**Title:** Evaluating Continuum Mechanical Quantities at the Atomic Scale

**Presenter:** Jonathan Zimmerman

**Affiliation:** Sandia National Laboratories

**Abstract:** Continuum theory is commonly used to analyze the mechanics of materials and structures.
However, it is often advantageous to use atomistic modeling and simulation methods to gain insight
on phenomena such as deformation leading to the creation of material defects and the transport of
energy in materials. While these methods can provide a wealth of information, clear connections
between nanoscale mechanics and engineering scale analysis need to be made. Among the many efforts
to derive expressions for calculating continuum variables within an atomic system is the work by
Hardy (1982), who used averaging volumes and weighting functions associated with fixed spatial
points within the continuum Euler balances of mass, momentum and energy. An alternative approach
is to construct a similar formulation to Hardy's in the reference or material frame. I will present
work done to implement such expressions for Lagrangian and Eulerian analysis of material deformation
into LAMMPS’ USER-ATC package, and will touch on several examples that use this capability, such as
studying the plastic deformation of nanocrystalline metals, verification of inter-atomic potentials
used to simulate the shock response of materials, and application of the continuum J-integral –
a metric used to quantify the energetic driving force for crack propagation and defect motion –
at the nanoscale.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04- 94AL85000.