Prof. Blaise Bourdin from Louisiana State University, invited by Prof. Yongxing Shen, gave us a talk tomorrow afternoon. In the seminar, Professor Blaise Bourdin first recalled the construction of the variational models of fracture and their approximation by Gamma-convergence, the well-known Ambrosio-Tortorelli functionals. He discussed the strength and flaws of these approaches. Then, he focused on more recent results dealing with the analysis of Ambrosio-Tortorelli functionals when the regularization parameter is held constant. He showed how such a model can be used to properly handle propagation and nucleation of cracks, even in situations where Global Minimization and Gamma-convergence lead to unphysical evolutions. He illustrated the properties of these models with validation and verification numerical simulations in multiples situations.

Time & Date: 02:00 p.m.-03:00 p.m., Aug. 11th, 2017 (Friday)

Location: 228 conference room, JI Building

Title: Variational phase-field models of fracture

Abstract

Twenty years after its inception, the variational approach to brittle fracture, and its "phase-field" implementations have become widely used.

In this talk, I will first recall the construction of the variational models of fracture and their approximation by Gamma-convergence, the well-known Ambrosio-Tortorelli functionals. I will discuss the strength and flaws of these aproaches. Then, I will focus on more recent results dealing with the analysis of Ambrosio-Tortorelli functionals when the regularization parameter is held constant. I will show how such a model can be used to properly handle propagation and nucleation of cracks, even in situations where Global Minimization and Gamma-convergence lead to unphysical evolutions.

I will illustrate the properties of these models with validation and verification numerical simulations in multiples situations.

Bio

B.Bourdin is a professor of Mathematics and adjunct faculty of the Center for COmputation& Technology at Louisiana State university.

His research interest rests at the intersection of applied mathematics, theoretical mechanics and computational science.

After graduating from the University Paris Nord in 1998 under prof. G.Francfort's supervision, B. Bourdin did post-docs at the Danish Technical University (DTU), Caltech, and New York University. He joined LSU as an assistant professor in 2002. Since then, he has contributed to the analysis of phase field modes in defect mechanics, its extensions to a borad range of engineering and industrial applications, and the development of efficient numerical schemes.