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Carnegie Mellon Center for Nonlinear Analysis
Multiscale Modeling in Peridynamic Solid Mechanics


Pablo Seleson
The University of Texas at Austin
Institute for Computational Engineering and Sciences

: 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.