phase of a force deformation test often
represented the collapse of a bumper component. The overall
slope of the compression phase is the bumper system stiffness
measured in pounds (force) per foot. The numerical average
and one standard deviation of the bumper stiffness values
were then used to create a bumper stiffness corridor. The
average stiffness for this category was 29,591 lbf/ft with a
standard deviation of 10,524 lbf/ft.

Figure 4. Force vs. deflection plot for test CC15 including the
compression and rebound phase. The front bumper system
permanently deforms at approximately 15,300 lbf.
Table 2. List of test components that permanently yielded in the
car-to-car full overlap category.

Figure 3. Force vs. deflection plot for the car-to-car full overlap tests.
The average slope and standard deviation are overlaid on the test
data.

The test shown below in Figure 4 is an example of a force
deflection plot in which the front bumper system (striking
vehicle) collapsed and could no longer support the
compressive forces. In this case, the left bumper bracket and
front reinforcement bar were compromised. The stiffness for
this test was determined from the peak force rather than the
peak deflection to better represent the resistance prior to
collapse. The average slope would have been underestimated
had the peak deflection been used as a stiffness determinant.
Two-thirds (12 of 18) of the tests in this category had a bumper
reinforcement bar or bumper brackets that collapsed. A list of
damaged components for these tests is detailed in Table 2.
The average force for bumper reinforcement bar collapse was
12,800 lbf. Of the twelve tests that included bumper bar
collapse, nine were front bumper systems. It was postulated
that the front bumper systems for road vehicles are softer than
rear bumper system because of the airbag system. The front
bumper systems are possibly tuned with the deployment
sequence of the vehicle. It was also observed that bumpers
constructed from aluminum had a tendency to be stiffer than
any other material tested.

LTV-to-LTV (LL), Full Vertical Overlap, Full
Horizontal Overlap
The LTV-to-LTV, full overlap category included a total of 6 tests
as shown in Figure 5. Manufacturers included Chrysler, Ford,
General Motors and Honda. The average stiffness for this
category was 32,145 lbf/ft with a standard deviation of 11,387
lbf/ft.
The bumper construction and mounting differs between
pickups and sedans. Pick-ups tend to lack bumper covers and
energy absorbers. Additionally, the mounting structure
consisted of brackets that are directly fastened to a box frame.
Because of these differences in design, component yielding
occurred within the compliance of the brackets. In some tests
the rear bumper pitched instead of causing the bumper
reinforcement bar to permanently deform. In other cases the
bumper may not collapse but rather deform through indentation
of the bumper fascia.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
and did not permanently deform. All three Ford Taurus tests
resulted in similar stiffness slopes near the upper limit of the
corridor.

LTV-to-Car (LC), Full Vertical Overlap, Full
Horizontal Overlap
The LTV-to-car, full overlap category included a total of 8 tests
as shown in Figure 7. Manufacturers included Ford, General
Motors, Toyota, Isuzu and Honda. The average stiffness for this
category was 29,245 lbf/ft with a standard deviation of 13,446
lbf/ft.

Figure 5. Force vs. deflection plot for the LTV-to-LTV full overlap tests.
The average slope and standard deviation are overlaid on the test
data.

Five of the eight tests included a bumper system that
collapsed, all of which were front bumpers. A majority of these
front bumpers were from sport utility and minivan vehicles that
closely resemble the construction of sedans. Two of the five
bumpers were constructed from a fiberglass composite
material. The average force for bumper reinforcement collapse
for the five tests was 9,786 lbf.

Car-to-LTV (CL), Full Vertical Overlap, Full
Horizontal Overlap
The car-to-LTV, full overlap category included a total of 8 tests
as shown in Figure 6. Manufacturers included Ford, General
Motors, Toyota, Isuzu and Honda. The average stiffness for this
category was 28,296 lbf/ft with a standard deviation of 11,608
lbf/ft.

Figure 7. Force vs. deflection plot for the LTV-to-car full overlap tests.
The average slope and standard deviation are overlaid on the test
data.

Heavy Vehicle-To-Car/LTV (HC) (HL), Full
Vertical Overlap, Full Horizontal Overlap
Figure 6. Force vs. deflection plot for the car-to-LTV full overlap tests.
The average slope and standard deviation are overlaid on the test
data.

