Title: Atomic-to-continuum (AtC) mulitiscale coupling using peridynamics

Speaker: Richard Lehoucq and Stewart Silling, Sandia National Laboratories

Date/Time: Wednesday, April 25, 2007, 9:00am – 10:00am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: Peridynamics (Silling 2000) is a microcontinuum theory that employs a nonlocal force model in order to describe long-range material interaction. This suggests that peridynamics can be applied to space and time scales that are typically beyond the domain of an atomistic simulation. In our presentation, we consider the efficacy of using peridynamics for atomic-to-continuum (AtC) coupling. First, we re-derive the peridynamic equation of motion by introducing a stress flux and peridynamic stress tensor. These are well posed quantities so that coupling to the finite element discretization of the Cauchy equation of motion is possible. The resulting peridynamic equation of motion does not contain spatial derivatives and so overcomes some limitations of classical continuum mechanics. This lack of spatial derivatives is possible because material interactions occur via a summation of force interactions between particles. Second, we present a scheme for homogenizing and scaling peridynamic material models. This provides an approach for AtC coupling where interatomic potentials can be used directly in portions of the material at the smallest scale, and the larger scale response is easily derivable from the same potentials. This AtC scheme may provide a step toward the use of peridynamics in coarse-graining a lattice-based model of a solid.

CSRI POC: Richard Lehoucq, (505) 845-8929