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Quasistatic evolution problems for material failure due to fatigue

Project description

A rigorous mathematical approach to the problem of fatigue

Unforeseen fractures in materials can have devastating consequences, particularly for large components under large loads such as airplanes, ships, cranes, buildings and bridges. Fracture mechanics is a field of its own, largely within the realm of engineering. Its goal is to better understand the initiation and propagation of cracks in various materials under different loading conditions in order to predict, diagnose and ultimately avoid failure. Mathematical models and descriptions are key to understanding fatigue behaviour; therefore, the EU-funded FatiguEvoPro project is applying a mathematical eye to the problem. The project’s work could not only improve fracture prediction but also result in a new application field within the realm of mathematics.

Objective

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.

Coordinator

TECHNISCHE UNIVERSITAET MUENCHEN
Net EU contribution
€ 159 460,80
Address
Arcisstrasse 21
80333 Muenchen
Germany

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Region
Bayern Oberbayern München, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
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Total cost
€ 159 460,80