This category had similar damage results when compared to
the LTV-to-LTV category. This is in part due to the fact that the
rear bumper systems are mostly pick-up bumpers. Yielding
occurred when the rear bumper system rotated rather than
plastically deforming. Three of the eight tests (CL1, CL2, and
CL6) involved the front bumper system of a Ford Taurus. The
Ford Taurus front bumper was noted as being relatively stiff

The heavy vehicle-to-car/LTV, full overlap category included a
total of 5 tests as shown in Figure 8. Manufacturers included
Ford, General Motors, Toyota, Peterbilt, International,
Freightliner and Honda. The average stiffness for this category
was 51,799 lbf/ft with a standard deviation of 29,699 lbf/.
In general, the heavy vehicle front bumper systems were stiffer
than their car and LTV counterparts. Tests HC2 and HC4 were
Peterbilt front bumpers and followed a distinctly similar force
deflection characteristic. Both of these tests involved subject
vehicles in which the struck car was left with only bumper
fastener (bolt) impressions onto the rear bumper covers. This
allowed for precise alignment of the bumpers at the time of
impact. Preliminary tests were first conducted to create the bolt

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
impression onto the bumper covers before proceeding with the
tests shown in Figure 8. The subsequent tests were then
performed with the intent of grossly exceeding the damage
documented on the subject vehicle to present a worst case
scenario. Tests HC3 and HC4 followed a different pattern in
both stiffness and damage. The bumper systems of the struck
vehicles were comparatively less stiff than the heavy vehicle
front bumpers and deformed to a greater extent. This created a
large variation in the standard deviation for this category. It
should be noted that in all five tests the heavy vehicle bumper
fascia's plastically deformed. The stiffness of the front bumper
system was generated from the interaction with the box frame
and underlying bumper brackets rather than the bumper fascia
which were all constructed from a thin gauge metal.

Figure 9. Force vs. deflection plot for all car/LTV-to-trailer hitch tests.
The average slope and standard deviation are overlaid on the test
data.

Figure 8. Force vs. deflection plot for the heavy vehicle-to-car/LTV full
overlap tests. The average slope and standard deviation are overlaid
on the test data.

All Car/LTV-to-Trailer Hitch
The car/LTV-to-trailer hitch, full overlap category included a
total of 8 tests as shown in Figure 9. Manufacturers included
Ford, General Motors, Toyota, Honda, and Nissan. The
average stiffness for this category was 24,052 lbf/ft with a
standard deviation of 4,163 lbf/ft.
All tests were conducted with the intent of collapsing the front
bumper reinforcement bars. Trailer hitch ball mount collisions
are a common crash type. They often lead to a distinct focal
damage pattern ideal for aligning the vehicles at impact as
shown in Figure 10. No test exceeded a peak force of 11,200
lbf. The average force for bumper collapse was 8,323 lbf. Test
TH5 was the only test that did not involve a ball mount and only
included the receiver box tubing although the data followed the
same pattern as the remaining 7 tests. Ideally a bi-phasic slope
would be used in the simulation to calculate ΔV and
acceleration. The linearity of the average slope would tend to
over predict the calculated values.

Figure 10. Overhead view of a trailer hitch equipped with a ball mount
intruding into the front bumper system in test TH3 at maximum
compression.

All Override/Underride
The Override/Underride category included a total of 14 tests as
shown in Figure 11. Manufacturers represented within this
category were General Motors, Ford, Lexus, Saturn, Hyundai,
Hino, Chrysler, Nissan, Sterling and Toyota. The average
stiffness for this category was 7,089 lbf/ft with a standard
deviation of 3,764 lbf/ft.
During the tests the bumpers engaged and usually then slid
over one another resulting in damage to components including
the hood, grill, headlights, radiator support, truck lid, body
panels, bumper and bumper covers. As the stiff structures were
generally not damaged during the testing, the average stiffness
is much lower than the other categories. There was a large
variation in the vehicles tested, which included cars and LTV's.
This may explain the relatively large standard deviation.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
Struble et al. [11] characterized the override/underride crash
condition by analyzing a series of staged flat barrier NCAP
frontal crash tests referred to as the Volpe Tests. The load cell
barrier data was used to determine the crush energy
distribution of the structure above and below the top of the front
bumper structures. They concluded that in those tests the
upper structures absorbed only 10 to 29 percent of total crush
energy. Although validation testing has not been conducted for
the quasi-static override/underride test condition the average
stiffness value was approximately 25 percent of the average
car/LTV-to-car/LTV stiffness values. This test condition is an
area of future research for the authors.

Figure 12. Force vs. deflection plot for all vehicle horizontal offset tests.
The average slope and standard deviation are overlaid on the test
data.

Case Study

Figure 11. Force vs. deflection plot for all vehicle override/underride
tests. The average slope and standard deviation are overlaid on the
test data.

