Fracture in heterogeneous brittle materials
Feb 3, 2023
2:30PM to 3:30PM
Date(s) - 03/02/2023
2:30 pm - 3:30 pm
Prof. Blaise Bourdin
Dept. of Mathematics & Statistics, McMaster University
In this talk, I will describe recent attempts at devising a rigorous framework for the analysis and numerical simulation of crack propagation in heterogeneous materials. I will focus on the challenge of devising a mathematically sound and mechanistically coherent concept of effective toughness and computing it.
I will first explain how classical theories such as homogenization fail to provide a meaningful answer to this question. Then, I will propose a framework based on the idea of homogenization in trajectory space. I will how it can account for new toughening mechanisms induced by heterogeneities. Finally, I will present classes of meta-materials exhibiting unconventional fracture properties.
Blaise Bourdin is the Tier 1 Canada Research Chair in Mathematical and Computational Aspects of Solid Mathematics and Professor of Mathematics at McMaster University.
After graduating from the Université Paris 13 (France) in 1998, Bourdin joined The Technical University of Denmark, California Institue of Technology and New York University as a Post-Doctoral Fellow. He joined the Department of Mathematics at Louisiana State University as an Assistant Professor in 2002 and raised to the ranks of Associate Professor, Full Professor, and A.K. & Shirley Barton Professor. B. Bourdin moved to the Department of Mathematics & Statistics at McMaster University in July 2021, and received a Canada Research Chair in July 2022.
Bourdin’s formal training is at the confluence of solid mechanics, scientific computing, and applied mathematics. His main interest is on multi-disciplinary modeling, analysis, and numerical simulation in mechanical science with a specific focus on defect mechanics and optimal design. He pioneered the phase-field approach to brittle fracture, one today’s most influential method in the field.
He is the recipient of research grants from the U.S. National Science Foundation, the Louisiana Board of Regents, the Natural Sciences and Engineering Research Council of Canada, and industry totalling over $6M. He is the author of one book and over 40 peer-reviewed publications, including three ESI highly cited papers in two disciplines (mathematics and engineering).
In-Person: ABB 102