Descrizione del progetto
Un approccio matematico rigoroso al problema della fatica
Le fratture impreviste dei materiali possono avere conseguenze devastanti, in particolare per i componenti di grandi dimensioni sotto grandi carichi quali aerei, navi, gru, edifici e ponti. La meccanica della frattura è un campo a sé stante, in gran parte nell’ambito dell’ingegneria. Il suo obiettivo è quello di comprendere meglio l’insorgenza e la propagazione di cricche in vari materiali in diverse condizioni di carico, al fine di prevedere, diagnosticare e infine evitare il cedimento. Le descrizioni e i modelli matematici sono fondamentali per comprendere il comportamento della fatica; ecco perché il progetto FatiguEvoPro, finanziato dall’UE, sta analizzando il problema con un occhio matematico. Il lavoro del progetto potrebbe non solo migliorare la previsione delle fratture, ma anche portare a un nuovo campo di applicazione nel mondo della matematica.
Obiettivo
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.
Campo scientifico
Parole chiave
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Meccanismo di finanziamento
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinatore
80333 Muenchen
Germania