Documentation:FIB book/Accident Reconstruction: Comparison Between FEA and Multi Body Method Analysis

Introduction

Understanding how and why vehicle crashes occur is essential for improving automotive safety and reducing injuries. Since the creation of the first anthropomorphic test device (ATD), car manufacturers and safety regulations have been innovating to allow for us to collect data on crashes and develop new safety precautions. With modern technology and greater computing power, we can now use virtual simulations to better understand vehicle accidents. Crash reconstruction modeling helps engineers, researchers, and policymakers analyze accidents by simulating real-world collisions. These models provide insights into impact forces, structural deformations, and occupant safety and are critical for designing safer vehicles and refining industry regulations. However, the accuracy and data acquired from these simulations may differ depending on the simulation. For this reason, it is critical to understand the benefits and downfalls of each simulation to allow for the highest quality and most reliable data.

Two common techniques for crash reconstruction are Finite Element Analysis (FEA) and Multi-Body Methods (MBM). FEA offers a detailed, physics-based approach that breaks a structure into small elements, allowing for precise simulations of material deformation and energy absorption. While highly accurate, it requires significant computing power and time. On the other hand, MBM simplifies vehicles into interconnected rigid or flexible bodies, making it computationally efficient but less precise when it comes to capturing material behavior and localized damage.

This paper will compare FEA and MBM in the context of crash reconstruction, examining their strengths, weaknesses, and sources of error. It will also explore validation techniques to assess their accuracy and reliability in real-world scenarios. By analyzing these factors, this study aims to provide a clearer understanding of when each method is most appropriate and how they contribute to advancements in crash analysis.

Crash Reconstruction Modeling Approaches

Crash modelling is founded upon the physical laws of conservation of energy and of momentum. In any collision, the total momentum of the system (including vehicles and occupants) before the crash is equal to the total momentum of the system after the crash. Similarly, all the kinetic energy contained in the system prior to impact is transformed into deformation, heat and sound. Modelling how momentum is transferred throughout the system and how energy dissipates during the crash help gauge how the accident occurred.

Components of the system are also analyzed for plastic deformation, elastic deformation, and fracture. Material response to extreme forces is examined taking into account unique behaviours of the properties of the various materials in the system.

Defining the initial and boundary conditions of the system is essential to modelling the collision. Boundary conditions include accurate surfaces and constraints on movement. Initial conditions include vehicle speeds, mass distributions, the angles of impact and pre-crash directional dynamics of the bodies involved in the crash.

Contact mechanics help to understand the interactions between contact surfaces within the collision. The contact surfaces must be defined, and crash modelling is facilitated through the calculations of normal and tangential forces during impact as well as calculations of friction, sliding and potential separation of parts from the contact surfaces. Important considerations in the analysis of contact mechanics are the presence and response of crumple zones and the impacts of occupants with the inside of their vehicles.

Further, the movement of vehicle occupants during a collision is an important consideration for crash reconstruction modelling. ATDs or cadavers are used to simulate a human body’s motion in reference to the overall motion of the vehicle. The effectiveness of safety components like seatbelts and airbags can be evaluated, alongside the likelihood and severity of injuries such as whiplash and head strikes to the vehicle’s interior.

Crash modelling takes measurements over incremental time steps, to solve for instantaneous velocities, accelerations, deformations and forces present in the system. To validate the models they are compared with corresponding physical crash data, and tuned to match experimental conditions to observed results.

Finite Element Analysis (FEA)

Finite Element Analysis (FEA) is a prominent engineering simulation tool used for a wide variety of applications. In vehicle crash reconstruction, FEA assigns material properties to small interconnected elements making up a complex system and analyzes each element for stress, strain and deformation under crash conditions. Instantaneous values can be obtained for the aforementioned items, and an incremental analysis can be conducted to determine exactly what occurred and at what point in the collision [15].

Strengths and Limitations

FEA as a tool for crash reconstruction has its strengths and limitations. Using FEA, it is possible to achieve detailed insights on the complete response of materials to the crash conditions [15]. The tool can accurately model localized elastic and plastic deformation, and failure mechanisms which help to understand the absorption of energy in crumple zones and the level of protection provided to vehicle occupants. Specific locations of localized stresses can also be pinpointed to predict where failure is most likely to occur. Moreover, FEA has a high degree of versatility permitting the user to model virtually any crash scenario. However, simulations tend to be time consuming and use a large amount of energy [15]. They are complex to set up and fine tune in cases where results are inconsistent, and any inaccuracies to input data can greatly affect outputs.

