One of the most demanding market in terms of quality, reliability, on board equipment, safety and price is related the automotive industry. Therefore, efforts are paid in the way of minimizing costs and improving product's performance. Costs are reduced using high performance design and engineering products, including tools for numerical simulation.
In cases when contact between the passenger and the interior of the vehicle occurs the kinematic parameters record high variation during a very short time interval leading to high accelerations. The regulations used for model validation impose severe limits for these accelerations.
Biomechanical parameters that characterize the human body cannot be adapted to different impact situation, thus the measure to be taken is to adapt the parts' configuration and structural response to these parameters.
Experimental models used now are very sophisticated and can provide accurate information about the part that is studied. One of the major shortcomings of experiments is that a new part is required for each run and the measurement chain must be constructed exactly the same way according to the task book of the particular job.
New methods for the investigation of structural performances are needed. The most used and important one is numerical simulation by means of finite elements method [6, 8, 9, 12, 13, 14, 21, 22, 23].
One of the main advantages of the numerical simulation is that, once the environment is set and the numerical models were defined, various scenarios can be tested.
But there is still room for physical testing, because numerical models must be validated using experiments. But even so, the expenses on testing are limited, because the number of experiments can be reduced to minimum. Starting from initial design or from a previous model, the current model is validated and updated according to specifications. But there may be one thing that is still missing and this is regarding the removal of some uncertainties from the numerical model. Most of the simulation models are built considering a homogenous distribution of properties. Unfortunately in some cases the manufacturing process alters the initial performances of the designed product [9]. Thus the numerical model must comply with these changes in order to improve the results.
A vehicle interior assembly, the cockpit module, was tested and analyzed using experiments and numerical simulation. The assembly must comply with the ECE 21 (in Europe) or FMVSS 201 (USA) safety measures regarding the passengers' protection.
The cockpit module consists in the instrument panel (figure 1 - position 1), steering column, air conditioning (figure 1 - positions 2, 3), glove box, cross car beam (figure 1 - position 4), different storage area, navigation and audio system and different decorative elements. The main components are manufactured by polypropylene (PP) like ExxonMobil Chemical EXXTRAL® BMT 222 for the dashboard and ExxonMobil Chemical EXXTRAL® HMU 202 for the windshield demister.
The material model and materials stress - strain curves were analyzed. Engineering stress - strain data was obtained and used for the definition of real stress - strain data used for the numerical simulation.
The numerical models were solved using LS-Dyna v.970 code, an explicit, general purpose, and widely appreciated solver for transient, slow and high velocity dynamics simulations [3, 6, 12, 15, 19, 22, 23].
Structure response, impact parameters, failure model and damage pattern were analyzed and results from the numerical simulation were compared with the experiment.
2. Mechanical characterisation of thermoplastics materials
For materials used to manufacture the cockpit module the mechanical properties were obtained performing a number of traction experiments. A special test machine manufactured by Zwick/Roell was used. The traction test velocity was of according to the materials' specification datasheet.
Stress - strain curve is the graphical representation of the mechanical properties of the material. These curves are built using the results from traction experiments, as traction force versus specimen deformation. Figure 2 present a specific traction force versus specimen deformation curve for thermoplastic materials. In figure 2 there are represented a number of points like the elasticity limit , the maximum traction force and the traction force at break .
Table 1 presents the values obtained for the physical and mechanical properties of the materials, according to manufacturer's specifications and traction test results.
Table 1. Mechanical and physical properties of the materials
Material name
Dimension
Nominal
Measured
ExxonMobilChemical
EXXTRAL BMT 222
Density
Elasticity modulus
Maximum traction force
-
Strain at necking
Maximum stress
Strain at break
ExxonMobilChemical
EXXTRAL HMU 202
Density
Elasticity modulus
Maximum traction force
-
Strain at necking
Maximum stress
Strain at break
The differences between nominal and measured values may be explained by the fact that the specimens used for tractions test were extracted from the specific areas of the cockpit module and it is possible that the technological process have had altered the mechanical properties.
For the calculation of engineering stress, equation (1) is used:
(1)
and for engineering strain, equation (2):
(2)
Where:
- is the measured traction force;
- is the cross sectional area of the specimen;
- is the specimen's length;
- is the initial specimen's length;
This way the engineering stress - strain curve (figure 3) is obtained.
For the calculation of strain, incremental method is used. The current stress - strain state of the specimen results from of the previous stress - strain state.
