Data-based stochastic 3D structure modelling for automatic learning of mechanical properties

German-French research project on the topic:

A large number of materials have a polycrystalline structure. This means that they consist of many individual crystals that are separated from each other by grain boundaries. This also includes titanium aluminides, which are used, for example, in the construction of engines or gas turbines. The 3D microstructure of such materials, i.e., the spatial-geometrical arrangement of the individual crystals, has a decisive influence on the mechanical properties, such as the fracture behaviour of the materials.

Stochastik, Uni Ulm, Project Smile, Figure: 2D visualisation of (differently coloured) single crystals in a titanium aluminide.
Figure: 2D visualisation of (differently coloured) single crystals in a titanium aluminide.

The tomographic reconstruction of the 3D microstructure of real materials is very time-consuming and cost-intensive. Therefore, mathematical models are needed to systematically investigate the influence of the microstructure on mechanical material properties. They allow the simulation of virtual, but realistic 3D microstructures on the computer. The mechanical properties of these structures are then determined by numerical simulations. In particular, the use of AI methods to accelerate the numerical simulation of the fracture behaviour of titanium aluminides is a promising approach. The method development required to establish this approach is the subject of the SMILE project, in which Prof. Dr. Evgeny Spodarev, Prof. Dr. Volker Schmidt and Dr. Matthias Neumann at the Institute of Stochastics at Ulm University, together with their French partners Dr. François Willot, Prof. Dr. Henry Proudhon and Dr. Samy Blusseau from Mines ParisTech, are making a contribution to Franco-German cooperation in the field of AI.

In combination with stochastic 3D structure modelling, the efficient numerical simulation of mechanical properties developed in the SMILE project will be able to generate a large database to quantify the microstructure influence on the fracture behaviour of titanium aluminides. Here, AI methods will be used to automatically learn mechanical properties of the structures based on numerical simulations on virtual microstructures. In particular, AI is used for an efficient  selection of training data in order to keep the computational effort for the numerical simulations, which are required for learning, as low as possible. In addition, the SMILE project also includes a data-driven component to ensure that the methodology, which is developed in SMILE on the basis of virtual structures, can also be applied to real microstructures. This means that the obtained results will be validated using tomographic image data measured during the course of the project. More precisely, the spatial arrangement (3D) of the microstructure of titanium aluminides as well as their temporal evolution under mechanical loading (4D) will be resolved. The SMILE project combines complementary expertises of the German-French partners at Ulm University and Mines Paris Tech to enable an efficient elucidation of microstructure-property relationships for titanium aluminides using AI. The project thus makes an important contribution to the further digitisation of materials science.


SMILE is funded by the Federal Ministry of Education and Research (BMBF) and the Ministère de l' enseignement supériereur, de la recherche et de l' innovation (MESRI).


Prof. Dr. Evgeny Spodarev

Director of the Institute
Institute of Stochastics

Helmholtzstr. 18, Room No. 165
D-89069 Ulm

Tel.: +49 (0) 7 31 - 50 23530
Fax: +49 (0) 7 31 - 50 23649

E-Mail: evgeny.spodarev(at)
web: Prof. Dr. Evgeny Spodarev

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