Common Sources of Error

There are a few common sources of error in FEA usage. First, the quality and resolution of the mesh determine the simulation’s accuracy. Creating a mesh that is too coarse will fail to capture intricacies in localized deformation [15]. This can result in underestimating certain stresses and failure points, and withdrawing an unclear and incomplete understanding of how the crash occurred. Creating a mesh that is excessively fine on the other hand significantly increases computational costs without necessarily ensuring meaningful accuracy improvements [15]. Results have a notable dependency on mesh size.

Similarly, the misrepresentation of material properties in the system can lead to error. If material properties are poorly calibrated to the models of the vehicle bodies involved in the crash, the simulation will inaccurately demonstrate the deformation and energy absorption of components. In addition, material data obtained in static conditions and extrapolated to the high strain rates observed in vehicle crashes can lead to systematic errors in the results of FEA [15].

Finally, definitions of initial and boundary conditions must be precise. Any discrepancies contact geometry or interactions between the vehicles and the road surface generate inaccurate results.

Example Applications of FEA

The following are examples of how FEA can be applied for crash reconstruction:

1. Frontal Impacts. A simulation is conducted to see how the crumple zones deform alongside the engine bay and passenger compartment of the vehicle during a collision in which the examined vehicle has hit another vehicle or an obstacle head-on [15].
2. Side Impacts. A simulation is used to examine protrusion into the passenger compartment of the vehicle when the examined vehicle is struck by another vehicle in its side [15].
3. Rollovers. A simulation analyzes the structural integrity and deformation of the roof during vehicle rollover, including its potential injuring of vehicle occupants.
4. Pedestrian Impact. A simulation models the interactions between a vehicle's hood and a pedestrian ATD to assess potential injury risks [15].
5. Vehicle Component Analysis. A simulation evaluates how safety features perform under loading conditions (ie. crumple zones, door beams, seat structures, etc) [15].

Multi-Body Methods (MBM)

Multi-Body Methods (MBM) is a widely used approach in crash reconstruction for simulating the dynamic behavior of interconnected rigid or flexible bodies, such as vehicles and human occupants, during collisions. By representing complex structures as simplified assemblies of interconnected elements, MBM enables efficient analysis of system dynamics across different impact scenarios, making it particularly useful for reconstructing crash events and assessing injury mechanisms [6].

Strengths

One of the key advantages of MBM is its computational efficiency compared to FEA. Because MBM reduces the modeling complexity by approximating structures as interconnected rigid bodies, it allows for rapid simulations and iterative testing of different crash scenarios. The reduced computational demand makes MBM a valuable tool for preliminary crash analysis, enabling researchers to explore multiple impact conditions without excessive processing time. This method is commonly used to simulate vehicle-pedestrian collisions, assess the effectiveness of safety measures, and refine injury prediction models [6].

Common Sources of Error

Despite its advantages, MBM has several notable limitations. One of the most significant drawbacks is its reduced accuracy in modeling localized deformations and material failures. Because MBM treats bodies as rigid or semi-rigid structures, it may not fully capture energy dissipation, force transmission, and material failure dynamics that occur in real-world crashes and can introduce errors. As a result, MBM models may be less precise in predicting injury severity and structural integrity assessments compared to FEA-based simulations [6].

Another common source of error is the sensitivity of MBM models to initial conditions and input parameters. The accuracy of MBM reconstructions depends on precisely defining pre-impact conditions, vehicle speed, pedestrian orientation, and impact angles. Small errors in these inputs can lead to significant deviations in the predicted crash dynamics [6].

Example Applications of MBM

Despite its limitations, MBM remains a valuable tool in crash analysis, particularly in cases where computational efficiency and large-scale system dynamics are prioritized over localized material deformations. Two examples are as follows:

Vehicle-Pedestrian Crash Reconstruction: MBM has been widely used to reconstruct vehicle-pedestrian collisions, helping researchers analyze pedestrian kinematics, injury mechanisms, and safety system effectiveness. By integrating multi-objective optimization algorithms, MBM can improve reconstruction accuracy and enhance forensic investigations [6].

Vehicle Impact Analysis: MBM simulations assist in understanding the dynamic behavior of vehicles during crashes, particularly in assessing vehicle stability, rollovers, and post-impact trajectories. These insights contribute to the design of safer automotive structures and the development of improved crash mitigation strategies [6].

Error Analysis and Validation Methods

FEA and MBM are powerful tools in accident analysis, but their effectiveness relies on their ability to accurately replicate real-world crash dynamics. Errors in simulations can arise due to limitations in numerical methods, incorrect input parameters, or oversimplified modeling assumptions. As a result, error analysis and validation techniques play a crucial role in ensuring the credibility of these models.