Using incremental method, element strain is calculated using equation (3)
(3)
For the entire deformation process equation (3) becomes:
(4)
Using equation (3), a correspondence between engineering and real strain can be set.
(5)
Commonly used equation for the definition of real stress is (6):
(6)
Figure 3 presents the materials curves both in engineering stress - strain and real stress strain coordinates.
For the validation of the material model numerical simulation by means of finite elements method was used. Unlike other papers concerning numerical modelling of material [1, 2, 3, 6, 10, 12, 16, 17, 19, 20, 23] and application of the finite element method for it, the numerical model used for the material model validation is close in element size and identical in element type and mathematical formulation with those used to define the structure of the entire assembly of the cockpit module.
The traction force obtained form the simulation is compared with the traction force recorded from experiments (figure 4a) and for a better appreciation of the material mathematical models the error obtained between the nominal traction force and calculated forces is evaluated (figure 4b).
3. Testing and simulation environment
Once the mechanical and physical properties of the materials were defined, the numerical model may be validated.
Experiments were performed and the structural performances of an existing cockpit module were evaluated. For EU (European Union) countries experiments are performed according to ECE 21 specifications using a gravitational pendulum consisting in a spherical rigid impactor that is supported by roll bearings to a rigid frame. Figure 5a) presents the CAD model of the test bench while figure 5b) presents the real testing equipment. The CAD model was used in order to manufacture the mechanical components of the equipment and was for dimensional and geometrical validation of the manufactured product.
Special transducers were used to measure the impact parameters like the impactor's acceleration during the event, structure response (acceleration) and impactor's arm angular position. Figure 6 presents the test bench and the data acquisition solution used for the experiment.
3.1. Determination of the impact area
Subsequently, the impact area was determined. Using a 3D measuring arm - ROMER SIGMA 2018 - a volunteer sitting on the passenger's seat was measured in order to determine the initial configuration of the dummy used for the numerical simulation. Figure 7 presents the measuring process of the volunteer. It worth mentioning the fact that the volunteer was selected so it will corresponds to the 80% male dummy.
The numerical simulation environment consists in the seat position and the cockpit module. The cockpit module was installed inside the vehicle in the required position (figure 8a). Subsequently the vehicle structure was removed in order to simplify the simulation model and the passenger in sitting position was added. (figure 8b).
The potential impact area was determined with respect to the passenger's motion. For the first case (figure 9a) the passenger is constrained in motion with the seat, while for the second case the passenger is allowed to get off the seat (figure 9b).
3.2. Experiment
Figure 10 presents the recorded data for the impactor's arm angular position and the impactor's acceleration. The units for the measured signal values are in volts and seconds for the time. The time for data acquisition is set to 10 seconds, in order to record the multiple impacts between the impactor and the dashboard. This because the rebound height of the impactor must be determined in order to calculate the terminal kinetic energy and, thus, the energetic coefficient of restitution.
Figure 11 presents the scaled results for the impactor's velocity and the main phases of the impactor's motion (acceleration, impact, rebound) are identified. Also the required impactor's velocity at contact time with the cockpit module can be check for conformity with the specification contained by the ECE 21 regulation.
Figure 12a) presents the arm's angular position when the first impact with the dashboard occurred, while figure 12b) presents the time of the second impact between the impactor and the dashboard.
As it was expected the structure was damaged during the impact. A section of the windshield air deflector has failed and broken into pieces (figure 13).
An accurate method for the identification of the impact time is required because the maximum recorded signal for the arm's angular position may not be a good measure to evaluate its vertical position, since the impactor is moving while striking the dashboard. The recorded value for the arm's position for the first and second impact will be taken as a reference for the vertical position of the impactor.
Figure 14 presents the time sequence containing the first and the second impact. The marked points are: 1 - the time and angular position of the first impact (figure 12a); 2 - the time of the end of the first impact; 3 - the position of the arm's angular position at the maximum height after the first impact and 4 - the time and angular position of the second impact (figure 12b).
The square of the coefficient of restitution (energetic), , is defined as the negative of the ratio of the elastic strain energy released during restitution to the internal energy of deformation absorbed during compression [5, 21].
The strain energy released during restitution will increase the impactor's kinetic energy. The arm is supported using ball bearings thus the friction forces can be neglected. Due to the swing arm configuration of the test bench and considering that in this case the maximum values of the kinetic and potential energies are equal the arm's angular position time history can be used to determine the coefficient of restitution.