All Offset Horizontal Overlap, Full Vertical
Overlap
The offset horizontal, full vertical overlap category included a
total of 10 tests as shown in Figure 12. Manufacturers
represented within this category were General Motors, Ford,
Lexus, Infiniti, Great Dane and Toyota. The average stiffness
for this category was 27,577 lbf/ft with a standard deviation of
19,964 lbf/ft.
All the tests resulted in damage to bumpers and bumper
brackets, one test had damage to a rear body panel. While the
average stiffness is similar to the other categories, the
deviation is unusually large. This is due in part to the large
range of the offset used, which varied from about a 45%
overlap to a nearly corner-to-corner test. Also, there was a
large variation in the vehicles tested, which included cars,
LTV's and a trailer equipped with an ICC bumper. This large
variety was necessitated by the limited number of offset tests
that have been conducted. More testing may allow further
differentiation of this category, and more limited corridors for
the stiffness value.

A specific crash was reviewed in which a force deflection curve
had already been generated for a reconstruction (CC9). This
was a low-speed collision involving a 2001 Volvo V70 as the
striking vehicle and a 2005 Chevrolet Malibu Maxx as the
struck vehicle. Photographs and repair estimates for both
vehicles were provided to the reconstructionist. The repair
estimate for the Volvo stated the need to replace the front
bumper license plate bracket while the repair estimate for the
Chevrolet stated the need to replace the rear bumper cover.
Damage to both vehicles was limited to the bumper systems as
the interacting vehicle structures. An imprint of a license plate
bracket onto the rear bumper cover of the struck vehicle was
used to align the bumpers for the test. Bumper height
measurements were obtained to confirm the bumper
alignment. The car-to-car full overlap singular slope stiffness
values reported in this paper were then used to numerically
compute vehicle velocity and acceleration. The numerical
algorithm applied to simulate the crash is located in the
Appendix. These results were then compared to the multi slope
stiffness curves (best fit) generated for the specific force
deflection data for test CC9. The low-speed numerical crash
simulation was modeled and executed in Matlab 7.14
(Mathworks, Inc.).
Figure 13 shows the extent of damage to the Volvo. The lower
aspect of the license plate bracket is fractured and front
bumper cover appears undamaged. The Volvo was not
available for inspection by the reconstructionist. The driver of
the Volvo stated that he was at a stop light behind the
Chevrolet when his foot slipped off the brake and his car rolled
into the car in front of him.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
affect the peak acceleration or peak force for the crash
simulation, however it can alter the crash pulse duration and
delta-v. In this case, the quasi-static test would ideally have
been stopped once the Chevrolet reinforcement collapsed in
order to capture the hysteresis at that point. Since the test was
continued far beyond the bumper collapse, the restitution of the
bumper system represents components being crushed beyond
the point of collapse.

Figure 13. Photographs of the Volvo involved in the crash being
investigated.

Figure 14 demonstrates the damage incurred to the Chevrolet.
The rear bumper cover has areas of abrasion just right of
center. The lower photograph in Figure 14 shows an outline of
the license plate bracket imprinted onto the bumper cover that
resulted from the collision. The Chevrolet was also not
available for inspection.
The force deflection data produce in test CC9 was used to
simulate the actual collision. Areas of inflection or local maxima
often represent a point in which a component is compromised
during the test. Figure 15 shows the force deflection data for
test CC9. The peak force of 25,554 lbf occurred at 0.94 ft of
deflection, however the rear bumper reinforcement bar for the
Chevrolet collapsed at 15,000 lbf with 0.52 ft of deflection. The
bumper yield point was used as an upper threshold for damage
and signified the end of the simulation. The hysteresis or
rebound phase of the force deflection curve could be used to
model the separation phase of the collision. For simplicity a
coefficient of restitution (ε) of 0.3 was used for the rebound
phase of the crash simulation. Inclusion of the rebound phase
is an area of future research. Using a range of restitutions
could address this issue. Changing the restitution value will not

Figure 14. Photographs of the Chevrolet involved in the crash being
investigated.

The best fit stiffness slope for the test data was divided into two
phases. The first slope was measured from the test data to be
10,091 lbf/ft at 0.22 ft of deflection. The simulation continues
from this point with a secondary slope of 42,200 lbf/ft until the
bumper collapse at 0.52 ft of deflection. Maximum engagement
is satisfied and the rebound phase begins until the forces reach
zero.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

Figure 17. Acceleration time history plot of the struck vehicle for each
crash simulation.
Figure 15. Force deflection data set for test CC9 overlaid with the best
fit, average, minus one standard deviation and plus one standard
deviation stiffness slopes. The stiffness corridors were obtained from
the car-to-car full overlap data.

