Materials Modeling, From Multiple Scales, of Instabilities and Bifurcation
The Elliott research group looks at bifurcation and stability problems of complex materials and structural systems. Problems of interest include solid-to-solid phase transitions, hierarchical materials such as honeycomb structures, nano-structures such as nanotubes, and complex nano-clusters. The group develops and uses rigorous computational algorithms based on continuation and bifurcation theory that take advantage of group-theory results to systematically map out equilibrium configurations for the models considered. Models are developed and drawn from multiple physical length scales and include electronic structure density functional theory (ES-DFT), emperical atomistic modeling, continuum mechanics, and structural beam theory.
Ongoing work involves the development and extension of the group's branch-following and bifurcation (BFB) methodology to support high-performance systems in a heterogeneous (possibly cloud-based) computing environment; development, testing, and application of next-generation ES-DFT codes; coupling commercial finite element method (FEM) codes to empirical atomistic models to study solid-to-solid phase transitions; and design of multi-state architectured materials using BFB and FEM technologies.
A Research Spotlight featuring the group's work appeared on the MSI website in July 2014.
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