(9)
The corresponding position of the impactor and arm according to the notations from figure 14 are presented in figure 15.
In order to simplify the calculations, the total mass of the arm and impactor can be expressed as the impactor's reduced mass that will be used to evaluate the rebound kinetic energy.
A simple calculation method can be used to determine the angles of the swing arm when the impactor is in contact with the dashboard, at the end of the impact and the maximum rebound height.
(10)
Table 2 presents the resulting angular positions of the swing arm.
Table 2. Angular positions of the swing arm
Position
Signal value [V]
Angular position
[deg]
[rad]
Point 1
3.649
180.509
3.1504
Point 2
3.695
183.115
3.1959
Point 3
2.938
140.239
2.4476
Point 4
3.644
180.226
3.1455
The signal is measured starting from 0.462 [V]
The maximum potential energy of the impactor after rebound is:
(11)
The notations from equation 11 are: is the reduced mass of the impactor, g is the gravitational acceleration and is the rebound height of the impactor (equation 12), (figure 15)
(12)
The notations from equation 12 are: is the length of the arm (e.g. 1140 mm), and , are the angular positions of the swing arm corresponding to positions 1 and 3 as presented in figure 15.
The energetic coefficient of restitution is defined by:
(13)
The impactor is fully stopped therefore its initial kinetic energy is entirely consumed during the compression. In the same way, the internal energy available during the restitution will lead to an increase of the kinetic energy that will take the impactor to the defined height.
Thus, the energetic coefficient of restitution can be defined as:
(14)
The numerical models can provide information abound the initial velocity of the impactor and the rebound velocity. The kinematic coefficient of restitution is defined as:
(15)
4. Numerical model
The numerical model was built using more than 120 000 shell finite elements with less than 5% triangles. The main components of the cockpit module were defined as different parts according to them properties of material type and thickness.
The main elements were linked together using rigid constrains (*CONSTRAINED_NODAL_RIGID_BODY) or elastic (*ELEMENT_DISCRETE). The structure was constrained in motion and support defined (*BOUNDARY_SPC). As there are many parts in the model a method for interference between them was required thus contact was added (*CONTACT_AUTOMATIC_SURFACE_TO _SURFACE). Thickness and contact forces were analysed in order to evaluate them influence over the simulation results. Mass compensation was used for the other components that were not represented in the cockpit module model.
The reduced mass of the impactor used for the numerical simulation is . Its initial velocity is of when an area that does not contain an airbag system is impacted.
The impactor is perfectly rigid (MAT20 *MAT_RIGID). The units system used for the simulation is defined by mm for lengths, ms for time, for density thus for forces kN and J for energy units were used.
Stress - strain data are implemented in the computational model using specialized cards. When these data are available, the most used material model for LS-Dyna simulations is *MAT_24 or *MAT_PIECEWISE_LINEAR_PLASTICITY. The material model stress - strain curves defined by points and also the strain at failure may be defined.
Although the numerical model is constructed using shell elements LS-Dyna solver uses the shell thickness in order to compute the stress strain profile. The number of integration points through the shell's thickness is specified using *CONTROL_SHELL card. As a consequence the *MAT_24 material model was updated in order to handle the shell thickness and therefore *MAT_123 or *MAT_MODIFIED_PIECEWISE_LINEAR_PLASTICITY can be used.
This adaptation is required by the model that may deform by bending. Setting a number of integration points that must fail before the elements fails will ensure a better response of the structure for both in-plane loads (tension, compression) and out-of-plane load (bending, twisting).
The numerical model is presented in figure 16.
5. Results and discussion
5.1. Analyzed parameters
For most applications the parameter that reflects the structure's performances is HIC (Head Injury Criteria) defined by equation (7). The criteria is calculated during an interval of 36 milliseconds or 15 milliseconds, a is the measured acceleration expressed as multiple of g (gravitational acceleration). A value bellows 1000 units means that the structure provides satisfactory protection for the passengers.
(7)
A more detailed investigation of the structure and the numerical model can be performed. Thus, the numerical model will be analyzed in terms of HIC criteria, average acceleration, local/peak values, time and coefficient of restitution.
5.2. Energy balance
Virtual testing world allows different models to be developed and tested. But even if this virtual world is quite permissive the engineer must design and test in agreement with the real world information and data.
