Coarse-grained molecular dynamics for multiscale material
Xiantao Li, PSU
Typical material processes span over a wide range of spatial and
Direct simulations based on detailed atomic interactions are
restricted to small
systems, short time scales, and unrealistic strain rate.
dynamics (CGMD) is a technique developed as a reduced model to
these modeling difficulties.
The idea of coarse-grained molecular models is to retain atomic
interactions to model
critical material behavior, and introduce continuum mechanics
where/when the displacement is smooth. There are several
challenges in developing
a coarse-grained molecular model, including
(1) Reduction of the atomic degrees of freedom;
(2) Sampling the scale-dependent random noise
(3) Incorporating transport phenomena, such as diffusion and heat
(4) Modeling realistic loading rate.
This talk will focus on spatial reduction, and I will present a
systematic approach to coarse-grain molecular dynamics models. The
coarse-grained models are derived by Galerkin projection to a
sequence of Krylov subspaces. On the coarsest space, the model
corresponds to a finite element discretization of the continuum
elasto-dynamics model. On the other hand, the projection to the
finest space yields the full molecular dynamics description. The
models in between serve as a smooth transition between the two
scales. Using this systematic approach, one can build a hierarchy of
models with increasing accuracy. With the successive expansion of
approximation spaces, phonon reflections, a typical indication of
the modeling error, is greatly reduced. Examples, including
dislocation and crack propagation, will be presented as test
problems. If time permits,
I will discuss the modeling of heat conduction.