Description du projet
Une approche mathématique rigoureuse du problème de la fatigue
Les ruptures imprévues dans les matériaux peuvent avoir des conséquences dévastatrices, en particulier pour les grandes structures soumises à de fortes charges comme les avions, les navires, les grues, les bâtiments et les ponts. La mécanique de la rupture est un domaine à part entière, qui relève en grande partie de l’ingénierie. Son but est de mieux comprendre l’apparition et la propagation des fissures dans divers matériaux sous différentes conditions de charge afin de prévoir, de diagnostiquer et, en fin de compte, d’éviter les défaillances. Les modèles et les descriptions mathématiques sont essentiels pour comprendre le comportement face à la fatigue; c’est pourquoi le projet FatiguEvoPro, financé par l’UE, porte un regard mathématique sur le problème. Les travaux du projet pourraient non seulement améliorer la prédiction des ruptures, mais aussi déboucher sur un nouveau champ d’application dans le domaine des mathématiques.
Objectif
This research project deals with evolutionary problems arising in the modelling of material failure caused by fatigue. In Materials Science, fatigue is the process by which a solid exhibits a loss of its elastic properties as a consequence of repeated cycles of loading and unloading, and it is responsible for the majority of unforeseen structural failures. Infamous accidents have shown how the consequences of fatigue can be catastrophic, causing tremendous financial losses, serious injuries, and deaths.
In contrast to the active Engineering research on the topic, fatigue phenomena have been so far scarcely investigated by mathematicians. Since Mathematical Analysis has played a crucial role for the proof of consistency of variational models in Fracture Mechanics, it is clear that this field would benefit from a cogent and cutting-edge mathematical theory of fatigue.
The aim of FatiguEvoPro is to prove the existence of evolutions for mechanical models of material fatigue. The existence of quasistatic evolutions for Rate-Independent Systems featuring fatigue will be investigated within damage, brittle fracture, and cohesive fracture.
The models of FatiguEvoPro describe the current state of the mechanical system in terms of a memory variable which takes into account the whole history of its evolution. The resulting weak control of this variable is the main source of difficulty in the proof of existence of evolutions. The new effective techniques developed to solve this problem have great potential for applications in different contexts.
The achievements of FatiguEvoPro will develop a new branch of the variational modelling of Fracture Mechanics and will strengthen the mutual interest between mathematicians and engineers on a topic of utmost importance. The planned training activities will improve the applicant's skills in networking, teaching, communication, and project management, establishing his position as a leading young researcher in the field.
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MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
80333 Muenchen
Allemagne