Experimental methods are very costly by this point of view, because a detailed investigation of the event requires a very sophisticated instrumentation using strain gauges, force and displacement transducers. Even in this case the results may reflect localized phenomena that can lead to an under or over evaluation of the generalized response.
By this point of view numerical methods allow a much in depth analysis of the structures. The structured numerical model contains finite elements that are organized in parts according to their mathematical and material model and, in case of shell elements, thickness. Finite element method consists in the decomposition of complex structures, and the application generally known rules and equations in order to obtain the results.
The element stiffness matrices can be derived from the principle of minimum potential energy I.
I=strain energy - work done by external forces
(8)
The total energy of a mechanical system must be conserved. In case of a mechanical system with initial kinetic energy the total energy balance must be reflected in the internal energy accumulated due to deformation, friction, heat and/or sound wave propagation and the change of the kinetic energy.
The total energy of the system is, in this case, the initial kinetic energy of the false head used both for the experiment and for the numerical simulation.
As mentioned, the virtual model can work in ideal condition. It is obvious that the impact test will produce damages and ruptures in the tested parts and all of these because in some areas the stress will be above the ultimate stress value.
Firstly, the model is designed in order to allow high strains so that parts will not collapse. This step is performed in order to check the energy balance in order to ensure the good performances of the numerical model.
Figure 17 presents the energy balance in terms of kinetic energy, internal (deformation) energy and total energy. There are no changes or important deviations from the nominal value in the total energy. If any, they are due to the failed elements. The procedure for the model with damage, implemented via the material model, is to remove from the calculation the elements with high stress or strain.
From the components used to define the geometry of the numerical model the parts that contribute to more than 10% of the system internal energy were selected. Although the model consists in a quite high number of parts (52), the previously mentioned condition is fulfilled only by two components - the impact section of the dashboard and the stiffening structure located under (as the windshield air deflector).
Figure 18 presents the parts that play a significant role in the internal energy history.
Thus, the potential area of parts for optimization can be defined because changes in the structural performances of these parts will improve the response of the entire assembly.
Also, different methods for assigning part properties in terms of thickness and material formulation can be applied to a few numbers of parts and the control of these changes or modelling improvements is more accurate.
5.3. Numerical procedures for the random assignment of parts' thickness
After the experiment, the stiffening structure (figures 1 and 13) was damaged. The small fragments of the part were analyzed and the thickness was measured. The nominal value of the part is of 2.5 mm. For some fragments the thickness was below this value. It may be a result of the manufacturing process and therefore the numerical model must be updated in order to consider these aspects. One procedure consists in very detailed measurements of the part and an update to the numerical model. But it may be a very expensive procedure in terms of time and equipment.
The free edges of the main part and failed fragments can be easily measured (figure 19). Using these values the deviation from the nominal thickness is computed. As the variation of the thickness occurred for more than one instances and for more than one sections of the analyzed part a new requirement for assembly modelling has to be stated.
The section selected for the random distribution is the one that was damaged during the impact. In order to accomplish this task a collaborative environment between the finite elements solver and new software is required [4, 7, 8, 13, 18].
A custom code written in Matlab was created and used for the random distribution. The input is the initial file with the numerical model and the outputs are a file with the sections for which the random procedure was applied and the second one is the initial file with the lines containing the elements selected for random distribution remove. There are two files generated by the code.
Figure 20 presents the organization of the custom written code.
The code can update the thickness, material properties or both of them for one element. The material properties may be added because in some cases, due to the manufacturing process, the model is not homogenous.
A procedure, to consider these changes from the nominal value of the thickness, is to set a random distribution within the elements consisted by the selected part.
The paper will further concern only the application of the first option, regarding the changes in the part thickness.
The parameters of the random procedure are the deviation from standard expressed in percents and number of levels for the thickness distribution for the elements.
Three random procedures may be implemented. The difference between these procedures (figure 21) is related the number of dependencies created between neighbour elements.
The first one is an element based procedure because it is element oriented. In this case the neighbour elements or the currently selected element are not taken into account (Figure 21a). The property assigned to the current element may be any of that defined by setting the random level. So, it is possible for two elements in row to have one with the nominal/maximum thickness and the next one to have the minimum thickness. The distribution of thickness in the part is not accurate.
The second one is also element based (Figure 21b). The current elements and its neighbours are identified and even if it is about a random procedure there are some rules added. Considering the number of order, two consecutive elements can not have one the maximum (nominal thickness) and the next one the minimum thickness. The random distribution can be done only to a level of -1, 0 or +1 starting from the current element. The extreme values are also considered and for the minimum thickness the distribution is 0, +1, while for the maximum thickness the distribution is -1, 0.
