Model Simplification and Reduction Methods for Collision Simulation

PhD Context

The mastery of impact phenomena in deformable structures, characterized by extreme mechanical loads and described mathematically by strongly nonlinear and non-smooth formulations, constitutes a major challenge in road safety. Collisions, involving various uses and users (pedestrians, cyclists, drivers, passengers, etc.), cause severe injuries and involve rapid interactions between complex mechanical structures and/or the human body.
In order to reduce the severity of injuries, numerous protective devices have been developed
(guardrails, crash attenuators, bumpers, crash boxes, seat belts, airbags, etc.). Their design aims to dissipate or redistribute impact energy so as to reduce the loads transmitted to occupants and vulnerable users. The validation of these devices relies on mechanical criteria correlated with trauma (ASI, THIV, etc.) and ensuring a level of injury compatible with regulatory requirements. The evolution of mobility (electric vehicles, micro mobility, coexistence of heterogeneous users, new seating postures in autonomous vehicles) diversifies and complicates the scenarios involving these impact phenomena, making it even more necessary to model protective devices in order to optimize them and improve their behavior.
The design and validation of these devices with respect to standards rely heavily on numerical
simulation, which has become essential to limit the use of costly experimental testing. These simulations involve models describing mechanical behavior and accounting for large deformations, separation/contact phases with impact, adhesion/sliding phases with friction, plasticity, damage, and fracture. The time integration of the associated problems is particularly costly due to the strong nonlinearity—and even non-smoothness—of the formulations. It requires very small-time steps, notably due to the use of explicit schemes, as well as complex contact handling across numerous interfaces. Furthermore, increasing model fidelity exacerbates issues of numerical robustness. Computational time and robustness issues are incompatible with optimization processes, sensitivity analysis, and the exploration of multiple scenarios. In this context, drastically reducing simulation times while maintaining a reliable predictive capability for quantities of interest constitutes a central challenge for road safety and for the development of optimized protective devices. This scientific and technological bottleneck is compounded by the issue of digital sobriety, as the intensive use of high-performance computing resources entails a significant energy cost.

Objectives and Methodology

The main objectives of the PhD project are to simplify or reduce high-fidelity models of collision scenarios involving deformable structures, by adapting the level of description to different regions (slightly or highly deformed), by controlling complexity (retaining only the dominant physical mechanisms during a collision), and by enabling the construction of robust meta-models within reasonable timeframes. The main challenge lies in reducing the time associated with time integration, which constitutes a major bottleneck in the design process.
This PhD, which builds upon previous work, aims to strike a balance between complexity
and accuracy and will be structured around three complementary axes:

Axis 1 - Model simplification and reduction through complexity control in slightly
deformed regions:

Summary: The objective of this axis is to investigate methodologies for simplifying the modeling of weakly deformed parts of the mechanical system. Complexity is controlled in order to retain only the mechanisms necessary and sufficient to describe the overall behavior. A functional approach may be favored (modal viewpoint, use of simple and/or rheological elements), thus making it possible to avoid a detailed description of individual components and technological architecture.
Scientific challenge: Identifying the minimal level of physical complexity and functional modeling required, ensuring reliable predictions without compromising the validity of the regulatory criteria to be satisfied.

Axis 2 - Model reduction and simplification through complexity control in highly
deformed regions:

Summary: The objective of this axis is to investigate methodologies for simplifying the modeling of highly deformed parts of the mechanical system. Simplified models may be used for the parts of the structure playing a major role in energy dissipation. Given the presence of large deformations, numerous contact-impact interactions, and adhesion/sliding phenomena with friction, suitable reduction methods will be favored (Proper Orthogonal Decomposition (POD), Proper Generalized Decomposition (PGD)).
Scientific challenge: Determining reduction strategies compatible with strong geometric and
material nonlinearities as well as with contact-impact conditions, while ensuring numerical stability and accuracy of the quantities of interest.

Axis 3 - Construction of robust meta-models based on surrogate models for optimization:

Summary: The objective of this axis is to derive, from these simplified models, meta-models
enabling the computation of output quantities of interest at low computational cost. The robustness of these meta-models will also be assessed by studying the influence of the variability of certain parameters on the outputs. Intrusive or non-intrusive approaches may be considered for the construction of the meta-models. Developments based on polynomial bases with specific properties may also be explored.
Scientific challenge: Designing parametric meta-models capable of accurately representing
strongly nonlinear and non-smooth responses, while ensuring a significant reduction in computational time compatible with optimization processes.

The Laboratory of biomechanics an impact mechanics (LBMC, UMR_T9406) is a joint unit between  the University Gustave Eiffel and the University Claude Bernard Lyon 1.

The LBMC gathers more than 80 members (50 staff members, around 30 PhD students and 10 research assistants and post-docs), in addition 20 trainees are welcomed every year. LBMC members have complementary skills: impact biomechanics, structural mechanics, uncertainties, tissues biomechanics, anatomy and surgery, physical ergonomics, movement analysis, musculoskeletal biomechanics.

Candidate Profile

Candidate holding a Master’s degree (M2) and/or an engineering degree in Mechanics, with :

— solid background in Continuum Mechanics (CM) and structural dynamics.
— strong foundations in Mathematics, Numerical Methods, and Algorithms.
— experience in using numerical simulation software based on the Finite Element Method.
— experience in development with the Python programming language.