# Workshop: New trends in the variational modeling of failure phenomena

Understanding the failure behavior of a great amount of different materials is currently among the most fascinating challenges lying at the interface between mathematics, physics, and materials science.
Macroscopic phenomena such as plasticity, damage or fracture are considered to be the result of atomistic interactions and effects occurring on mesoscopic scales.
Characterizing the interplay of such different material scales is therefore a key problem for the description of the physics behind the phenomena.
This leads to a variety of interesting challenges spanning from fundamental modeling issues to rigorous mathematical foundations of the theory and their versatility to simulations.

A comprehensive mathematical understanding of failure phenomena relies on a variety of different techniques, and on the combination of ideas from various fields including continuum mechanics, calculus of variations, geometric measure theory, partial differential equations, and nonlinear functional analysis.

The workshop is expected to deal with different themes spanning from modeling questions for failure phenomena to the underlying mathematical theory. Topics that will be addressed include:

- Mathematical modeling of plasticity, dislocations, damage, fracture, delamination,
- Effective theories for homogenization, discrete-to-continuum limits, dimension reduction,
- Variational methods, energetic and weak formulations, fine properties of underlying function spaces,
- Phase-field models, sharp interface limits, free-boundary problems,
- Computational aspects: discretization and discrete-to-continuum convergence, quasicontinuum and multiscale methods

**Organizers:**

Elisa Davoli, Manuel Friedrich, and Riccardo Scala

**List of speakers:**

- Lucia De Luca
- Irene Fonseca
- Gilles A. Francfort
- Alessandro Giacomini
- Peter Gladbach
- Martin Jesenko
- Dorothee Knees
- Martin Kružík
- Giuliano Lazzaroni
- Giovanni Leoni
- Ilaria Lucardesi
- Edoardo Mainini
- Marco Morandotti
- Matteo Negri
- Gianluca Orlando
- Marcello Ponsiglione
- Riccarda Rossi
- Tomáš Roubíček
- Anja Schlömerkemper
- Francesco Solombrino
- Nicolas Van Goethem
- Caterina Ida Zeppieri
- Barbara Zwicknagl
- Carolin Kreisbeck
- Viktor Shcherbakov
- Rita A. Ferreira

The Workshop

*New trends in the variational modeling of failure phenomena*is organized thanks to a grant by the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), a programme-oriented research institute for mathematics and physics at the University of Vienna. Partial support is acknowledged from the SFB 65 Project

*Taming Complexity in Partial Differential Systems*, financed through a grant by the Austrian Science Fund (FWF).