The third random procedure is a 2 - dimensional procedure (Figure 21c). This procedure is related to the nodes that are used to define an element. The custom built code searches through the numerical model definition to identify any existing elements that may have one or more nodes in common with the currently selected element. Once these elements are identified, the random procedure is applied in to order to assign the different properties. The random level is stored for each element.
The numerical procedure for this assignment is shortly described. The code starts with -1 entry for the element random level and the identification of neighbour elements is applied. If in the main list containing the elements, the random level for the current elements is -1, then a property is assigned. For the neighbour, a property of -1, 0, +1 from the current level is assigned. In this case, for any two elements, the number of steps between the random levels is limited to 2.
If an element it was already selected as a neighbour of a previously defined element, than, its random level property is used as a start in order to define the random level for its own neighbours and the procedure is repeated.
Using the internal energy history the parts with greater participation were selected. The model can be even more sub structured in order to decrease the area for design update. As a consequence from the stiffener / air deflector part (figure 1, figure 18) only the section that was damaged (figure 13, figure 19) was selected for the random procedure.
The code is applied for different numbers of random level. The finite elements structure is coloured according to the property assigned to each element (figure 22). Also the corresponding legends with some statistical results are presented. A random level of 2, 4 and 6 is applied. The deviation from the nominal thickness if of -3% (minimum thickness is 2.42 mm). The distribution of the elements is in a good agreement with the Gaussian or standard normal distribution. This fact and the results of the random distribution are used to validate the custom written code.
5.4. Results
A number of numerical simulations were performed and the results compared. The first simulation is with a material model without failure. The second model has a material formulation with failure and it was previously validated using experiment. At this stage the main criteria for the evaluation of the numerical model's performance was the value of HIC (Head Injury Criteria) that is used in order to validate the components from the vehicle interior in case of impact. The event duration is less than 36 milliseconds thus HIC was calculated during a 15 milliseconds time interval. For the numerical simulation and for experiment with an error between measured and calculated data of 4.4%. The parameters are within the limits of ECE 21 specifications.
The third model uses the random distribution of the thickness as a method for improving the accuracy of the results. Figure 23 presents the section used for the random distribution as it is integrated into the computational model.
Two sets of data are available. There are the raw data as obtained from the experiment and simulation and there are the filtered data. Filtering is required in order to remove the noise or some other reads that may alter the results, thus making the evaluation of the post processed data more effective in terms of decisions efficiency. Figure 24 presents the raw data used as inputs for data filtering. The measurements were performed at the gravity centre of the impactor.
Regarding the safety criteria (e.g. HIC), the raw data can be used as they are obtained. Table 3 presents the values of the safety parameter as obtained from the experiment and simulations.
Differences between the experiment and the previously analyzed model are in a good agreement, within a generally accepted error (+4.4%). It is important to underline the differences between the experiment and the simulation model using a material formulation without failure. There is an important difference between the results (+104 %). As a consequence part damage and material failure must be taken considered.
Regarding the simulation with a random distribution of the thickness, there is an improvement of the results, the error for HIC index as obtained from the simulation and experiment is of only +2,8%.
Table 3. HIC safety index
HIC [-]
Error
Experiment
249
-
Model without failure
508
104%
Model with failure (constant thickness)
260
4.4%
Model with failure (random thickness)
255
2.8%
In order to outline the differences between the computational models a specialized filter was used (SAE 180 Hz). The filter is used in automotive engineering in order to smooth data and make results more readable. Figure 25 presents the filtered data.
There may be noticed some similarities between the results. All curves show two peaks located at different times. The location in time of the first peak is for all the curves within a very tight interval. By that time, all of the components of the cockpit module are in contact, including the metallic section (cross beam) used for fixing the assembly. The acceleration values are different due to the material modelling (without failure, with failure) and to the thickness assignment to the parts (constant thickness, random thickness).
The time location of the second peak is different. By now the section should have failed. For the model without failure the parts integrity is maintained. Thus from all of the cases, this one is the stiffer and the recorded acceleration does prove this statement. For the models with failure the maximum recorded accelerations are comparable. There is only an issue of time location of the peaks.
Table 4 presents the results obtained form the simulations and experiment.
