The University of Nottingham Ningbo China organised the

Research Summer School

“Free discontinuity problems and applications in fracture mechanics”

August 14-18,2017

Organiser 

Hayk Mikayelyan (University of Nottingham Ningbo China)

Sponsors

National Science Foundation of China

Faculty of Science and Engineering 

University of Nottingham Ningbo China

Speakers

John Andersson (Royal Inst. of Technology, Sweden)

Regularity of sets defined by partial differential equations

We will talk about some techniques that are used to show regularity for the free boundary in free boundary problems. In particular, we will discuss linearization and techniques to prove convergence for linearizing sequences.

First we will consider the (normalized) obstacle problem, which is the easiest setting for a free boundary problem. We will discuss how linearization can be used to show regularity of the free boundary. 

In the final part of the lectures we will show how the same techniques can be used to show that the crack in a stationary Griffith's model for crack propagation is C^1.

Blaise Bourdin (Louisiana State University, USA)

Variational phase-field models of fracture

In these series of lectures, we focus on variational phase field models of brittle fracture.

We will first recall their construction as variational approximations of Francfort and Marigo's model of brittle fracture, derived from Ambrosio and Tortorelli's approximation of the Mumford Shah.

We will discuss their implementation and use a combination on close form computations and numerical simulations to highlight some of the weaknesses of this approach.

Then, we will discuss an alternative construction of variational phase field models as gradient damage laws, and highlight the differences between approaches.

Gilles Francfort (University Paris-Nord, France)

Brittle fracture: A variational approach

In this series of lectures, we propose to build variational fracture as a kind of weak formulation of the classical Griffith model for quasi-static brittle fracture evolution.

Once this is done we will briefly show how existence of a crack evolution can be secured for this model.

Then we will discuss initiation and kinking within that framework. In particular we will demonstrate that the classical engineering view of a kink is incompatible with a Griffith view of fracture.

Finally, time permitting, we will present extensions of the model to cohesive fracture.

Schedule