JournalsowrVol. 8 / No. 1DOI 10.4171/owr/2011/04

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
Mini-Workshop: Mathematical Analysis for Peridynamics cover

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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.