The iterative simulation completes the crash sequence and
generates a velocity and acceleration time history based on the
force deflection data. The area under the force deflection curve
represents the work energy produced in the collision. The
velocity time history shown in Figure 16 was calculated from
the best fit stiffness slope simulation. The point of common
velocity at 0.75 seconds is also the point of maximum
engagement.

The pertinent output data for each simulation was summarized
in Table 3. Change in velocity is often the most significant
metric for crash severity used in accident reconstruction. The
- 1 sigma corridor produced a ΔV within 5 percent of the best fit
output. For this case study the +1 sigma overestimated the
crash severity by nearly 40 percent. Overall the stiffness
corridor would have captured the collision event by producing
an upper and lower limit within a reasonable degree of
accuracy.
In the event that test data is not available to the
reconstructionist, an exemplar vehicle matchup,
photogrammetry or three dimensional models can be used to
estimate mutual crush. The estimation of crush can provide a
metric to iterate the crash simulation based on the appropriate
stiffness corridors reported in this paper.
Using a classic damage based crush analysis for the Volvo
with vehicle specific A and B stiffness coefficients and uniform
crush of 3 inches across the front of the Volvo yielded a BEV of
10.3 mph. Utilizing the conservation of momentum, the ΔV for
the Chevrolet would be in excess of 10 mph. This
demonstrates how the classic damage based analysis can over
predict the vehicle ΔV's in low-speed collisions.

Figure 16. Velocity time history calculated from the crash simulation
using the best fit slope data.

Next, the car-to-car full overlap stiffness corridors were then
used as the stiffness input to execute the crash simulation. The
average stiffness for this corridor was 29,591 lbf/ft with a
standard deviation of 10,524 lbf/ft. The uniform slopes were
overlaid with the best fit and test CC9 force deflection plot in
Figure 15. The simulation was ended at 0.52 feet of deflection
for each simulation. The acceleration time histories for the
struck vehicle are plotted together in Figure 17 to compare
peak values and crash duration. The average stiffness slope
for this simulation produced an acceleration profile closest to
the best fit data.

Table 3. Summary of results for the low-speed simulations completed
for various stiffness slopes.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

Residual Crush
The residual crush for each of the force deflection tests was
measured and plotted with the corresponding peak deflection
as shown in Figure 18. The relationship is fairly linear and
indicates that the bumper systems rebound approximately 30
percent from maximum deflection.

serves as an additional tool for accident reconstruction when
test data is limited or damage to the vehicles being
investigated is not measureable.
Table 4. Average slopes for all test categories.

Further testing and analysis will allow finer differentiation of the
vehicle categories and definition of the system stiffness
characteristics.

Figure 18. Residual crush for each of the force deflection tests
performed.

SUMMARY/CONCLUSIONS
This paper has presented 76 quasi-static tests conducted on
road vehicle bumper systems representing front to rear impacts
between various vehicles. Force and deflection data for the
tests was captured and plotted. These tests were conducted to
obtain data to facilitate the reconstruction of various roadway
crashes. In the absence of case specific testing, this large
volume of test data can be used in a reconstruction. To better
match specific impacts, categories were chosen representing
combinations of various vehicle types common in roadway
collisions. The stiffness characteristics of the bumper-tobumper system was measured from each test and the average
values for each category were determined. Table 4 gives the
averages and standard deviations for the categories. The
average stiffness values were similar for the various
combinations of car and LTV impacts, perhaps reflecting
similarity in general bumper system construction and impact
response for passenger and light transport vehicles.
The average and standard deviation values create stiffness
corridors as shown in Figures 6, 7, 8, 9 and 11-12. The
corridors represent stiffness bounds that can be used in the
calculation of collision parameters, such as ΔV and peak
accelerations, using the numerical collision simulation
describes by Scott [8] Mutual crush can be approximated
through exemplar vehicle, three dimensional models or
photogrammetry to determine peak deflection. This method

