Project title: Free Discontinuity Problems and Applications in Fracture Mechanics

Amount funded: 400,000 RMB

Duration: Jan 2017 - Dec 2018

Abstract:

Fracture mechanics is one of the oldest fields in material science concerned with the study of the propagation of cracks in materials, which still has many unanswered questions. The most challenging problem though seems to be the analysis of the situation at the crack-front or, in two dimensional models, crack-tip. This is where one expects the crack to grow further and this is where one wants to predict crack's behaviour. The major breakthrough in this field was achieved by an English aeronautical engineer Alan Arnold Griffith in 1920, who was the first to describe rigorously the stress of the fracture. 

In 1998 Gilles Francfort and Jean-Jacques Marigo suggested a rigorous mathematical model based on Griffith's concepts. This model is considered as one of the most reliable and realistic for brittle fracture. The project apples the advanced methods of the theory of free boundary problems, recently successfully adapted in free discontinuity context by Hayk Mikayelyan and John Andersson, to the quasi-static crack propagation model of Francfort and Marigo. The goal is the derivation of an equation for the curvature of the crack at the crack-tip (2D) and crack-front (3D).