Xiantao Li, PSU

Abstract:

Typical material processes span over a wide range of spatial and temporal scales. Direct simulations based on detailed atomic interactions are restricted to small

systems, short time scales, and unrealistic strain rate. Coarse-grained molecular dynamics (CGMD) is a technique developed as a reduced model to overcome

these modeling difficulties.

The idea of coarse-grained molecular models is to retain atomic interactions to model critical material behavior, and introduce continuum mechanics approximations

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 conduction;

(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.