REFERENCES

1. Bailey, M., Wong, B., and Lawrence, J., “Data and Methods for
Estimating the Severity of Minor Impacts,” SAE Technical Paper
950352, 1995, doi:10.4271/950352.
2. Brach, R., “Modeling of Low-Speed, Front-to-Rear Vehicle
Impacts,” SAE Technical Paper 2003-01-0491, 2003,
doi:10.4271/2003-01-0491.
3. Carpenter, N. and Welcher, J., “Stiffness and Crush Energy
Analysis for Vehicle Collision and its Relationship to Barrier
Equivalent Velocity (BEV),” SAE Technical Paper 2001-01-0500,
2001, doi:10.4271/2001-01-0500.
4. Cipriani, A., Bayan, F., Woodhouse, M., Cornetto, A. et al., “Low
Speed Collinear Impact Severity: A Comparison Between Full
Scale Testing and Analytical Prediction Tools with Restitution
Analysis,” SAE Technical Paper 2002-01-0540, 2002,
doi:10.4271/2002 01 0540.
5. Campbell, K., “Energy Basis for Collision Severity,” SAE Technical
Paper 740565, 1974, doi:10.4271/740565.
6. Happer, A., Hughes, M., Peck, M., and Boehme, S., “Practical
Analysis Methodology for Low Speed Vehicle Collisions Involving
Vehicles with Modern Bumper Systems,” SAE Technical Paper
2003-01-0492, 2003, doi:10.4271/2003-01-0492.
7. Ojalvo, I., Weber, B., Evensen, D., Szabo, T. et al., “Low Speed
Car Impacts with Different Bumper Systems: Correlation of
Analytical Model with Tests,” SAE Technical Paper 980365, 1998,
doi:10.4271/980365.
8. Scott, W., Bain, C., Manoogian, S., Cormier, J. et al., “Simulation
Model for Low-Speed Bumper-to-Bumper Crashes,” SAE Int. J.
Passeng. Cars - Mech. Syst. 3(1):21-36, 2010, doi:10.4271/201001-0051.
9. Scott, W., Bonugli, E., Guzman, H., and Swartzendruber, D.,
“Reconstruction of Low-Speed Crashes using the Quasi-Static
Force vs. Deformation Characteristics of the Bumpers Involved in
the Crashes,” SAE Int. J. Passeng. Cars - Mech. Syst. 5(1):592611, 2012, doi:10.4271/2012-01-0598.
10. Strother, C., Woolley, R., James, M., and Warner, C., “Crush
Energy in Accident Reconstruction,” SAE Technical Paper 860371,
1986, doi:10.4271/860371.
11. Struble, D., Welsh, K., and Struble, J., “Crush Energy Assessment
in Frontal Underride/Override Crashes,” SAE Technical Paper
2009-01-0105, 2009, doi:10.4271/2009-01-0105.
12. Thompson, R.W. and Romily, D.P. “Simulation of Bumpers During
Low Speed Impacts”, Proceeding of the Canadian Multidisciplinary
Road Safety Conference III. Saskatoon, Saskatchewan, Canada,
1993.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

CONTACT INFORMATION
Enrique Bonugli
Biodynamic Research Corporation
5711University Heights Blvd., Suite 107
San Antonio, Texas 78249
Phone: [phone]
Fax: [phone]
[e-mail]

ACKNOWLEDGMENTS
The authors acknowledge the work of BRC's Research Test
Center who performed all of the force deflection tests.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

APPENDIX

ALGORITHM FOR THE IMPACT SIMULATION MODEL BY SCOTT ET AL.
The numerical simulation starts at t=0 (j=1) with the vehicles in contact and the initial conditions required are vehicle speeds (V1,1,V2,1),
and the center of mass positions (X1,1,X2,1) along the line the vehicles are traveling. Since the vehicles are in contact but not deformed
the undeformed distance (UD) between the two centers of mass is

At the first time position A1,1 = A2,1=0, and the vehicles move forward through the first time step at their initial velocities and the velocities
at the second time position (j=2) are the same as the initial conditions, V1,1=V1,2 and V2,1= V2,2. At the second time position the vehicles'
center of mass positions are

This movement of the centers of mass of each vehicle creates an overlap of the vehicles, and the deformation (Dj) at the second and
following time positions (j=>2) is

The impact force Fi,j that acts on each vehicle during the jth time step (j>=2) is based on the input IF-D function and Newton's Third Law,

The force Fi,j (i=1,2) acts on the vehicles during the jth time step where j>=2. Newton's Second Law is used to calculate the acceleration
of each vehicle during the jth time step,

The impact forces accelerate the vehicles over the jth time step. The time position is incremented, j = j+1, and the velocities at the new
time position j are calculated,

The algorithm then checks to see if the vehicles have reached a common velocity. If the vehicles have reached a common velocity
Function (Dj) is changed to represent the rebound phase of the input IF-D function. The simulation then calculates the vehicle center of
mass positions at the new time position,

The simulation then recalculates the variables and continues to move forward in time until Fi,j (i=1,2) reaches zero and the crash is over.

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)
Table 5. List of all test vehicles and alignement by category.

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FORCE (LBF) V DEFLECTION (FT) PLOTS FOR ALL TESTS

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Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

Bonugli et al / SAE Int. J. Trans. Safety / Volume 2, Issue 2 (July 2014)

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