Methods for assessing Accuracy in Crash Reconstruction

Ensuring the accuracy of crash reconstruction models is essential for their reliability in forensic analysis, vehicle design, and safety regulations. Both FEA and MBM require validation to confirm their predictions align with real-world crash dynamics. Several techniques are employed, including:

1. Bayesian Validation

Bayesian validation quantifies uncertainty in crash simulations by incorporating prior knowledge, experimental crash data, and probabilistic modeling. This method refines model predictions by continuously updating parameters based on new data, allowing for more accurate reconstructions of crash events. Unlike traditional validation methods, Bayesian approaches account for multiple sources of error, including bias in model assumptions and variability in real-world crash data. By utilizing a hierarchical modeling structure, Bayesian validation can adapt to different but related crash scenarios, improving predictive accuracy over time. This makes it particularly useful for evaluating the reliability of Finite Element Analysis (FEA) and Multi-Body Methods (MBM) in crash reconstruction [7].

2. Experimental Crash Testing Comparisons

One of the most direct validation techniques involves comparing simulation results with real-world crash tests. While organizations like the National Highway Traffic Safety Administration (NHTSA) and the Insurance Institute for Highway Safety (IIHS) conduct full-scale crash tests, component-level testing also plays a key role in model validation. One example is a study that validated an FEA crash-can model by comparing simulation results with experimental compression tests, demonstrating how real-world data can refine crash models and improve accuracy [8].

3. Sensitivity Analysis

Sensitivity analysis evaluates how changes in input parameters (such as material properties, impact speeds, or boundary conditions) affect simulation results. This method helps identify which parameters have the most significant influence on crash outcomes, allowing researchers to prioritize the most critical variables when refining models. A study utilizing Taguchi and ANOVA methods demonstrated how factors such as airbag distance and inflator gas temperature influence occupant head injuries in frontal crash simulations, confirming the importance of sensitivity analysis in crashworthiness design [9].

Comparison of Common Error Metrics

To assess the reliability of crash reconstruction models, several key error metrics are commonly evaluated:

1. Energy Conservation Errors

Crash simulations should adhere to the fundamental principle of energy conservation. Any discrepancies in the total energy before and after impact may indicate inaccuracies in the model. In FEA, artificial energy dissipation or numerical damping can occur due to mesh distortion, contact algorithm limitations, or time step selection. MBM models may fail to account for energy absorbed through plastic deformations, leading to underestimation of impact severity.

2. Discrepancies in Deformation and Force Predictions

Accurate prediction of material deformation is crucial for evaluating crashworthiness. FEA provides high accuracy in localized deformations but can introduce errors if the mesh resolution is too coarse or too fine. MBM simplifies deformation modeling, often treating structures as rigid bodies, which can result in unrealistic force transmission and incorrect injury predictions.

3. Sensitivity to Input Parameters

The accuracy of crash reconstructions depends on the precision of input data, such as vehicle speed, impact angle, and material properties. Small errors in defining boundary conditions or contact interactions can lead to significant variations in results. FEA models are particularly sensitive to material properties, while MBM models are more influenced by initial impact conditions and assumptions about joint stiffness and damping.

Validation Techniques

Several validation techniques are employed to ensure the credibility of crash simulation models:

1. Experimental Crash Testing Comparisons

As discussed earlier, real-world crash tests conducted by organizations such as the National Highway Traffic Safety Administration (NHTSA) and the Insurance Institute for Highway Safety (IIHS) provide benchmark data to assess the accuracy of simulation models. These controlled crash tests allow researchers to compare simulation results with actual crash test outcomes, enabling them to refine material properties, impact conditions, and computational assumptions. By aligning simulation models with experimental crash data, researchers can improve the reliability of Finite Element Analysis (FEA) and Multi-Body Methods (MBM) in reconstructing vehicle crashes.

2. Statistical Error Analysis

Statistical methods such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and correlation coefficients are commonly used to quantify discrepancies between simulation results and experimental data. These metrics help assess how well FEA and MBM models predict crash outcomes, including impact forces, vehicle deformations, and occupant injuries. High correlation coefficients indicate strong agreement between simulated and real-world crash results, while large RMSE values suggest systematic errors that require correction. By applying statistical error analysis, researchers can identify inconsistencies in crash models and make necessary refinements to improve accuracy.

3. Benchmarking Against Real-World Accident Data

Real-world accident reports and black box event data recorder (EDR) outputs provide critical validation data for crash models. By reconstructing actual crashes using FEA and MBM, and comparing the results with police reports, insurance investigations, and crash databases such as CIREN (Crash Injury Research and Engineering Network), researchers can assess the practical applicability of their models. This benchmarking process ensures that computational crash simulations accurately reflect real-world crash dynamics, improving their use in forensic analysis, safety assessments, and vehicle design.

