- L’institut, UMR 5295
- Tutelles et Partenaires
Tutelles et Partenaires
Modèles hybrides AI-physique pour la simulation multi-échelles de structures architecturées
Technological innovation is pushing the limits of the use of materials. New devices for health, vehicles and renewable energy require new lightweight, multifunctional parts without compromising their mechanical properties. The advancement in designing optimized structures is limited by the numerical models capabilities when non-linear multiscale, multi-physics models are necessary. The current development of AI models is not adapted to such design problems. A new generation of AI-inspired models, informed with physical evolution equations, is necessary to solve multi-scale problems. A deep review of AI models is necessary, with the introduction of physically based models in the core architecture of one of the most common model, i.e. Deep Neural Networks (DNN). This project objective is to transform the field of efficient numerical simulation of multiscale structures, introducing, for the first time, AI inspired models
Subject description with bibliography
In the wake of the 4th Industrial Revolution, technological innovation is pushing the limits of the use of materials. New devices for health, vehicles and renewable energy require new lightweight, multifunctional parts without compromising their mechanical properties. The appearance of additive manufacturing, among other new processing capabilities, has considerably expanded the range of bio-inspired, architectured geometries, which may provide an answer to the design constraints (Ashby, 2013). In these structures, the determination of the parts’ combined response, in terms of mechanics, heat transfer, chemical evolution and fluid transfer is very complex, resulting from a combination of physical mechanisms, operating at different length scales.
Among multi-physics problems, the evaluation of the mechanical response of complex, architectured materials is a real challenge. Standard methodology to solve highly non-linear, multi-scale problems is to simulate, at each scale, the full mechanical fields using numerical methods (i.e. Finite Element Analysis, or FFT methods). Those methods require costly computing resources that have an important energetic impact. Local response is generally computed (Maugin, 1992; Rice, 1971) and homogenization methods are further used to upscale the information in an average sense (homogenization), or to downscale information to provide boundary conditions and allow local computations (localization) (Charalambakis, 2010; Chatzigeorgiou, Charalambakis, Chemisky, & Meraghni, 2016). This procedure is very predictive but still suffers from a prohibitive computational cost (Tikarrouchine et al., 2018). Reduced order models have been developed to tackle this issue. The concept is to define reduced basis where full-field solutions can be accurately represented using a reduced number of variables, selected from their sensitivity. Two approaches are nowadays popular: (i) a posteriori model reduction, where a learning process lead to the definition of a reduced bases (POD, reduced basis models (Maday, 2009)); (ii) a priori model reduction (PGD-like approach (Azaïez, Belgacem, Casado-Díaz, Rebollo, & Murat, 2018; Chinesta, Keunings, & Leygue, 2014)), where the reduced model is constructed directly without dedicated learning process. Several authors have tried to apply such methods to the problem of homogenization (Fritzen & Leuschner, 2015; Metoui, Pruliere, Ammar, & Dau, 2018). If the time reduction is theoretically very important, the performances are practically limited by the numerical treatment of non-linearities, especially considering multi-parametric problems. For those problems, computational time related to the construction of the basis functions is often comparable to the computational time using legacy full-field methods (Metoui et al., 2018). AI based on Deep Neural Network is very attractive, except that the use of ready-to-use AI framework is not suitable for two major reasons: (i) they rely on a high learning database, too costly to realize in the field of design of complex structures and (ii) their predictive capabilities in terms of providing accurate local information (i.e. stress concentration that would initiate a catastrophic failure) is very limited.
We propose a change of paradigm in the design of complex structures. We will use hybrid physical/Artificial Intelligence models, introducing physical evolution equations directly into the AI model (e.g. in the stimuli response of neurons considering Deep Neural Networks).
Considering architectured geometries at the microscopic scale, the hybrid model can play the role of a savvy trained reduced model, which can drastically cut down the expected computational time of structures designed with a complex microarchitecture for density and/or mechanical properties optimization. For the first time to our knowledge, we propose to insert physical modelling in the core of AI models by placing laws of physics in terms of constrain equation in the training process. We believe that such architecture is ideal to eliminate the drawbacks of commonly-used reduced order model, and therefore be an elegant and very efficient solution to solve the very complex problem of homogenization considering non-linear responses.
Scientific challenges of the PhD project
The most difficult challenge is to develop a reduced-order model that can simulate the response of multiscale systems where material non-linearities occurs. As mentioned earlier, the numerical treatment of non-linearities is a challenge for reduced-order models. To tackle this issue, the alternative adopted here is to develop an hybrid methodology where a neural network will predict with a great precision the material non-linearities at (i) a local scale and (ii) the scale of the architected cell., i.e. a geometrical pattern that constitutes a multi-scale structure. There is currently no solution readily available that tackle the issues described. The only attempt has been developed by a team at TU Bergakademie Freiberg (TUF) restricted to elastic-plastic models, considering only a proportional loading. To go beyond, the use of recursive neural networks (RNN) is very promising and is expected to ensure a great precision even in the case of non-proportional loadings, that occur very often in the analysis of multiscale structures. Our approach is to integrate AI networks at different scales of the multi-scale problems, transitioning from a full legacy model to a full AI model that contains physical constrains. The global approach is illustrated in Figure 1.
