The University of Texas at Austin
Institute for Computational Engineering and Sciences
seleson@ices.utexas.edu
Abstract: The peridynamic model is a nonlocal reformulation
of classical continuum mechanics. As a nonlocal model, peridynamics possesses
a length scale represented by its interaction range, or horizon. This
motivates the use of peridynamics as a multiscale material model, in the sense
that the same equation may exhibit different behavior depending on the choice
of length scale. This work investigates connections between peridynamics and
both molecular dynamics and classical elasticity. We show that, for finite
horizons, peridynamics can be cast as an upscaling of molecular dynamics,
allowing peridynamics to reproduce nonlocal behavior inherent to nonlocal
discrete models, at a lower computational cost. This behavior is lost for a
vanishing horizon, in the limit where the model becomes local, as is the case
in classical local models. We also investigate how the use of different
kernels in peridynamics can modulate the nonlocal interaction, producing
effectively nearly-local or local behavior, even when the peridynamic horizon
is fixed. For multiscale purposes, we are interested in the coupling of
different length scales; this talk will provide insights related to the
coupling of local and nonlocal models using peridynamics.