PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Statistical Coarse-graining of Molecular Dynamics into Peridynamics
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Speaker:Richard Lehoucq, Sandia National Labs
Abstract:
A distinction between molecular dynamics (MD) and classical continuum mechanics (CM) is that the former assumes a nonlocal model of force interaction. This distinction complicates any practical scheme for coarse-graining MD into classical CM, for instance when the finite element method is used for the classical CM discretization. This paper describes a method for representing a collection of atoms at finite temperature as a peridynamic (PD) body. In direct analogy with MD, PD, a continuum theory, uses a nonlocal model of force and avoids the notion of strain germane to classical CM. The PD representation is then homogenized and rescaled to enable a statistical coarse-graining of MD. The coarse-graining avoids the use of a unit cell and the Cauchy-Born rule. In contrast with classical CM, the PD homogenized system of linear springs and masses is shown to have the same dispersion relation as the original spring-mass system. A non-local notion of PD stress is also presented.

Room Reservation Information

Room Number:MB216
Date:10 / 01 / 2007
Time:03:35pm - 04:25pm