The whole project will be carried out by researchers of the I2M Institute. The project team is constituted of (i) Yves Chemisky (PI) (Professor at Université de Bordeaux). I am an expert in the development of multiscale, multi-physics models and their efficient numerical implementation. And lead developer of the Material constitutive modelling library ‘Simcoon’ (https://github.com/3MAH/simcoon. (ii) Etienne Prulière (Associate Professor at Arts et Métiers ParisTech) who is a recognized expert in numerical simulation and Model Reduction. He is an active member of our research team 3MAH and the lead developer of the Finite Element library ‘fedoo’ (https://github.com/3MAH/fedoo) that integrates a Proper Generalized Decomposition (PGD) model reduction method. In the 3MAH team we have started a project on AI-physics models for composite materials. A PhD student, recruited in 2019 (defense scheduled in summer 2022) complete the AI-physics project team. Collaboration within the AI network in Bordeaux will help to build an ideal environment to develop a cutting edge research project at the frontier between AI and physics. The AI network also will ensure a knowledge and technology transfer, considering cooperation with industry partners, to assist them in the integration of AI models for the design of mechanical components for aerospace and health applications.
The most significant outcome of this project is to envision the possibility to downscale the computational time of complex, non-linear and multiscale simulation during ‘online’ simulations, once ‘offline’ database has been generated. This project fully fits the strategy of UB, whose aim is to integrate AI at the heart of all its fields of excellence and will participate to strengthen the AI community in Bordeaux. The knowledge acquired during the project and its dissemination will rank I2M, together among top-level institutes for AI applied to mechanics and engineering.
In terms of perspective, an important area of investigation is the development multi-scale simulation of structures that will rely only on AI models (that carry out physical information). We have indeed started a collaboration with the team at TU Bergakademie Freiberg to develop a set of hybrid AI tools that should form a network of neural network: One to deal with the non-linear local response, the one presented here that will ensure the scale transition, and a last network that shall deal with the response of a structure. This would lead to a drastic reduction of online computational time (estimation up to a factor of 1000), allowing to simulate and optimize very complex structures in a very short time
- Ashby, M. (2013). Designing architectured materials. Scripta Materialia, 68(1), 4–7. https://doi.org/10.1016/j.scriptamat.2012.04.033
- Azaïez, M., Belgacem, F. Ben, Casado-Díaz, J., Rebollo, T. C., & Murat, F. (2018). A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems. SIAM Journal on Mathematical Analysis, 50(5), 5426–5445. https://doi.org/10.1137/17M1137164
- Charalambakis, N. (2010). Homogenization Techniques and Micromechanics. A Survey and Perspectives. Applied Mechanics Reviews, 63(3), 030803. https://doi.org/10.1115/1.4001911
- Chatzigeorgiou, G., Charalambakis, N., Chemisky, Y., & Meraghni, F. (2016). Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials. International Journal of Plasticity, 81, 18–39. https://doi.org/10.1016/j.ijplas.2016.01.013
- Chinesta, F., Keunings, R., & Leygue, A. (2014). The proper generalized decomposition for advanced numerical simulations: A primer. In SpringerBriefs in Applied Sciences and Technology. https://doi.org/10.1007/978-3-319-02865-1
- Fritzen, F., & Leuschner, M. (2015). Nonlinear reduced order homogenization of materials including cohesive interfaces. Computational Mechanics. https://doi.org/10.1007/s00466-015-1163-0
- Maday, Y. (2009). Reduced basis method for the rapid and reliable solution of partial differential equations. In Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006. https://doi.org/10.4171/022-3/60
- Maugin, G. A. (1992). The thermomechanics of plasticity and fracture. In Cambridge texts in applied mathematics. Cambridge University Press, Cambridge. https://doi.org/10.2307/3618611
- Metoui, S., Pruliere, E., Ammar, A., & Dau, F. (2018). A reduced model to simulate the damage in composite laminates under low velocity impact. Computers and Structures. https://doi.org/10.1016/j.compstruc.2018.01.012
- Rice, J. R. (1971). Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity. Journal of the Mechanics and Physics of Solids, 19(6), 433–455. https://doi.org/10.1016/0022-5096(71)90010-X
- Tikarrouchine, E., Chatzigeorgiou, G., Praud, F., Piotrowski, B., Chemisky, Y., & Meraghni, F. (2018). Three-dimensional FE2method for the simulation of non-linear, rate-dependent response of composite structures. Composite Structures, 193. https://doi.org/10.1016/j.compstruct.2018.03.072
PhD candidate profile
The ideal PhD candidate should have strong skills in numerical methods in engineering and development.
Ideally, he could have a first experience with at least a few of the following:
- AI models, especially considering Neural Network (using Tensorflow, PyTorch).
- Numerical methods in Engineering
- Non-linear mechanics and continuum Mechanics
- Homogenization and multiscale models
The PhD candidate shall be proficient in the use of C++ and Python languages, since our simulation tools are written in these 2 languages. Even if not required, a first experience with any of these languages will be appreciated. He should also be able to savvy use simulation tools.
International students that have graduated with a Master degree (or equivalent) in Mechanical Engineering are welcome to apply, but the application other students with a degree related to Numerical Simulation of physical phenomena will also be examined with attention.
As an example, the following Master degrees from Bordeaux correspond to the required skills: (i)The research Master MEFA (MÉcanique Fondamentale et Application) (ii) The Master CSIM (Calcul et Simulation en Mécanique) (iii )The engineering degree of ENSEIRB MATMECA : ‘Matériaux et structures’ or ‘Calcul Intensif et Sciences des données’ final year.
The PhD candidate should also be willing to work within an international environment, and open to a close cooperation with the TU Bergakademie University of Freiberg. A curious, open-minded attitude candidate with a strong sense of initiative will be preferentially examined.
To apply, you should send you application form in the platform https://aap.u-bordeaux.fr/ . The deadline for submission is May, 17th at 12am.
Mise à jour le 14/04/2021