Comparison of FEA and MBM

Relative Accuracy

The accuracy of both FEA and MBM models rely on the accuracy of their respective input parameters. MBM models require accurate mass and inertia values of each respective body in the model, initial conditions such as linear velocity, angular velocity and position, external forces, contact forces between respective bodies [10], and road conditions which relate to the vehicle tire and road interaction [11]. In addition to these inputs, MBM models should have greater accuracy when the vehicle is split into more bodies to reduce the number of simplifications used in the simulation [10].  FEA models rely on the accuracy of material properties for all materials being analyzed during the crash, precise vehicle and or person geometry in a CAD model, initial conditions such as linear velocity, angular velocity and position, vehicle suspension characteristics [12], and boundary conditions which may vary given the type of crash that is analyzed [13]. The accuracy of FEA models also relies on the size and density of the selected mesh, which are the dimensions of each element and how many elements are contained in a specific area or volume [14]. Lastly, an FEA model’s accuracy is additionally determined by the order and time steps used for the integration scheme used in the model [15]. If all of these inputs are accurately determined and a small mesh size and the correct integration scheme is selected, the relative accuracy of an FEA model is likely to be higher than an MBM model in terms of modelling localized deformation, energy dissipation, and subsequently injury severity of any vehicle occupants or pedestrians. Due to the simplified nature of MBM models, they tend to over or under-report parameters associated with injury criteria and deformation of vehicles [16].

Computational Efficiency

In general, MBM models have a higher computational efficiency than FEA models. The efficiency of each model is dependent on several aspects of the model, which are selected before simulation. For an MBM model, increasing the number of bodies that are used to model the system will decrease the computational efficiency of the model. Increasing the number of bodies in the system will increase the number of possible interactions between bodies, the number of equations of motion that must be simulated, the number of degrees of freedom in the system, and the number of coordinate frames that must be used in the simulation [17]. This has tradeoffs, as increasing the number of bodies increases the accuracy of the model. The computational efficiency of FEA models is determined by the mesh density [14], integration scheme [15], and the geometric complexity of the object that is being modelled [19]. A coarse mesh (large elements) will increase the computational efficiency but decrease the accuracy of the mode, and a fine mesh (small elements) will decrease efficiency but increase accuracy. Because of this, it is crucial to select an appropriate mesh element size [14]. Integration schemes are classified into implicit and explicit schemes, and within those categories, the degree of the integration scheme can also be changed. In general, an implicit scheme has higher computational costs than an explicit scheme, but they are typically more accurate when the same degree of integration and number of time steps is used [20]. Lower-degree integration schemes are more computationally efficient than higher-degree schemes. Higher degree schemes are more accurate, but the increase in accuracy decreases with the increasing degree of integration, meaning the high computational cost of these high-degree schemes is often not worth the increased accuracy [15]. If an object has complex geometry (the geometry includes concave faces and smooth edges, for example), it will require the use of a finer mesh for an accurate FEA model [21]. As previously stated, this means that the computational efficiency will decrease due to the smaller mesh element size, resulting in higher computational costs for more complex geometry.

Applicability to Different Crash Scenarios

MBM models are typically used to analyze the complex dynamics of the bodies that together represent a vehicle and its passengers. This is particularly useful when determining the speed and position of vehicles or pedestrians leading up to a crash. The trajectories of the vehicles and or pedestrians can be simulated given the initial crash conditions and compared to the trajectories which would have occurred based on the post-crash positions of the vehicles, passengers, and pedestrians involved [6]. MBM models are used to analyze vehicle safety systems as they can simulate a passenger's detailed dynamics during a crash. Precise seating positions and passenger heights can be easily modified prior to simulation. MBM models are also useful for analyzing rollover conditions. They are often used to represent the rigid chassis of a vehicle in rollover analysis while the roof is modelled using FEA. FEA models are used to analyze the energy absorption of a vehicle in a crash. FEA allows for the analysis of the deformation of vehicle components. Given the material properties of the deformed portion of the vehicle, the energy absorbed and the speed at which the collision occurred can be determined [12]. FEA models can also be used to analyze injury severity and cause. FEA models of body parts are often used in combination with FEA and MBM models of vehicles in accidents to determine the crash accelerations and car deformations that result in varying degrees of injury. Typically, a whole body will not be an FEA model; the majority of the body is usually modelled using an MBM model, and the region of interest is modelled using FEA.

