Research Topic

[KIM] Topic: QC3D – High-performance 3D Quasicontinuum

Team: Steve Whalen, Min Shi, Ellad Tadmor

Funding: Pending

Figure: A QC3D model for an atomic force microscope (AFM) tip. The AFM cantilever and most of the tip and substrate are modeled using continuum finite elements (using local QC). The regions of the tip and substrate that come in contact are modeled atomistically (nonlocal QC).

Description: The Quasicontinuum (QC) method is a mixed continuum and atomistic approach for simulating the mechanical response of polycrystalline materials. The method reproduces the results of fully-atomistic techniques at a fraction of the computational cost. Both zero temperature and finite temperature versions of the method have been developed.

The key idea of QC is the selective representation of atomic degrees of freedom. Instead of treating all atoms making up the system, a small relevant subset of atoms is selected to represent, by appropriate weighting, the energetics of the system as a whole. Based on their kinematic environment, the energies of individual "representative atoms" are computed either in nonlocal fashion in correspondence with straightforward atomistic methodology or within a local approximation as befitting a continuum model. The representation is of varying density with more atoms sampled in highly deformed regions (such as near defect cores) and correspondingly fewer in the less deformed regions that are closerly approximated by a uniformly strained crystal. The model is adaptively updated as the deformation evolves.

The current project is focused on extending the original QC implementation to three dimensions (3D), adding support for multilattice crystals (i.e. crystals with more than one atom per unit cell), and developing a high-performance parallel code optimized for today's massively parallel supercomputers.

Publications on QC3D General Publications on the QC Method: