# Mini-Workshop: Mathematical Analysis for Peridynamics

### Etienne Emmrich

Universität Bielefeld, Germany### Max Gunzburger

Florida State University, Tallahassee, United States### Richard B. Lehoucq

Sandia National Laboratories, Albuquerque, USA

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## Abstract

A mathematical analysis for peridynamics, a nonlocal elastic theory, is the subject of the mini-workshop. Peridynamics is a novel multiscale mechanical model where the canonical divergence of the stress tensor is replaced by an integral operator that sums forces at a finite distance. As such, the underlying regularity assumptions are more general, for instance, allowing discontinuous and non-differentiable displacement fields. Although the theoretical mechanical formulation of peridynamics is well understood, the mathematical and numerical analyses are in their early stages. The mini-workshop proved to be a catalyst for the emerging mathematical analyses among an international group of mathematicians.

## Cite this article

Etienne Emmrich, Max Gunzburger, Richard B. Lehoucq, Mini-Workshop: Mathematical Analysis for Peridynamics. Oberwolfach Rep. 8 (2011), no. 1, pp. 169–199

DOI 10.4171/OWR/2011/04