Table 4. Parameters from impact analysis
experiment
Model without failure
Model with failure (constant thickness)
Model with failure (random thickness)
Parameter
measured
recorded
error
recorded
error
recorded
error
72.02
92.46
28.38%
74.76
3.80%
72.03
0.01%
29.53
29.93
1.35%
28.4
-3.83%
28.49
-3.52%
44.96
61.13
26.45%
48.48
7.26%
45.71
1.64%
72.02
92.46
22.11%
74.73
3.63%
72.03
0.01%
3.5
1.9
-84.21%
1.7
-105.8%
2.3
-52.7%
9.2
7.9
-16.46%
5.1
-80.4%
8.5
-8.24%
5.7
6
5.26%
3.4
40.35%
6.2
8.77%
As presented in table a number of parameters were analyzed: - maximum recorded acceleration, the average acceleration, - acceleration recorded at the first peak, - acceleration recorded at the second peak, - time location of the first peak, - time location of the second peak, - time interval between peaks.
The reference model is considered the experiment. The parameters that were compared, and have an error computed, are the maximum recorded acceleration, average acceleration and time interval between the two peaks.
The simulation model without failure offers good results in terms of time between peaks and average acceleration, but the maximum acceleration and the HIC index are outside the acceptable tolerance interval (±5% from nominal for accelerations, ±10% for time because the time scale is more discrete).
The simulation model with failure offers good results in terms of maximum acceleration, average acceleration and HIC index. In terms of structural performances this numerical model can be, and it was, validated for virtual testing.
The simulation model with failure and random distribution of the thickness with an -3% deviation from the nominal offers very good results in terms of maximum acceleration, average acceleration, HIC index and time between peaks.
Concluding with these results it may be said that particular modelling techniques are applicable for improving the performances of numerical models.
It is one of the cases when the energetic coefficient of restitution and the kinematic coefficient of restitution are equivalent. Table 5 presents the values for the coefficient of restitution:
Table 5. Coefficient of restitution
experiment
Model without failure
Model with failure (constant thickness)
Model with failure (random thickness)
Parameter
measured
recorded
error
recorded
error
recorded
error
Initial kinetic energy [J]
152
152
0%
152
0%
152
0%
Maximum potential energy [J]
14.5
-
-
-
-
-
-
Initial velocity [m/s]
6.69
6.69
0%
6.69
0%
6.69
0%
Rebound velocity [m/s]
-
2.33
-
1.89
-
2.06
-
COR
0.308
0.348
-12.83%
0.282
8.47%
0.307
0.238%
The results, listed in tables 3, 4 and 5, accentuate the performances of the numerical model that is using the random distribution of the thickness for the section being damaged during the impact. From a total of nine performance criteria presented, the model with the random distribution of the thickness is within the specified error for eight criteria.
6. Conclusions
For modelling and usual analysis of mechanical structures it is considered that the whole structure and its components accomplish one of the fundamental conditions of strength of materials - the condition of continuity. The great variety of problems in engineering practice yields sometimes situations where discontinuities, in terms of variable thickness of different mechanical properties, appear in some components.
This paper presents some modelling techniques useful for the optimization of the numerical models in terms of improving the structural response for impact applications.
Using experiments performed with equipment constructed according to ECE 21 / FMVSS 201 regulations, the results obtained using three numerical models are compared and solutions for numerical modelling are presented.
The first step was concerning the material model used. As some parts have to be damaged a material model capable of material failure must be used. The differences between the results obtained using a model without failure and a model with failure compared to the experiments were discussed.
The second procedure is regarding the random distribution of the thickness properties of the elements for a selected area with a user specified tolerance. Procedures implemented in custom written code and the algorithms used for the random distribution were presented.
This application was required because the parts measurements presented some deviations from the nominal value, probably due to the manufacturing process.
Results (accelerations: maximum, average, peak; time: peak time, time between peaks; coefficient of restitution) obtained using the numerical model were evaluated and compared with the experiment.
Even the second model used (model with failure and constant thickness) offered good results, the third model (model with failure and random thickness) can bring the results much closer to the ones from the experiment.
Although simulation codes are very powerful in terms of computational performance and accuracy of results, a collaborative environment between these codes and custom written computer programs can improve the structures' response by considering the real life distribution of properties within the analyzed parts. Results from these simulations (e.g. coefficient of restitution) can be further used to develop analytical model for the study the passenger's motion during vehicle frontal impact.
