Department of Mathematical Sciences
Colloquium
Friday, January 30th, 2026
11:00AM-11:50AM
Stratton Hall 202
Speaker: Blaise Bourdin, McMaster University
Title: Phase field models of fracture with arbitrary strength surfaces
Abstract: Crack propagation in brittle materials can be described in terms of trade-off between a bulk and surface energies, characterized by a material's fracture toughness. Crack nucleation, however, is a much more complex process involving fracture toughness, material strength, i.e. the range of stresses a material can sustain while deforming elastically, and complex scale effects.
Phase-field models of fracture have become ubiquitous due to their ability to account for complex fracture patterns in a wide range of materials and multi-physics settings. When seen as gradient damage models, they properly account for tensile crack nucleation only.
A case can be made that crack nucleation cannot be accounted for in variational models based on Griffith-like surface energy, and it has been suggested that one needs to renounce to the variational nature of the models. Instead, I will propose a new approach using a cohesive energy depending on the crack opening. Unlike existing models, this approach is capable of handling arbitrary strength surfaces and cohesive energies, and behaves in a Griffith-like manner for "large" crack openings.
In this talk, I will present the proposed model and its properties, including a postulated "sharp interface" limit, its properties, and its numerical implementation.
This is a joint work with J.-J. Marigo (Institut Polytechnique de Paris, France), C. Maurini (Sorbonne Université, France), and C. Zolesi (Institut Polytechnique de Paris, France).