Phase Field Models of Fracture Course

Assistants: A wide variety of assistants were invited to this course: the whole international consortium of Newfrac project, including among others all the ESRs and supervisors, and the doctoral students and professors from the Doctoral Program on Engineering Mechanics and Industrial Management of Universidad de Sevilla. In total, 58 participants had the pleasure of taking part in this course and discussing the subject with Professor Blaise Bourdin.

Lecturer: Prof. Blaise Bourdin, Department of Mathematics, Louisiana State University, Baton Rouge, USA

Course Abstract: In the last 25 years or so a new view fracture in brittle materials has emerged. It is based on a reinterpretation of Griffith’s classical criterion as a variational principle for a free-discontinuity energy. This new analysis approach gave rise to a new class of numerical models, commonly referred to as phase-field models. The goal of this course is to give a rigorous construction of both theory and detail its application to a range of problems. I will start by introducing Francfort and Marigo’s variational approach to fracture, insisting on how it addresses two common shortcomings of the classical LEFM theory: path identification and kinking. I will then construct a family of phase-field approximations, and describe their implementation. I will then describe an alternate construction of these models and show how it can be used to attack the issues of nucleation and size effects. Finally, I will describe open problems in the field.

Schedule:

• Lecture 1: The construction of variational models of fracture from Griffith criterion
• Lecture 2: Their phase-field approximation
• Lecture 3: Implementation, extension, and nucleation

Duration: 6 hours

Organization: Newfrac Innovative Training Network, and Universidad de Sevilla - 3er Plan Propio de Docencia