Controversy

Crash reconstruction modelling has been the subject of many controversies. There are continuous arguments in the field regarding the accuracy of simulation software and how they can be manipulated to show desired results depending on inputs and assumptions. Oftentimes, these issues can render the findings of vehicle crash reconstruction simulations effectively useless to the parties involved. One such situation materialized in the British Columbian Supreme Court regarding a crash involving two tractor-trailers driving along Highway #1 near Revelstoke on February 3rd, 2010 [21]. Two engineers, one hired by each side, were tasked with conducting a crash reconstruction to pinpoint the cause of the accident and provide evidence before the court. Upon gathering the crash data and running the simulation, the two engineers settled on fundamentally different conclusions for who was at fault and what exactly occurred [21]. After presenting opposing findings before the court, the engineers who “relied on the available evidence from the accident scene… agreed that this was a challenging accident scene…[and] agreed that this accident was less conducive to the use of PC Crash simulation” [21]. As a result, the Judicial Justice hearing the case dismissed the evidence presented by the engineers and settled the case himself instead, using available evidence and testimony. When questioned further, both engineers “described a difficult accident scene and the limitations on the use of the usual software to reconstruct the accident” [21].

This controversy is important because it highlights the failure of crash reconstruction modelling software to identify what occurred in a crash being judged before the courts. At the most crucial levels, crash reconstruction modeling is inconsistent in providing clear and trustworthy results. There is an inherent human bias in the analysis of crash data and modelling, but an ideal system should provide consistent results for identical input conditions regardless of the software operator.

Conclusion and Recommendations

Crash reconstruction modeling is key to understanding vehicle collisions and guiding safety improvements. This report compared two primary simulation methods, Finite Element Analysis (FEA) and Multi-Body Methods (MBM), focusing on their technical capabilities, limitations, and validation approaches.

Summary of Findings

FEA is highly detailed and accurate for modeling localized deformations, material failures, and occupant injury mechanisms. It provides valuable insight into structural response and energy absorption but is computationally expensive and requires extensive model setup. MBM, on the other hand, models the crash event using interconnected rigid bodies, making it significantly faster and easier to run across multiple scenarios. While it lacks the fine detail of FEA, it excels at simulating vehicle trajectories, impact sequences, and force transmission across large systems.

Validation techniques for both methods are critical, especially when inputs such as material properties or initial conditions are uncertain. Common approaches include comparing simulations to physical crash test data, using statistical models like Bayesian analysis, and conducting sensitivity studies. The best use cases for these models are as follows:

• FEA: Detailed studies of structural deformation, crash energy absorption, and injury prediction. Often used in regulatory crash test replication and advanced safety system design.
• MBM: High-level crash dynamics, occupant kinematics, and rapid scenario testing. Ideal for early-stage investigation or when working with limited computational resources.

Combined Use of MBM and FEA

The most effective crash reconstructions often rely on both MBM and FEA. MBM can simulate the overall crash event, capturing the movement of the vehicles, impact timing, and forces on simplified components. These simulations help identify critical areas or events during the crash. FEA can then be applied to these specific zones to analyze localized deformation, material failure, and occupant protection systems in more detail. Using both methods in tandem leverages their strengths, allowing for broad system-level understanding and detailed insight where it matters most.

Future Trends and Advancements

Crash modeling is evolving rapidly with the integration of machine learning, real-time simulation, and improved material models. AI tools are being developed to optimize initial conditions based on limited crash data. Hybrid approaches that combine MBM and FEA within a single simulation framework are also becoming more accessible. As computational power continues to increase, higher-fidelity models will become more practical, reducing the trade-off between speed and detail. Additionally, improved sensor data and vehicle telemetry will provide more accurate inputs for reconstruction models in the future.

Future Research Priorities

Crash modelling has made considerable advancements over the last decade in the versatility of initial and boundary conditions it can simulate and the variety of situations it can model. Where it continues to struggle is with result objectivity. Many of the conclusions that can be drawn from FEA and MBM are at the discretion of the simulation operator, and settling on the cause of a complex crash through simulations involves a certain level of subjectivity. Future research in the field should prioritize objectivity and reduce ambiguity in various possible conclusions that can be drawn from identical input conditions. When these improvements are made, crash reconstruction modelling will be an infallible source of reason in all claims and cases involving plaintiffs in vehicle collisions.

Final Remarks

Choosing the right tool or combination of tools depends on the specific objectives of a crash analysis. FEA and MBM each play a distinct and complementary role in modern crash reconstruction. When used together, they provide a comprehensive understanding of both the global dynamics and localized damage of a crash, leading to more accurate conclusions and better-informed design and safety decisions.

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Please note that we will be hyperlinking all the references using the Wiki software for final draft

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