# Phase-Field Models of Fracture (19w5207)

## Organizers

(Louisiana State University)

(Technische Universität Braunschweig)

(Kanazawa University)

## Description

The Banff International Research Station will host the "Phase-Field Models of Fracture" workshop in Banff from March 3, 2019 to March 8, 2019.

Phase-field models of fracture were originally devised in the mathematics community as numerical approximation of the variational theories of brittle fracture, based on revisiting Griffith's theory from the 1920's with modern mathematical tools.
The underlying idea of these models is to represent cracks --two-dimensional surfaces in three dimensions and curves in two dimensions-- using a smooth auxiliary phase-field'' diffused over a small regularization length.
Part of their appeal is that their deep theoretical roots can be leveraged to address many of the most pressing challenges in fracture mechanics including crack path identification, crack nucleation prediction, and the need for efficient three-dimensional numerical simulations
As such, they have seen an explosive growth in the last few years, in particular in the mechanics and engineering communities.
As the community of users and the range of applications have gotten larger, it has become increasingly difficult to ensure proper communication between key players from the mathematics and applications communities.

This workshop brings together a broad multi-disciplinary group from academia and the industry at various stage of their career.
The make-up of the organization committee is meant to reflect the diversity of viewpoints expected, with organizers from the applied mathematics, theoretical mechanics, and computational science communities, originating from three continents.
The objectives of the workshop are manifold:
It seeks to restore proper communication between the communities involved by informing each other of the key success and challenges.
It will tackle a new class of inverse problems arising from optimal design of materials and structures or materials characterization, for instance.
Finally, it will allow candid comparison of recently developed numerical approaches, and elaboration of benchmark problems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).